Information about forthcoming Psychometrika manuscripts http://www.psychometricsociety.org/journal/submissions/accepted.html Section:Application Reviews & Case Studies (ARCS)Article Title:Hierarchical Diagnostic Classification Models Morphing into Unidimensional 'Diagnostic' Classification Models—A CommentaryAuthor(s):Matthias von Davier and Shelby HabermanAbstract:This commentary addresses the modeling and final analytical path taken and the terminology used in the paper "Hierarchical Diagnostic Classification Models - A Family of Models for Estimating and Testing Attribute Hierarchies" by Templin and Bradshaw. It raises several issues concerning use of cognitive diagnostic models that either assume attribute hierarchies or assume a certain form of attribute interactions. The issues raised are illustrated with examples, and references are provided for further examination. Keywords:latent structure model;latent class analysis;diagnostic models;Guttman scaling;hierarchical models]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Evaluating Predictors of Dispersion: A Comparison of Dominance Analysis and Bayesian Model AveragingAuthor(s):Yiyun Shou and Michael SmithsonAbstract:Conventional measures of predictor importance in linear models are applicable only when the assumption of homoscedasticity is satisfied. Moreover, they cannot be adapted to evaluating predictor importance in models of heteroscedasticity (i.e., dispersion), an issue that seems not to have been systematically addressed in the literature. We compare two suitable approaches, Dominance Analysis (DA) and Bayesian Model Averaging (BMA), for simultaneously evaluating predictor importance in models of location and dispersion. We apply them to the beta general linear model as a test-case, illustrating this with an example using real data. Simulations using several different model structures, sample sizes, and degrees of multicollinearity suggest that both DA and BMA largely agree on the relative importance of predictors of the mean, but differ when ranking predictors of dispersion. The main implication of these findings for researchers is that the choice between DA and BMA is most important when they wish to evaluate the importance of predictors of dispersion. Keywords:heteroscedasticity;predictor importance;Dominance Analysis;Bayesian Model Averaging;beta regression;beta GLM.]]> Section:Book ReviewsArticle Title:Review of T. RAYKOV, & G.A. MARCOULIDES (2010). Introduction to Psychometric Theory.Author(s):Berhhard Gschrey and Ali UnluAbstract:Exploratory process factor analysis (EPFA) is a data-driven latent variable model for multivariate time series. This article presents analytic standard errors for EPFA. Unlike standard errors for exploratory factor analysis with independent data, the analytic standard errors for EPFA take into account the time dependency in time series data. In addition, factor rotation is treated as the imposition of equality constraints on model parameters. Properties of the analytic standard errors are demonstrated using empirical and simulated data.Keywords:Factor Analysis, Time Series Analysis, Standard Error, Dynamic Factor Analysis]]> Section:Theory & MethodsArticle Title:Analytic Standard Errors for Exploratory Process Factor AnalysisAuthor(s):Guangjian Zhang, Michael Browne, Anthony Ong and Sy Miin ChowAbstract:Exploratory process factor analysis (EPFA) is a data-driven latent variable model for multivariate time series. This article presents analytic standard errors for EPFA. Unlike standard errors for exploratory factor analysis with independent data, the analytic standard errors for EPFA take into account the time dependency in time series data. In addition, factor rotation is treated as the imposition of equality constraints on model parameters. Properties of the analytic standard errors are demonstrated using empirical and simulated data.Keywords:Factor Analysis, Time Series Analysis, Standard Error, Dynamic Factor Analysis]]> Section:Theory & MethodsArticle Title:Generalized Functional Extended Redundancy AnalysisAuthor(s):Heungsun Hwang, Hye Won Suk, Yoshio Takane, Jang-Han Lee and Jooseop LimAbstract:Functional extended redundancy analysis (FERA) was recently developed to integrate data reduction into functional linear models. This technique extracts a component from each of multiple sets of predictor data in such a way that the component accounts for the maximum variance of response data. Moreover, it permits predictor and/or response data to be functional. FERA can be of use in describing overall characteristics of each set of predictor data and in summarizing the relationships between predictor and response data. In this paper, we extend FERA into the framework of generalized linear models (GLM), so that it can deal with response data generated from a variety of distributions. Specifically, the proposed method reduces each set of predictor functions to a component and uses the component for explaining exponential-family responses. As in GLM, we specify the random, systematic, and link function parts of the proposed method. We develop an iterative algorithm to maximize a penalized log-likelihood criterion that is derived in combination with a basis function expansion approach. We conduct two simulation studies to investigate the performance of the proposed method based on synthetic data. In addition, we apply the proposed method to two examples to demonstrate its empirical usefulness.Keywords:Functional data analysis;functional extended redundancy analysis;generalized linear models;data reduction;exponential family responses;penalized likelihood.]]> Section:Application Reviews & Case Studies (ARCS)Article Title:An idiographic approach to estimating models of dyadic interactions with differential equationsAuthor(s):Joel Steele, Emilio Ferrer and John R. NesselroadeAbstract:We present an idiographic approach to modeling dyadic interactions using differential equations. Using data representing daily affect ratings from romantic relationships, we examined several models conceptualizing different types of dyadic interactions. We fitted each model to each of the dyads and the resulting AICc values were used to classify the most likely configuration of interaction for each dyad. Additionally, the AICc from the different models were used in parameter averaging across models. Averaged parameters were used in models involving predictors of relationship dynamics, as indexed by these parameters, as well as models wherein the parameters predicted distal outcomes of the dyads such as relationship satisfaction and status. Results indicated that, within our sample, the most likely interaction style was that of independence, without evidence of emotional interrelations between the two individuals in the couple. Attachment-related avoidance and anxiety showed significant relations with model parameters, such that ideal levels of affect for males were negatively influenced by higher levels of avoidance from their partner while their own levels of anxiety had positive effects on their levels of dyadic coregulation. For females coregulation was negatively influenced by both time in the relationship and their partner's level of avoidance. Analysis involving distal outcomes showed modest influences from the individual's level of ideal affect.Keywords:dyadic interactions;model averaging;differential equations;dyadographic analysis;idiographic]]> Section:Theory & MethodsArticle Title:Consistency of Nonparametric Classification in Cognitive DiagnosisAuthor(s):Shiyu Wang and Jeffrey A. DouglasAbstract:Latent class models for cognitive diagnosis have been developed to classify examinees into one of the $2^{K}$ attribute profiles arising from a K-dimensional vector of binary skill indicators. These models recognize that response patterns tend to deviate from the ideal responses that would arise if skills and items generated item responses through a purely deterministic conjunctive process. An alternative to employing these latent class models is to minimize the distance between observed item response patterns and ideal response patterns, in a nonparametric fashion that utilizes no stochastic terms for these deviations. Theorems are presented that show the consistency of this approach, when the true model is one of several common latent class models for cognitive diagnosis. Consistency of classification is independent of sample size, because no model parameters need to be estimated. Simultaneous consistency for a large group of subjects can also be shown given some conditions on how sample size and test length grow with one another.Keywords:cognitive diagnosis, nonparametric classification, large sample theory]]> Section:Theory & MethodsArticle Title:A Unified Framework for the Comparison of Treatments with Ordinal ResponsesAuthor(s):Tong-Yu Lu, Wai-Yin Poon and Siu Hung CheungAbstract:Different latent variable models have been used to analyze ordinal categorical data which can be conceptualized as manifestations of an unobserved continuous variable. In this paper, we propose a unified framework based on a general latent variable model for the comparison of treatments with ordinal responses. The latent variable model is built upon the location-scale family and is rich enough to include many important existing models for analyzing ordinal categorical variables, including the proportional odds model, the ordered probit-type model, and the proportional hazards model. A flexible estimation procedure is proposed for the identification and estimation of the general latent variable model, which allows for the location and scale parameters to be freely estimated. The framework advances the existing methods by enabling many other popular models for analyzing continuous variables to be used to analyze ordinal categorical data, thus allowing for important statistical inferences such as location and/or dispersion comparisons among treatments to be conveniently drawn. Analysis on real data sets is used to illustratethe proposed methods.Keywords:latent variable model;location-scale family;ordinal responses.]]> Section:Theory & MethodsArticle Title:Three-mode factor analysis by means of Candecomp/ParafacAuthor(s):Alwin Stegeman and Tam T. T. LamAbstract:A three-mode covariance matrix contains covariances of N observations (e.g., subject scores) on J variables for $K$ different occasions or conditions. We model such an JK x JK covariance matrix as the sum of a (common) covariance matrix having Candecomp/Parafac form, and a diagonal matrix of unique variances. The Candecomp/Parafac form is a generalization of the two-mode case under the assumption of parallel factors. We estimate the unique variances by Minimum Rank Factor Analysis. The factors can be chosen oblique or orthogonal. Our approach yields a model that is easy to estimate and easy to interpret. Moreover, the unique variances, the factor covariance matrix and the communalities are guaranteed to be proper, a percentage of explained common variance can be obtained for each variable-condition combination, and the estimated model is rotationally unique under mild conditions. We apply our model to several datasets in the literature, and demonstrate our estimation procedure in a simulation study.Keywords:three-mode factor analysis;multitrait-multimethod;Candecomp;Parafac;Minimum Rank Factor Analysis]]> Section:Theory & MethodsArticle Title:Title: Additive Multilevel Item Structure Models with Random Residuals: Item Modeling for Explanation and Item GenerationAuthor(s):Sun-Joo Cho, Paul De Boeck, Susan E. Embretson and Sophia Rabe-HeskethAbstract:An additive multilevel item structure model with random residuals is proposed that includes latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels. The inclusion of covariates at the two levels can be helpful for explanation purposes and also for prediction purposes as in an item generation context. The parameters can be estimated with an alternating imputation posterior algorithm that makes use of adaptive quadrature, and the performance of this algorithm is evaluated in a simulation study. The model is used to analyze a mathematical aptitude test from explanation and item generation perspectives.Keywords:alternating imputation posterior with adaptive quadrature, item generation, multilevel model, random item parameters]]> Section:Theory & MethodsArticle Title:Modeling Viewpoint Shifts in Probabilistic ChoiceAuthor(s):Tomoya Okubo and Shin-ichi MayekawaAbstract:A number of mathematical models for overcoming intransitive choice have been proposed and tested in the literature of decision theory. This article presents the development of a new stochastic choice model based on multidimensional scaling. This allows decision-makers to have multiple viewpoints, whereas current multidimensional scaling models are based on the assumption that a subject or group of subjects has only one viewpoint. The implication of our model is that subjects make an intransitive choice because they are able to shift their viewpoint. We also investigate the maximum likelihood estimation of the proposed model. Keywords:viewpoint shift;vector model;latent class model;Multidimensional scaling;decision theory]]> Section:Theory & MethodsArticle Title:Rasch trees: A new method for detecting differential item functioning in the Rasch modelAuthor(s):Carolin Strobl, Julia Kopf and Achim ZeileisAbstract:A variety of statistical methods have been suggested for detecting differential item functioning (DIF) in the Rasch model. Most of these methods are designed for the comparison of pre-specified focal and reference groups, such as males and females. Latent class approaches, on the other hand, allow to detect previously unknown groups exhibiting DIF. However, this approach provides no straightforward interpretation of the groups with respect to person characteristics. Here, we propose a new method for DIF detection based on model-based recursive partitioning that can be considered as a compromise between those two extremes. With this approach it is possible to detect groups of subjects exhibiting DIF, which are not pre-specified, but result from combinations of observed covariates. These groups are directly interpretable and can thus help generate hypotheses about the psychological sources of DIF. The statistical background and construction of the new method are introduced by means of an instructive example and extensive simulation studies are presented to support and illustrate the statistical properties of the method, that is then applied to empirical data from a general knowledge quiz. A software implementation of the method is freely available in the R system for statistical computing.Keywords:item response theory;IRT;Rasch Model;differential item functioning;DIF;Measurement invariance;structural change;model-based recursive partitioning.]]> Section:Theory & MethodsArticle Title:The nonsingularity of $\Gamma$ in covariance structure analysis of non-normal dataAuthor(s):Robert I. Jennrich and Albert SatorraAbstract:Covariance structure analysis of non-normal data is important because in practice all data are non-normal. When applying covariance structure analysis to non-normal data, it is generally assumed that the asymptotic covariance matrix $\Gm$ for the non-redundant terms in the sample covariance matrix $S$ is nonsingular. It is shown this need not be the case which raises a question of how restrictive this assumption may be and how difficult it may be to verify it. It is shown that $\Gm$ is nonsingular whenever sampling is from a nonsingular distribution including any distribution defined by a density function. In the discrete case necessary and sufficient conditions are given for the non-singularity of $\Gm$ and it is shown how to demonstrate $\Gm$ is nonsingular with high probability. Thus the non-singularity of $\Gm$ assumption is mild and one should feel comfortable about making it. These observations also apply to the asymptotic covariance matrix $\Gm$ that arises in structural equation modeling.Keywords:Covariance structure analysis, non-redundant components, non-singularity of Gamma, nonsingular distribution, discrete distribution, multivariate polynomials, smooth manifolds.]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Risk Patterns and Correlated Brain Activities. Multidimensional statistical analysis of fMRI data in economic decision making studyAuthor(s):Alena van Bömmel, Song Song, Piotr Majer, Peter Mohr and Wolfgang Karl HärdleAbstract:Decision making usually involves uncertainty and risk. Understanding which parts of the human brain are activated during decisions under risk and which neural processes underly (risky) investment decisions are important goals in neuroeconomics. Here, we analyze functional magnetic resonance imaging (fMRI) data on 17 subjects which were exposed to an investment decision task from Mohr et al (2010b). We obtain a time series of three-dimensional images of the blood-oxygen-level dependent (BOLD) fMRI signals. We apply a panel version of the dynamic semiparametric factor model (DSFM) presented in Park et al. (2009) and identify task-related activations in space and dynamics in time. With the panel DSFM (PDSFM) we can capture the dynamic behavior of the specic brain regions common for all subjects and represent the high-dimensional time series data in easily interpretable low dimensional dynamic factors without large loss of variability. Further, we classify the risk attitudes of all subjects based on the estimated low-dimensional time series. Our classication analysis successfully conrms the estimated risk attitudes derived directly from subjects' decision behavior. Keywords:risk;risk attitude;fMRI;decision making;semiparametric]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Analyses of model fit and robustness. A second look at a scaling model underlying ranking of countries according to reading literacyAuthor(s):Svend Kreiner and Karl Bang ChristensenAbstract:This paper addresses methodological issues concerning the scaling model used in the international comparison of student attainment in the Programme for International Student Attainment (PISA), with specific reference to whether PISA's ranking of countries is confounded by differential item functioning (DIF). To determine this, we reanalyzed the publicly accessible data on reading skills from the 2006 PISA survey. We also examined whether the ranking of countries is robust in relation to the errors of the scaling model. This was done by studying invariance across subscales, and by comparing ranks based on the scaling model and ranks based on models where some of the flaws of PISA's scaling model are taken into account. Our analyses provide strong evidence of misfit of the PISA scaling model and very strong evidence of DIF. These findings do not support the claims that the country rankings reported by PISA are robust. Keywords:differential item functioning;Ranking;Robustness;Educational testing;Programme for International Student Assessment;Rasch models;Reading literacy]]> Section:Theory & MethodsArticle Title:An analysis of Item Response Theory and Rasch Models based on the most probable distribution methodAuthor(s):Stefano Noventa, Luca Stefanutti and Giulio VidottoAbstract:The most probable distribution method is applied to derive the logistic model as the distribution accounting for the maximum number of possible outcomes in a dichotomous test while introducing latent traits and item characteristics as constraints to the system. The Item Response Theory logistic models, with a particular focus on the one parameter logistic model, or Rasch model, and their properties and assumptions, are discussed for both infinite and finite populations. Keywords:Rasch Model;item response theory;most probable distribution]]> Section:Theory & MethodsArticle Title:Quantile Lower Bounds to Reliability Based on SplitsAuthor(s):Tyler Hunt and Peter BentlerAbstract:Extending the theory of lower bounds to reliability based on splits given by Guttman (1945), this paper introduces quantile lower bound coefficients lambda4(Q) that refer to cumulative proportions of potential locally optimal "split-half" coefficients that are below a particular point Q in the distribution of split-halves based on different partitions of variables into two sets. Interesting quantile values are Q = .05, .50, .95, 1.00 with lambda4(.05) < lambda4(.50)< lambda4(.95) Keywords:reliability;split half;lower bounds;lambda 4.]]> Section:Theory & MethodsArticle Title:Combining Item Response Theory and Diagnostic Classification Models: A Psychometric Model for Scaling Ability and Diagnosing MisconceptionsAuthor(s):Liane Bradshaw and Jonathan L. TemplinAbstract:Traditional testing procedures typically utilize unidimensional item response theory (IRT) models to provide a single, continuous estimate of a student's overall ability. Advances in psychometrics have focused on measuring multiple dimensions of ability to provide more detailed feedback for students, teachers, and other stakeholders. Diagnostic classification models (DCM) provide multidimensional feedback by using categorical latent variables that represent distinct skills underlying a test that students may or may not have mastered. The Scaling Individuals and Classifying Misconceptions (SICM) model is presented as a combination of a unidimensional IRT model and a DCM where the categorical latent variables represent misconceptions instead of skills. In addition to an estimate of ability along a latent continuum, the SICM model also is able to provide multidimensional, diagnostic feedback in the form of statistical estimates of probabilities that students have certain misconceptions. Through an empirical data analysis, we show how this additional feedback can be used by stakeholders to tailor instruction for students' needs. We also provide results from a simulation study that demonstrate that the SICM MCMC estimation algorithm yields reasonably accurate estimates under large-scale testing conditions. Keywords:diagnostic classification models;item response theory;diagnosing student misconceptions;multidimensional measurement model;nominal response]]> Section:Theory & MethodsArticle Title:Evaluating the Equal-Interval Hypothesis with Test Score ScalesAuthor(s):Benjamin DomingueAbstract:The axioms of additive conjoint measurement provide a means of testing the hypothesis that testing data can be placed onto a scale with equal-interval properties. However, the axioms are difficult to verify given that item responses may be subject to measurement error. A Bayesian method exists for imposing order restrictions from additive conjoint measurement while estimating the probability of a correct response. In this study an improved version of that methodology is evaluated via simulation. The approach is then applied to data from a reading assessment intentionally designed to support an equal-interval scaling.Keywords:Conjoint Measurement;Rasch Model;Interval Scale]]> Section:Theory & MethodsArticle Title:Bayesian Hierarchical Multivariate Formulation with Factor Analysis for Nested Ordinal DataAuthor(s):Terrance Dean Savitsky and Daniel F. McCaffreyAbstract:This article devises a Bayesian multivariate formulation for analysis of ordinal data that records teacher classroom performance along multiple dimensions to assess aspects characterizing good instruction. Study designs for scoring teachers seek to measure instructional performance over multiple classroom measurement event sessions at varied occasions using disjoint intervals within each session and employment of multiple ratings on intervals scored by different raters; a design which instantiates a nesting structure with each level contributing a source of variation in recorded scores. We generally possess little \emph{a priori} knowledge of the existence or form of a sparse generating structure for the multivariate dimensions at any level in the nesting that would permit collapsing over dimensions as is done under univariate modeling. Our approach composes a Bayesian data augmentation scheme that introduces a latent continuous multivariate response linked to the observed ordinal scores with the latent response mean constructed as an additive multivariate decomposition of nested level means that permits the extraction of de-noised continuous teacher level scores and associated correlation matrix. A semi-parametric extension facilitates inference for teacher-level dependence among the dimensions of classroom performance under multi-modality induced by sub-groupings of rater perspectives. We next replace an inverse Wishart prior specified for the teacher covariance matrix over dimensions of instruction with a factor analytic structure to allow the simultaneous assessment of an underlying sparse generating structure. Our formulation for Bayesian factor analysis employs parameter expansion with an accompanying post-processing sign re-labeling step of factor loadings that, together, reduce posterior correlations among sampled parameters to improve MCMC mixing. We evaluate the performance of our formulation on simulated data and make an application for the assessment of the teacher covariance structure with a dataset derived from a study of middle and high school algebra teachers. Keywords:Bayesian hierarchical models, Ordinal data, latent models, Markov Chain Monte Carlo, Data Augmentation, Factor analysis, Parameter expansion, Dirichlet process]]> Section:Theory & MethodsArticle Title:Generalized Method of Moments - Instrumental Variable Estimators for Latent Variable ModelsAuthor(s):Kenneth A. Bollen, Stanislav Kolenikov and Shawn BauldryAbstract:The common Maximum Likelihood (ML) estimator for structural equation models (SEMs) has optimal asymptotic properties under ideal conditions (e.g., correct structure, no excess kurtosis, etc.) that are rarely met in practice. This paper proposes Model Implied Instrumental Variable - Generalized Method of Moments (MIIV-GMM) estimators for latent variable SEMs that are more robust than ML to violations of both the model structure and distributional assumptions. Under less demanding assumptions the MIIV-GMM estimators are consistent, asymptotically unbiased, asymptotically normal, and have an asymptotic covariance matrix. They are "distribution-free", robust to heteroscedasticity, and have overidentification goodness of fit J tests with asymptotic chi square distributions. In addition, MIIV-GMM estimators are "scalable" in that they can estimate and test the full model or any subset of equations and hence allow better pinpointing of those parts of the model that fit and do not fit the data. An empirical example illustrates MIIV-GMM estimators. A simulation study explores their finite sample properties and finds that they perform well across a range of sample sizes. Keywords:structural equation models;Latent variables;generalized method of moments;instrumental variables;factor analysis]]> Section:Theory & MethodsArticle Title:Rating Scales as Predictors - the Old Question of Scale Level and some AnswersAuthor(s):Gerhard TutzAbstract:Rating scales as predictors in regression models are typically treated as metrically scaled variables or, alternatively, are coded in dummy variables. The first approach implies a scale level that is not justified, the latter approach results in a large number of parameters to be estimated. Therefore, when dummy variables are used most applications are restricted to the use of few predictors. The penalization approach advocated here takes the scale level serious by using only the ordering of categories but is shown to work in the high dimensional case. We consider the proper modeling of rating scales as predictors and selection procedures by using penalization methods that are tailored to ordinal predictors. In addition to the selection of predictors the clustering of categories is investigated. Existing methodology is extended to the wider class of generalized linear models. Moreover, higher order differences that allow to shrink towards a polynomial as well as monotonicity constraints and alternative penalties are introduced. The proposed penalization approaches are illustrated by use of the Motivational States Questionnaire. Keywords:Rating scales;ordinal predictors;penalized likelihood;generalized linear models;smooth effects]]> Section:Application Reviews & Case Studies (ARCS)Article Title:School System Evaluation by Value-Added Analysis under EndogeneityAuthor(s):Jorge Manzi, Ernesto San Martin and Sébastien Van BellegemAbstract:Value-added is a common tool in educational research on effectiveness. It is often modeled as a (prediction of a) random effect in a specific hierarchical linear model. This paper shows that this modeling strategy is not valid when endogeneity is present. Endogeneity stems for instance from a correlation between the random effect in the hierarchical model and some of its covariates. This paper shows that this phenomenon is far from exceptional and can even be a generic problem when the covariates contain the prior score attainments, a typical situation in value-added modeling. Starting from a general, model-free definition of value-added, the paper derives an explicit expression of the value-added in an endogeneous hierarchical linear Gaussian model. Inference on value-added is proposed using an instrumental variable approach. The impact of endogeneity on the value-added and the estimated value-added is calculated accurately. This is also illustrated on a large data set of individual scores of about 200,000 students in Chile.Keywords:Value-added, endogeneity, hierarchical linear mixed model, instrumental variable, school effect.]]> Section:Theory & MethodsArticle Title:Spectral analysis of variance models: A Bayesian nonparametric approachAuthor(s):Christian Macaro and Raquel PradoAbstract:We consider spectral decompositions of multiple time series that arise in studies where the interest lies in assessing the influence of two or more factors. We write the spectral density of each time series as a sum of the spectral densities associated to the different levels of the factors. We then use Whittle's approximation to the likelihood function and follow a Bayesian nonparametric approach to obtain posterior inference on the spectral densities based on Bernstein-Dirichlet prior distributions. The prior is strategically important as it carries identifiability conditions for the models and allows us to quantify our degree of confidence in such conditions. A Markov chain Monte Carlo (MCMC) algorithm for posterior inference within this class of frequency-domain models is presented. We illustrate the approach by analyzing simulated and real data via spectral one-way and two-way models. In particular, we present an analysis of functional magnetic resonance (fMRI) brain responses measured in individuals who participated in a designed experiment to study pain perception in humans.Keywords:Spectral one-way and two-way models;Bayesian nonparametrics;Whittle's approximation;Bernstein-Dirichlet priors.]]> Section:Theory & MethodsArticle Title:A SPEEDED ITEM RESPONSE MODEL: LEAVE THE HARDER TILL LATERAuthor(s):Yu-Wei Chang, Rung-Ching Tsai and Nan-Jung HsuAbstract:A speeded item response model is proposed. We consider the situation where examinees may retain the harder items to the later test period in a time limit test. With such a strategy, examinees may not finish answering some of the harder items within the allocated time. In the proposed model, we try to describe such a mechanism by incorporating a speeded-effect term into the two-parameter logistic item response model. Bayesian estimation procedure of the current model using Markov chain Monte Carlo is presented and its performance over the two-parameter logistic item response model in a speeded test is demonstrated through simulations. The methodology is applied to the physics examination data of the Department Required Test for college entrance in Taiwan for illustration. Keywords:item response model;Markov chain Monte Carlo;test speededness.]]> Section:Theory & MethodsArticle Title:An inequality for correlations in some unidimensional monotone latent variable modelsAuthor(s):Jules EllisAbstract:It is shown that a unidimensional monotone latent variable model for binary items implies a restriction on the relative sizes of item correlations: The negative logarithm of the correlations satisfies the triangle inequality. This inequality is not implied by the condition that the correlations are nonnegative, the criterion that coefficient H exceeds .30, or manifest monotonicity. The inequality implies both a lower bound and an upper bound for each correlation between two items, based on the correlations of those two items with every possible third item. It is discussed how this can be used in Mokken's (1971) scale analysis. Keywords:nonparametric IRT;conditional association;partial correlation;monotonicity;Mokken scale analysis]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Harmonic Regression and Scale StabilityAuthor(s):Shelby Haberman and Yi-Hsuan LeeAbstract:Monitoring a very frequently administered educational test with a relatively short history of stable operation imposes a number of challenges. Test scores usually vary by season, and the frequency of administration of such educational tests is also seasonal. Although it is important to react to unreasonable changes in the distributions of test scores in a timely fashion, it is not a simple matter to ascertain what sort of distribution is really unusual. Many commonly used approaches for seasonal adjustment are designed for time series with evenly spaced observations that span many years, and therefore are inappropriate for data from such educational tests. Harmonic regression, a seasonal-adjustment method, can be useful in monitoring scale stability when the number of years available is limited and when the observations are unevenly spaced. Additional forms of adjustments can be included to account for variability in test scores due to different sources of population variations. To illustrate, real data are considered from an international language assessment. Keywords: seasonal adjustment;quality control;seasonality.]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Explanatory Multidimensional Multilevel Random Item Response Model: An Application to Simultaneous Investigation of Word and Person Contributions to Multidimensional Lexical QualityAuthor(s):Sun-Joo Cho, Jennifer Gilbert and Amanda GoodwinAbstract:This paper presents an explanatory multidimensional multilevel random item response model and its application to reading data with multilevel item structure. The model includes multilevel random item parameters that allow consideration of variability in item parameters at both item and item group levels. Item-level random item parameters were included to model unexplained variance remaining when item related covariates were used to explain variation in item difficulties. Item group-level random item parameters were included to model dependency in item responses among items having the same item stem. Using the model, this study examined the dimensionality of a person's word knowledge, termed lexical representation, and how aspects of morphological knowledge contributed to lexical representations for different persons, items, and item groups. Keywords:lexical representation, multidimensional item response model, multilevel item structure, random item parameters]]> Section:Theory & MethodsArticle Title:The Special Sign Indeterminacy of the Direct-Fitting Parafac2 Model: Some Implications, Cautions, and Recommendations for Simultaneous Component AnalysisAuthor(s):Nathaniel E. HelwigAbstract:Parafac2 is the most flexible Simultaneous Component Analysis (SCA) model that produces an essentially unique solution. In this paper, we discuss how Parafac2's special sign indeterminacy affects applications of SCA, and we reveal how an external criterion variable can be used to ensure that estimated Parafac2 weights are meaningfully signed across the levels of the nesting mode. We present an example with real data from clinical psychology that illustrates the importance of Parafac2's special sign indeterminacy, as well as the effectiveness of our proposed solution. We also discuss the implications of our results for general applications of SCA. Keywords:Parafac2;Parafac2 sign indeterminacy;Parafac2 uniqueness;Simultaneous Component Analysis;SCA;SCA uniqueness]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Modelling Dyadic Interaction with Hawkes ProcessAuthor(s):Peter Francis Halpin and Paul De BoeckAbstract:We apply Hawkes process to the analysis of dyadic interaction. Hawkes process is applicable to excitatory interactions, wherein the actions of each individual increase the probability of further actions in the near future. We consider the representation of Hawkes process both as a conditional intensity function and as a cluster Poisson process. The former treats the probability of an action in continuous time via non-stationary distributions with arbitrarily long historical dependency, while the latter is conducive to maximum likelihood estimation using the EM algorithm. We first outline the interpretation of Hawkes process in the dyadic context, and then illustrate its application with an example concerning email transactions in the work place.Keywords:dyadic interaction;event sampling;Hawkes process;EM algorithm;maximum likelihood]]> Section:Theory & MethodsArticle Title:Assessing Parameter Invariance in the BLIM: Bipartition ModelsAuthor(s):Deborah de Chiusole, Luca Stefanutti, Pasquale Anselmi and Egidio RobustoAbstract:In knowledge space theory, the knowledge state of a student is the set of all problems he is capable of solving in a specific knowledge domain and a knowledge structure is the collection of knowledge states. The basic local independence model (BLIM) is a probabilistic model for knowledge structures. The BLIM assumes a probability distribution on the knowledge states and a lucky guess and a careless error probability for each problem. A key assumption of the BLIM is that the lucky guess and careless error probabilities do not depend on knowledge states (invariance assumption). This article proposes a method for testing the violations of this specific assumption. The proposed method was assessed in a simulation study and in an empirical application. The results show that (1) the invariance assumption might be violated by the empirical data even when the model's fit is very good, and (2) the proposed method may prove to be a promising tool to detect invariance violations of the BLIM. Keywords:basic local independence model;knowledge space theory;parameter invariance]]> Section:Theory & MethodsArticle Title:A NON-DEGENERATE ESTIMATOR FOR VARIANCE PARAMETERS IN MULTILEVEL MODELS VIA PENALIZED LIKELIHOOD ESTIMATIONAuthor(s):Yeojin Chung, Sophia Rabe-Hesketh, Vincent Dorie, Andrew Gelman and Jingchen LiuAbstract:Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary estimates. This approach is equivalent to estimating variance parameters by their posterior mode, given a weakly informative prior distribution. By choosing the penalty from the log-gamma family with shape parameter greater than 1, we ensure that the estimated variance will be positive. We suggest a default log-gamma(2,0) penalty, which ensures that the maximum penalized likelihood estimator is approximately one standard error from zero when the maximum likelihood estimate is zero, thus remaining consistent with the likelihood while being non-degenerate. We also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a non informative prior. Our default method provides better estimates of model parameters and standard errors than the maximum likelihood or the restricted maximum likelihood estimators. The log-gamma family can also be used to convey substantive prior information. In either case—pure penalization or prior information—our recommended procedure gives non-degenerate estimates and in the limit coincides with maximum likelihood as the number of groups increases. Keywords:Bayes modal estimation, Hierarchical Linear Model, Mixed Model, Multilevel Model, Penalized likelihood, Variance Estimation]]> Section:Book ReviewsArticle Title:MAINDONALD, J. & W. J. BRAUN (2010).Data Analysis and Graphics Using R: An Example-Based ApproachAuthor(s):Paul Gerrard]]> Section:Theory & MethodsArticle Title:Constrained Candecomp/Parafac via the LassoAuthor(s):Paolo Giordani and Roberto RocciAbstract:The Candecomp/Parafac (CP) model is a well-known tool for summarizing a three-way array by extracting a limited number of components. Unfortunately, in some cases, the model suffers from the so-called degeneracy, that is a solution with diverging and uninterpretable components. To avoid degeneracy orthogonality constraints are usually applied to one of the component matrices. This solves the problem only from a technical point of view because the existence of orthogonal components underlying the data is not guaranteed. For this purpose, we consider some variants of the CP model where the orthogonality constraints are relaxed either by constraining only a pair, or a subset, of components or by stimulating the CP solution to be possibly orthogonal. We theoretically clarify that only the latter approach, based on the Least absolute shrinkage and selection operator and named CP-Lasso, is helpful in solving the degeneracy problem. The results of the application of CP-Lasso on simulated and real life data show its effectiveness. Keywords:Candecomp/Parafac;Degeneracy;Lasso;Orthogonality constraints.]]> Section:Theory & MethodsArticle Title:A note on the hierarchical model for responses and response times in tests of van der Linden (2007)Author(s):Jochen RangerAbstract:Findings suggest that in psychological tests not only the responses but also the times needed to give the responses are related to characteristics of the test taker. This observation has stimulated the development of latent trait models for the joint distribution of the responses and the response times. Such models are motivated by the hope to improve the estimation of the latent traits by additionally considering response time. In this article, the potential relevance of the response times for psychological assessment is explored for the model of van der Linden (2007) that seems to have become the standard approach to response time modeling in educational testing. It can be shown that the consideration of response times increases the information of the test. However, one also can prove that the contribution of the response times to the test information is bounded and has a simple limit. Keywords:response time;response time model;Item Response Theory]]> Section:Application Reviews & Case Studies (ARCS)Article Title:An application of the LC-LSTM framework to the Self-esteem instability caseAuthor(s):Guido Alessandri, Michele Vecchione, Brent M. Donnellan and John TisakAbstract:The present research evaluates the stability of self-esteem as assessed by a daily version of the Rosenberg's (1965) general self-esteem scale (RGSE). The scale was administered to 391 undergraduates for five consecutive days. The longitudinal data were analyzed using the integrated LC-LSTM framework, that allowed us to evaluate: (1) the measurement invariance of the RGSE, (2) its stability and change across the 5-day assessment period, (3) the decomposition of variance into stable and transitory elements, and (4) the instrument's criterion-related validity. Results provided evidence for measurement invariance, mean-level stability, and rank-order stability of daily self-esteem. Latent state-trait analyses revealed that variances in scores of the RGSE can be decomposed into five components: stable self-esteem (40%), stable negative method variance (9%), stable positive method variance (4%), ephemeral (or temporal-state) variance (36%), specific variance (1%) and random error variance (10%). Moreover, latent factors associated with daily self-esteem were associated with measures of depression, implicit self-esteem, and academic achievement. Keywords:Latent state-trait model;Self-esteem;Implicit self-esteem;measurement invariance;self-esteem instability]]> Section:Theory & MethodsArticle Title:Modeling Differences in the Dimensionality of Multiblock Data by Means of Clusterwise Simultaneous Component AnalysisAuthor(s):Kim De Roover, Eva Ceulemans, Marieke E. Timmerman, John Nezlek and Patrick OnghenaAbstract:Given multivariate multiblock data (e.g., subjects nested in groups are measured on multiple variables) one may be interested in the nature and number of dimensions that underlie the variables, and in differences in dimensional structure across data blocks. To this end, clusterwise simultaneous component analysis (SCA) was proposed which simultaneously clusters blocks with a similar structure and performs an SCA per cluster. However, the number of components was restricted to be the same across clusters, which is often unrealistic. In this paper, this restriction is removed. The resulting challenges with respect to model estimation and selection are resolved. Keywords:multigroup data;multilevel data;principal component analysis;Simultaneous Component Analysis;clustering;Dimensionality]]> Section:Theory & MethodsArticle Title:A Bayesian Modeling Approach for Generalized Semiparametric Structural Equation ModelsAuthor(s):Xin-Yuan Song, Zhao-Hua Lu, Jing-Heng Cai and Edward Hak-sing IpAbstract:In behavioral, biomedical, and psychological studies, structural equation models (SEMs) have been widely used for assessing relationships between latent variables. Regression-type structural models based on parametric functions are often used for such purposes. In many applications, however, parametric SEMs are not adequate to capture subtle patterns in the functions over the entire range of the predictor variable. A different but equally important limitation of traditional parametric SEMs is that they are not designed to handle mixed data types - continuous, count, ordered, and unordered categorical. This paper develops a generalized semiparametric SEM that is able to handle mixed data types and to simultaneously model different functional relationships among latent variables. A structural equation of the proposed SEM is formulated using a series of unspecified smooth functions. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the smooth functions and the unknown parameters. Moreover, we examine the relative benefits of semiparametric modeling over parametric modeling using a Bayesian model-comparison statistic, called the complete Deviance Information Criterion. The performance of the developed methodology is evaluated using a simulation study. To illustrate the method, we used a data set derived from the National Longitudinal Survey of Youth. Keywords:Bayesian P-splines;Latent variables;MCMC methods;Semiparametric models]]> Section:Theory & MethodsArticle Title:Using Deterministic, Gated Item Response Theory Model to Detect Test Cheating due to Item CompromiseAuthor(s):Zhan Shu, Robert A. Henson and Richard M. LuechtAbstract:The Deterministic, Gated Item Response Theory Model (DGM, Shu, 2010) is proposed to identify cheaters who obtain significant score gain on tests due to item exposure/compromise by conditioning on the item status (exposed or unexposed items). A "gated" function is introduced to decompose the observed examinees' performance into two distributions (the true ability distribution determined by examinees' true ability and the cheating distribution determined by examinees' cheating ability). Test cheaters who have score gain due to item exposure are identified through the comparison of the two distributions. Hierarchical Markov Chain Monte Carlo is used as the model's estimation framework. Finally, the model is applied in a real data set to illustrate how the model can be used to identify examinees having pre-knowledge on the exposed items.Keywords:Cheating, Model Estimation]]> Section:Theory & MethodsArticle Title:OBLIQUE ROTATON IN CANONICAL CORRELATION ANALYSIS REFORMULATED AS MAXIMIZING THE GENERALIZED COEFFICIENT OF DETERMINATIONAuthor(s):Hironori Satomura and Kohei AdachiAbstract:To facilitate the interpretation of canonical correlation analysis (CCA) solutions, procedures have been proposed in which CCA solutions are orthogonally rotated to a simple structure. In this paper, we consider oblique rotation for CCA to provide solutions that are much easier to interpret, though only orthogonal rotation is allowed in the existing formulations of CCA. Our task is thus to reformulate CCA so that its solutions have the freedom of oblique rotation. Such a task can be achieved using Yanai's (1974, 1981) generalized coefficient of determination for the objective function to be maximized in CCA. The resulting solutions are proved to include the existing orthogonal ones as special cases and to be rotated obliquely without affecting the objective function value, where ten Berge's (1983) theorems on suborthonormal matrices are used. A real data example demonstrates that the proposed oblique rotation can provide simple, easily interpreted CCA solutions.Keywords:canonical correlation analysis;oblique rotation;generalized coefficient of determination;suborthonormal matrices]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Monitoring Scale Scores Over Time via Quality Control Charts, Model-Based Approaches, and Time Series TechniquesAuthor(s):Yi-Hsuan Lee and Alina A. von DavierAbstract:Maintaining a stable score scale over time is critical for all standardized educational assessments. Traditional quality control tools and approaches for assessing scale drift either require special equating designs, or may be too time-consuming to be considered on a regular basis with an operational test that has a short time window between an administration and its score reporting. Thus, the traditional methods are not sufficient to catch unusual testing outcomes in a timely manner. This paper presents a new approach for score monitoring and assessment of scale drift. It involves quality control charts, model-based approaches, and time series techniques to accommodate the following needs of monitoring scale scores: continuous monitoring, adjustment of customary variations, identification of abrupt shifts, and assessment of autocorrelation. Performance of the methodologies is evaluated using manipulated data based on real responses from 71 administrations of a large-scale high-stakes language assessment. Keywords:Quality assurance;seasonal adjustment;change point;Shewhart chart;CUSUM chart;hidden Markov model;harmonic regression]]> Section:Theory & MethodsArticle Title:MULTIOBJECTIVE BLOCKMODELING FOR SOCIAL NETWORK ANALYSISAuthor(s):Michael J. Brusco, Patrick Doreian and Douglas SteinleyAbstract:To date, most methods for blockmodeling of social network data have focused on the optimization of a single objective function. There are a variety of social network applications, however, where it is advantageous to consider two or more objectives simultaneously. These applications can broadly be placed into two categories: (1) simultaneous optimization of multiple criteria for fitting a blockmodel based on a single network matrix, and (2) simultaneous optimization of multiple criteria for fitting a blockmodel based on two or more network matrices, where the matrices being fit can take the form of multiple indicators for an underlying relationship, or multiple matrices for a set of objects measured at two or more different points in time. A multiobjective tabu search procedure is proposed for estimating the set of Pareto efficient blockmodels. This procedure is used in three examples that demonstrate possible applications of the multiobjective blockmodeling paradigm. Keywords:social networks;blockmodeling;multiobjective programming;heuristics;tabu search.]]> Section:Theory & MethodsArticle Title:IRT Test Equating in Complex Linkage PlansAuthor(s):Michela BattauzAbstract:Linkage plans can be rather complex, including many forms, several links and the connection of forms through different paths. This article studies item response theory equating methods for complex linkage plans when the common-item nonequivalent group design is used. An efficient way to average equating coefficients that link the same two forms through different paths will be presented and the asymptotic standard errors of indirect and average equating coefficients are derived. The methodology is illustrated using simulations studies and a real data example. Keywords:asymptotic standard errors;chain equating;double equating;equating coefficients;item response theory;multiple equating;weighted bisector.]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Detecting Intervention Effects with a Multilevel Latent Transition Analysis with a Mixture IRT ModelAuthor(s):Sun-Joo Cho, Allan S. Cohen and Brian BottgeAbstract:A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for assessing stage sequential change over time at both student and teacher levels. Results from a LTA-MixIRTM and multilevel LTA-MixIRTM were compared in the context of an educational intervention study. Both models were able to describe homogeneities in problem solving and transition patterns. However, ignoring a multilevel structure in LTA-MixIRTM led to different results in group membership assignment in empirical results. Results for the multilevel LTA-MixIRTM indicated that there were distinct individual differences in the different transition patterns. The students receiving the intervention treatment outscored their business as usual (i.e., control group) counterparts on the curriculum-based Fractions Computation test. In addition, 27.4\% of the students in the sample moved from the low ability student-level latent class to the high ability student-level latent class. Students were characterized differently depending on the teacher-level latent class.Keywords:latent class model, mixture item response theory model, multilevel latent transition analysis]]> Section:Theory & MethodsArticle Title:Continuous orthogonal complement functions and distribution free goodness of fit tests in moment structure analysisAuthor(s):Robert I. Jennrich and Albert SatorraAbstract:Abstract:Keywords:$\chi^2$ tests;orthogonal complements;QR factorization;implicit function theorem.]]> Section:Theory & MethodsArticle Title:On the Likelihood Ratio Tests in Bivariate ACDE ModelsAuthor(s):Hao Wu and Michael C. NealeAbstract:The ACE and ADE models have been heavily exploited in twin studies to identify the genetic and environmental components in phenotypes. However, the validity of the likelihood ratio test (LRT) of the existence of a variance component, a key step in the use of such models, has been doubted because the true values of the parameters lie on the boundary of the parameter space of the alternative model for such tests, violating a regularity condition required for a LRT (e.g. Carey, 2005; Visscher, 2006). Dominicus et al. (2006) solves the problem of testing univariate components in ACDE models. Our current work as presented in this paper resolves the issue of LRTs in bivariate ACDE models by exploiting the theoretical frameworks of inequality constrained LRTs based on cone approximations. Our derivation shows that the asymptotic sampling distribution of the test statistic for testing a single bivariate component in an ACE or ADE model is a mixture of $\chi^2$ distributions of degrees of freedom (dfs) ranging from 0 to 3, and that for testing both the A and C (or D) components is one of dfs ranging from 0 to 6. These correct distributions are stochastically smaller than the $\chi^2$ distributions in traditional LRTs and therefore LRTs based on these distributions are more powerful than those used naively. Formulae for calculating the weights are derived and the sampling distributions are confirmed by simulation studies. Several invariance properties for normal data (at most) missing by person are also proved. Potential generalizations of this work are also discussed.Keywords:ACE model;Variance components;Likelihood ratio test;$\bar\chi^2$ distribution.]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Nonlinear Regime-Switching State-Space (RSSS) ModelsAuthor(s):Sy Miin Chow and Guangjian ZhangAbstract:Nonlinear dynamic factor analysis models extend standard linear dynamic factor analysis models by allowing time series processes to be nonlinear at the latent level (e.g., involving interaction between two latent processes). In practice, it is often of interest to identify the phases--namely, latent "regimes" or classes--during which a system is characterized by distinctly different dynamics. We propose a new class of models, termed nonlinear regime-switching state-space (RSSS) models, which subsume regime-switching nonlinear dynamic factor analysis model as a special case. In nonlinear RSSS models, the change processes within regimes, represented using a state-space model, are allowed to be nonlinear. An estimation procedure obtained by combining the extended Kalman lter (Anderson & Moore, 1979) and the Kim filter (Kim & Nelson, 1999) is proposed as a way to estimate nonlinear RSSS models. We illustrate the utility of nonlinear RSSS models by fitting a nonlinear dynamic factor analysis model with regime-specific cross-regression parameters to a set of experience sampling affect data. The parallels between nonlinear RSSS models and other well known discrete change models in the literature are discussed briefly.Keywords:Regime-switching;state-space;nonlinear latent variable models;dynamic factor analysis;Kim filter]]> Section:Theory & MethodsArticle Title:Observed-Score Equating: An OverviewAuthor(s):Alina A. von DavierAbstract:In this paper an overview of the observed-score equating (OSE) process is provided from the perspective of a unifying equating framework (von Davier, 2011b). The framework includes all OSE approaches: traditional and kernel equating (von Davier, Holland, & Thayer, 2004), IRT observed-score and local equating (van der Linden, 2003; Wiberg, van der Linden, & von Davier, 2012), and a few other methods. Issues related to the test and sampling designs and their relationship to measurement and equating are presented. Challenges to the equating process and approaches to equating evaluation are also discussed. The equating process is illustrated step-by-step with a real data example from a licensure test. Keywords:test equating, observed-scores, kernel equating, local equating, loglinear models, item response theory]]> Section:Theory & MethodsArticle Title:FACTOR ANALYSIS WITH EM ALGORITHM NEVER GIVES IMPROPER SOLUTIONS WHEN SAMPLE COVARIANCE AND INITIAL PARAMETER MATRICES ARE PROPERAuthor(s):Kohei AdachiAbstract:Rubin and Thayer (1982) proposed the EM algorithm for exploratory and confirmatory maximum likelihood factor analysis. In this paper, we prove the following fact: the EM algorithm always gives a proper solution with positive unique variances and factor correlations with absolute values that do not exceed one, when the covariance matrix to be analyzed and the initial matrices including unique variances and inter-factor correlations are positive definite. We further numerically demonstrate that the EM algorithm yields proper solutions for the data which lead the prevailing gradient algorithms for factor analysis to produce improper solutions. The numerical studies also show that, in real computations with limited numerical precision, Rubin and Thayer's (1982) original formulas for confirmatory factor analysis can make factor correlation matrices asymmetric, so that the EM algorithm fails to converge. However, this problem can be overcome by using an EM algorithm in which the original formulas are replaced by those guaranteeing the symmetry of factor correlation matrices, or by formulas used to prove the above fact.Keywords:Factor analysis;EM algorithm;improper solutions;maximum likelihood method]]> Section:Book ReviewsArticle Title:BOOK REVIEW Alina A. von Davier (Ed.) (2011). Statistical Models for Test Equating, Scaling, and Linking.Author(s):Marie Wiberg]]> Section:Book ReviewsArticle Title:Review of van der Linden & Glas (Eds.), "Elements of Adaptive Testing"Author(s):Usama S. Ali and Peter W. van Rijn]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Methods for mediation analysis with missing dataAuthor(s):Zhiyong Zhang and Lijuan WangAbstract:Despite wide applications of both mediation models and missing data techniques, formal discussion of mediation analysis with missing data is still rare. We introduce and compare four approaches to dealing with missing data in mediation analysis including listwise deletion, pairwise deletion, multiple imputation (MI), and a two-stage maximum likelihood (TS-ML) method. An R package bmem is developed to implement the four methods for mediation analysis with missing data in the structural equation modeling framework and two real examples are used to illustrate the application of the four methods. The four methods are then evaluated and compared under MCAR, MAR and MNAR missing data mechanisms through simulation studies. Both MI and TS-ML perform well for MCAR and MAR data regardless of the inclusion of auxiliary variables and for AV-MNAR data with auxiliary variables. Although listwise deletion and pairwise deletion have low power and large parameter estimate bias in many studied conditions, they may provide useful information for exploring missing mechanisms. Keywords:Mediation analysis, missing data, MI, TS-ML, bootstrap, auxiliary variables]]> Section:Theory & MethodsArticle Title:Assessing Item Fit for Unidimensional Item Response Theory Models Using Residuals from Estimated Item Response FunctionsAuthor(s):Shelby Haberman, Sandip Sinharay and Kyong Hee ChonAbstract:Assessing item fit is important in applications of the item response theory (IRT) models. Residual analysis (e.g., Hambleton, Swaminathan, & Rogers, 1991) is a popular method to assess item fit. We suggest a form of residual analysis that may be applied to assess item fit for unidimensional IRT models. The residual analysis consists of a comparison of the maximum likelihood estimate of the item characteristic curve with an alternative ratio estimate of the item characteristic curve. The large sample distribution of the residuals is proved to be standardized normal when the IRT model fits the data. We compare the performance of our suggested residual to the standardized residual of Hambleton et al. (1991) in a detailed simulation study. We then calculate our suggested residuals using data from an operational test. Keywords:2-parameter-logistic model;generalized partial credit model;item characteristic curve;IRT model fit]]> Section:Theory & MethodsArticle Title:Global convergence of the EM algorithm for unconstrained latent variable models with categorical indicatorsAuthor(s):Alexander WeissmanAbstract:Convergence of the expectation-maximization (EM) algorithm to a global optimum of the marginal log likelihood function for unconstrained latent variable models with categorical indicators is presented. The sufficient conditions under which global convergence of the EM algorithm is attainable are provided in an information-theoretic context by interpreting the EM algorithm as alternating minimization of the Kullback-Leibler divergence between two convex sets. It is shown that these conditions are satisfied by an unconstrained latent class model, yielding an optimal bound against which more highly constrained models may be compared. Keywords:EM algorithm;latent variable models;latent class models;information theory;Kullback-Leibler divergence;relative entropy;variational calculus;convex optimization;optimal bounds]]> Section:Theory & MethodsArticle Title:How should we assess the fit of Rasch-type models? Approximating the power of goodness-of-fit statistics in categorical data analysisAuthor(s):Alberto Maydeu-Olivares and Rosa MontanoAbstract:We describe a procedure to approximate asymptotically the power of goodness-of-fit statistics for multivariate discrete data under local alternatives of interest. We use this procedure to compare the performance of three statistics, R1, R2 (Glas, 1988) and M2 (Maydeu-Olivares & Joe, 2005, 2006) to assess the fit of a one-parameter logistic model (1PL). The accuracy of the asymptotic distribution of the test statistics under the null and under sequences of local alternatives was investigated. All three statistics were found to be more powerful than Pearson's X2 against two- and three-parameter logistic alternatives (2PL and 3PL), and against multidimensional 1PL models. M2 was found to have more accurate p-values. R1 and M2 were found to be most powerful to detect a 2PL and 3PL. R2 and M2 were found to be most powerful to detect a multidimensional 1PL. Two examples are provided to illustrate the results. Keywords:goodness of fit;IRT;maximum likelihood;Power;1PL;2PL;discrete data;Pearson's X2]]> Section:Application Reviews & Case Studies (ARCS)Article Title:A Hierarchical Modeling Approach to Data Analysis and Study Desgin in a Multi-Site Experimental FMRI StudyAuthor(s):Bo Zhou, Kinh H. Tieu, Ana Konstorum, Thao Duong and Hal S. SternAbstract:We propose a hierarchical Bayesian model for analyzing multi-site experimental fMRI studies. Our method takes the hierarchical structure of the data (subjects are nested within sites, and there are multiple observations per subject) into account and allows for modeling between-site variation. Using posterior predictive model checking and model selection based on the deviance information criterion (DIC), we show that our model provides a good .t to the observed data by sharing information across the sites. We also propose a simple approach for evaluating the e.cacy of the multi-site experiment by comparing the results to those that would be expected in hypothetical single-site experiments with the same sample size. Keywords:Multi-center study;Functional magnetic resonance imaging;Bayesian model;Multilevel analysis]]> Section:Theory & MethodsArticle Title:Generalized measurement invariance tests with application to factor analysisAuthor(s):Ed Merkle and Achim ZeileisAbstract:The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we construct tests of measurement invariance based on stochastic processes of casewise derivatives of the likelihood function. These tests can be viewed as generalizations of the Lagrange multiplier test, and they are especially useful for: (1) identifying subgroups of individuals that violate measurement invariance along a continuous auxiliary variable without prespecified thresholds, and (2) identifying specific parameters impacted by measurement invariance violations. The tests are presented and illustrated in detail, including an application to a study of stereotype threat and simulations examining the tests' abilities in controlled conditions. Keywords:measurement invariance;parameter stability;Factor analysis;structural equation models]]> Section:Application Reviews & Case Studies (ARCS)Article Title:State-Space Analysis of Working Memory in Schizophrenia: An FBIRN StudyAuthor(s):Firdaus Janoos, Gregory Brown and William Wells IIIAbstract:The neural correlates of working memory (WM) in schizophrenia (SZ) have been extensively studied using the multi-site fMRI data acquired by the Functional Biomedical Informatics Research Network (fBIRN) consortium. Although univariate and multivariate analysis methods have been variously employed to localize brain responses under differing task conditions, important hypotheses regarding the representation of mental processes in the spatio-temporal patterns of neural recruitment and the differential organization of these mental processes in patients versus controls have not been addressed in this context. This paper uses a multivariate state-space model (SSM) to analyse the differential representation and organization of mental processes of controls and patients performing the Sternberg Item Recognition Paradigm (SIRP) WM task. The SSM is able to not only predict the mental state of the subject from the data, but also yield estimates of the spatial distribution and temporal ordering of neural activity, along with estimates of the hemodynamic response. The dynamical Bayesian modeling approach used in this study was able to find significant differences between the predictability and organization of the working memory processes of SZ patients versus healthy subjects. Prediction of some stimulus types from imaging data in the SZ group was significantly lower than controls, reflecting a greater level of disorganization / heterogeneity of their mental processes. Moreover, the changes in accuracy of predicting the mental state of the subject with respect to parametric modulations, such as memory load and task duration, may have important implications on the neuro-cognitive models for WM processes in both SZ and healthy adults. Additionally, the SSM was used to compare the spatio-temporal patterns of mental activity across subjects, in a holistic fashion and to derive a low-dimensional representation space for the SIRP task, in which subjects were found to cluster according to their diagnosis. Keywords:State-space analysis, Markov chain models, schizophrenia, working memory, multi-site functional MRI]]> Section:Theory & MethodsArticle Title:Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric ResultsAuthor(s):Ernesto San Martin and Jean-Marie RolinAbstract:In this paper, we study the identification of a particular case of the 3PL model, namely when the discrimination parameters are all constant and equal to 1. We term this model, 1PL-G model. The identification analysis is performed under three different specifications. The first specification considers the abilities as unknown parameters. It is proved that the item parameters and the abilities are identified if a difficulty parameter and a guessing parameter are fixed at zero. The second specification assumes that the abilities are mutually independent and identically distributed according to a distribution known up to the scale parameter. It is shown that the item parameters and the scale parameter are identified if a guessing parameter is fixed at zero. The third specification corresponds to a semi-parametric 1PL-G model, where the distribution $G$ generating the abilities is a parameter of interest. It is not only shown that, after fixing a difficulty parameter and a guessing parameter at zero, the item parameters are identified, but also that under those restrictions the distribution $G$ is not identified. It is finally shown that, after introducing two identification restrictions either on the distribution $G$ or on the item parameters, the distribution $G$ and the item parameters are identified provided an infinite quantity of items is available.Keywords:2PL, 3PL model, location-scale distributions, fixed effects, random effects, identified parameter, parameters of interest, Hilbert space. ]]> Section:Theory & MethodsArticle Title:A New Zero-Inflated Negative Binomial Methodology for Latent Category IdentificationAuthor(s):Simon J. Blanchard, Wayne DeSarbo, A. Selin Atalay and Nukhet HarmanciogluAbstract:We propose a new statistical procedure that estimates unobserved categorization structures among a set of objects using sorting task data when people may assign objects to multiple piles simultaneously. This methodology accounts for heterogeneity through individual differences in the saliency of latent category structures. The results of a synthetic example and an empirical study involving categories of restaurant brands illustrate how the proposed methodology can account for a variety of category structures. Keywords:Categorization, Unobserved Categories, Heterogeneity, Sorting Task, Consumer Psychology]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Modeling Motivated Misreports to Sensitive Survey QuestionsAuthor(s):Ulf BoeckenholtAbstract:Asking sensitive or personal questions in surveys or experimental studies can both lower response rates and increase item non-response and misreports. Although non-response is easily diagnosed, misreports are not. However, misreports cannot be ignored because they give rise to systematic biases. The purpose of this paper is to present a modeling approach that identifies misreports and corrects for them. Misreports are conceptualized as a motivated process under which respondents edit their answers before they report them. For example, systematic biases introduced by overreports of socially desirable behaviors or underreports of socially less desirable ones can be modelled, leading to more valid inferences. The proposed approach is applied to a large-scale experimental study and shows that respondents who feel powerful tend to overclaim their knowledge. Keywords:response set, survey research, socially desirable responding, self-deceptive enhancement, item response models]]> Section:Book ReviewsArticle Title:Review of "Research Synthesis and Meta-Analysis: A Step-by-Step Approach" by H. M. CooperAuthor(s):Jingyun Yang and Joseph P. Gyekis]]> Section:Application Reviews & Case Studies (ARCS)Article Title:A Survey of the Sources of Noise in fMRIAuthor(s):Douglas N. Greve, Gregory Brown, Byron Mueller, Gary Glover and Thomas LiuAbstract:Functional magnetic resonance imaging (fMRI) is a non-invasive method for measuring brain function by correlating temporal changes in local cerebral blood oxygenation with behavioral measures. fMRI is used to study individuals at single time points, across multiple time points (with or without intervention) as well as to examine the variation of brain function across normal and ill populations. fMRI may be collected at multiple sites and then pooled into a single analysis. This paper describes how fMRI data is analyzed at each of these levels and describes the noise sources introduced at each levelKeywords:Functional MRI;Blood oxygen level dependent;Multi-Level Analysis;Sources of Noise]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Can Functional MRI Provide Quantitative Measures?Author(s):Thomas Liu, Gary Glover, Byron Mueller, Douglas N. Greve and Gregory BrownAbstract:In functional magnetic resonance imaging (fMRI), the blood oxygenation level dependent (BOLD) signal is often interpreted as a measure of neural activity. However, because the BOLD signal reflects the complex interplay of neural, vascular, and metabolic processes, such an interpretation is not always valid. There is growing evidence that changes in the baseline neurovascular state can result in significant modulations of the BOLD signal that are independent of changes in neural activity. This paper introduces some of the normalization and calibration methods that have been proposed for making the BOLD signal a more accurate reflection of underlying brain activity for human fMRI studies.Keywords:Functional MRI, Arterial Spin Labeling; Cerebral Blood Blow; Quantitative fMRI; Calibrated fMRI; Hypercapnia]]> Section:Theory & MethodsArticle Title:Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory ModelsAuthor(s):Anna Doebler and Heinz HollingAbstract:The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter $\theta$ is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given level of significance in many cases and therefore, the corresponding intervals are no longer confidence intervals in terms of the actual definition.
In the present work, confidence intervals are defined more precisely by utilizing the relationship between confidence intervals and hypothesis testing. Two approaches to confidence interval construction are explored that are optimal with respect to criteria of smallness and consistency with the standard approach. Keywords:confidence intervals;optimality;item response theory;monotone likelihood ratio;Adaptive Testing]]> Section:Theory & MethodsArticle Title:A Multicomponent Latent Trait Model for DiagnosisAuthor(s):Susan E. Embretson and Xiangdon YangAbstract:This paper presents a non-compensatory latent trait model, the multicomponent latent trait model for diagnosis (MLTM-D), for cognitive diagnosis. In MLTM-D, a hierarchical relationship between components and attributes is specified to be applicable to permit diagnosis at two levels. MLTM-D is a generalization of the multicomponent latent trait model (MLTM; Whitely, 1980; Embretson, 1984) to be applicable to measures of broad traits, such as achievement tests, in which component structure varies between items. Conditions for model identification are described and marginal maximum likelihood estimators are presented, along with simulation data to demonstrate parameter recovery. To illustrate how MLTM-D can be used for diagnosis, an application to a large-scale test of mathematics achievement is presented. An advantage of MLTM-D for diagnosis is that it may be more applicable to large-scale assessments with more heterogeneous items than are latent class models. Keywords:]]> Section:Theory & MethodsArticle Title:A Procedure for Dimensionality Analyses of Response Data from Various Test DesignsAuthor(s):Jinming ZhangAbstract:In some popular test designs (including computerized adaptive testing and multistage testing), many item pairs are not administered to any test takers, which may result in some complications during dimensionality analyses. In this paper, a modified DETECT index is proposed in order to perform dimensionality analyses for response data from such designs. It is proven in this paper that under certain conditions, the modified DETECT can successfully find the dimensionality-based partition of items. Furthermore, the modified DETECT index is decomposed into two parts, which can serve as indexes of the reliability of results from the DETECT procedure when response data are judged to be multidimensional. A simulation study shows that the modified DETECT can successfully recover the dimensional structure of response data under reasonable specifications. Finally, the modified DETECT procedure is applied to real response data from two-stage tests to demonstrate how to utilize these indexes and interpret their values in dimensionality analyses.Keywords:item response theory (IRT), dimensionality, multidimensional, DETECT, multistage testing, two-stage testing.]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Extracting Intrinsic Functional Networks with Feature-based Group Independent Component AnalysisAuthor(s):Vince Calhoun and Elena AllenAbstract:There is increasing use of functional imaging data to understand the macro-connectome of the human brain. Of particular interest is the structure and function of intrinsic networks (regions exhibiting temporally coherent activity both at rest and while a task is being performed), which account for a significant portion of the variance in functional MRI data. While networks are typically estimated based on the temporal similarity between regions (based on temporal correlation, clustering methods, or independent component analysis [ICA]), some recent work has suggested that these intrinsic networks can be extracted from the inter-subject covariation among highly distilled features, such as amplitude maps reflecting regions modulated by a task or even coordinates extracted from large meta analytic studies. In this paper our goal was to explicitly compare the networks obtained from a first-level ICA (ICA on the spatiotemporal functional magnetic resonance imaging (fMRI) data) to those from a second-level ICA (i.e. ICA on computed features rather than on the first-level fMRI data). Convergent results from simulations, task-fMRI data, and rest-fMRI data show that the second-level analysis is slightly noisier than the first level analysis but yields strikingly similar patterns of intrinsic networks (spatial correlations as high as 0.85 for task data and 0.65 for rest data, well above the empirical null) and also preserves the relationship of these networks with other variables such as age (for example default mode network regions tended to show decreased low frequency power for first-level analyses and decreased loading parameters for second-level analyses). In addition, the best-estimated second-level results are those which are the most strongly reflected in the input feature. In summary, the use of feature-based ICA appears to be a valid tool for extracting intrinsic networks. We believe it will become a useful and important approach in the study of the macro-connectome, particularly in the context of data fusion. Keywords:fMRI, connectivity, networks, intrinsic activity, independent component analysis, feature extraction, data fusion]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Dynamic GSCA (Generalized Structured Component Analysis) with applications to the analysis of effective connectivity in functional neuroimaging dataAuthor(s):Kwanghee Jung, Yoshio Takane, Heungsun Hwang and Todd S. WoodwardAbstract:We propose a new method of structural equation modeling (SEM) for longitudinal and time series data, named Dynamic GSCA (Generalized Structured Component Analysis). The proposed method extends the original GSCA by incorporating a multivariate autoregressive model to account for the dynamic nature of data taken over time. Dynamic GSCA also incorporates direct and modulating effects of input variables on specific latent variables and on connections between latent variables, respectively. An alternating least square (ALS) algorithm is developed for parameter estimation. An improved bootstrap method called a modified moving block bootstrap method is used to assess reliability of parameter estimates, which deals with time dependence between consecutive observations effectively. We analyze synthetic and real data to illustrate the feasibility of the proposed method. Keywords:Generalized structured component analysis (GSCA);Structural equation modeling (SEM);Longitudinal and time series data;Alternating least squares (ALS) algorithm;A modified moving block bootstrap method;Functional neuroimaging;Effective connectivity]]> Section:Theory & MethodsArticle Title:Testing Manifest Monotonicity Using Order-Constrained Statistical InferenceAuthor(s):Jesper Tijmstra, David J. Hessen, Peter G. M. van der Heijden and Klaas SijtsmaAbstract:The joint analysis of responses and response times in tests has become popular recently. Several models have been proposed for responses and response times in tests. Fewer options are available for testing the fit of such models. In this manuscript, a new approach to the analysis of model fit is proposed. The approach is based on the observed number of positive and negative responses between given time limits. Theses numbers are compared to the expected numbers implied by the model. A fit statistic can be defined as the sum of the squared residuals formed by the difference between observed and expected number of responses. It can be shown that this fit statistic is approximately chi-square distributed in case the item parameters have been determined with marginal maximum likelihood estimation. The validity and power of the test is demonstrated in a simulation study for a variant of the response time model proposed by van der Linden (2007). Keywords:item response model;response time model;fit test]]> Section:Theory & MethodsArticle Title:IMPROVED REGRESSION CALIBRATIONAuthor(s):Anders Skrondal and Jouni KuhaAbstract:The likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form which makes maximum likelihood estimation taxing. A popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation. We propose an improved regression calibration approach, a general pseudo maximum likelihood estimation method based on a conveniently decomposed form of the likelihood. It is both consistent and computationally efficient, and produces point estimates and estimated standard errors which are practically identical to those obtained by maximum likelihood. Simulations suggest that improved regression calibration, which is easy to implement in standard software, works wellKeywords:covariate measurement error, measurement model, generalized linear model, pseudo maximum likelihood estimation, regression calibration]]> Section:Theory & MethodsArticle Title:Uncovering the best skill multimap by constraining the error probabilities of the Gain-Loss ModelAuthor(s):Pasquale Anselmi, Egidio Robusto and Luca StefanuttiAbstract:The Gain-Loss Model is a probabilistic skill multimap model for assessing learning processes. In practical applications, more than one skill multimap could be plausible, while none corresponds to the true one. The article investigates whether constraining the error probabilities is a way of uncovering the best skill assignment among a number of alternatives. A simulation study shows that this approach allows the detection of the models that are closest to the correct one. An empirical application shows that it allows the detection of models that are entirely derived from plausible assumptions about the skills required for solving the problems. Keywords:knowledge space theory;knowledge structure;Gain-Loss Model;skill multimap;learning process;constrained parameter estimation]]> Section:Theory & MethodsArticle Title:The Heterogeneous P-Median Problem for Categorization Based ClusteringAuthor(s):Simon J. Blanchard, Daniel Aloise and Wayne DeSarboAbstract:The p-median offers an alternative to centroid-based clustering algorithms for identifying unobserved categories. However, existing p-median formulations typically require data aggregation into a single proximity matrix, resulting in masked respondent heterogeneity. A proposed three-way formulation of the p-median problem explicitly considers heterogeneity by identifying groups of individual respondents that perceive similar category structures. Three proposed heuristics for the heterogeneous p-median (HPM) are developed and then illustrated in a consumer psychology context using a sample of undergraduate students who performed a sorting task of major U.S. retailers, as well as through small Monte Carlo analysis. Keywords:]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Robust Structural Equation Modeling with Missing Data and Auxiliary VariablesAuthor(s):Ke-Hai Yuan and Zhiyong ZhangAbstract:The paper develops a two-stage robust procedure for structural equation modeling (SEM) and an R package rsem to facilitate the use of the procedure by applied researchers. In the first stage, M-estimates of saturated mean vector and covariance matrix of all variables are obtained. Those corresponding to the substantive variables are then fitted to the structural model in the second stage. A sandwich-type covariance matrix is used to obtain consistent standard errors (SE) of the structural parameter estimates. Rescaled, adjusted as well as corrected and F-statistics are proposed for overall model evaluation. Using R and EQS, the R package rsem combines the two stages and generates all the test statistics and consistent SEs. Following the robust analysis, multiple model fit indices and standardized solutions are in the corresponding output of EQS. An example with open/closed book examination data illustrates the proper use of the package. The method is further applied to the analysis of a data set from National Longitudinal Survey of Youth 1997 cohort, and results show that the developed procedure not only gives a better endorsement of the substantive models but also yields estimates with uniformly smaller standard errors than the normal-distribution-based maximum likelihood.Keywords:Auxiliary variables, estimating equation, missing at random, R package rsem, sandwich-type covariance matrix]]> Section:Application Reviews & Case Studies (ARCS)Article Title:Dimensionality of the latent structure and item selection via latent class multidimensional IRT modelsAuthor(s):Francesco Bartolucci, Giorgio E. Montanari and Silvia PandolfiAbstract:With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health condition of their patients, we investigate two relevant issues: dimensionality of the latent structure and discriminating power of the items composing the questionnaire. The approach is based on a multidimensional Item Response Theory model, which assumes a two-parameter logistic parametrization for the response probabilities. This model represents the health status of a patient by latent variables having a discrete distribution and, therefore, it may be seen as a constrained version of the latent class model. On the basis of the adopted model, we implement a hierarchical clustering algorithm aimed at assessing the actual number of dimensions measured by the questionnaire. These dimensions correspond to disjoint groups of items. Once the number of dimensions is selected, we also study the discriminating power of every item, so that it is possible to select the subset of these items which is able to provide an amount of information close to that of the full set. We illustrate the proposed approach on the basis of the data collected on a sample of 1051 elderly people hosted in a sample of Italian nursing homes. Keywords:EM algorithm;discriminating power;hierarchical clustering;quality of life]]> Section:Theory & MethodsArticle Title:The Infinitesimal Jackknife with Exploratory Factor AnalysisAuthor(s):Guangjian Zhang, Kristopher J Preacher and Robert I. JennrichAbstract:The infinitesimal jackknife (IJK), a nonparametric method for estimating standard errors, has been used to obtain standard error estimates in covariance structure analysis. In this article, we adapt it for obtaining standard errors for rotated factor loadings and factor correlations in exploratory factor analysis with sample correlation matrices. Both maximum likelihood estimation and ordinary least squares estimation are considered. Keywords:Exploratory Factor Analysis; Standard Error; EFA; Infinitesimal jackknife; IJK; Nonparametric standard error estimates; Model misspecification; Nonnormal data; Minimum deviance methods]]> Section:Theory & MethodsArticle Title:Optimal Designs for the Rasch ModelAuthor(s):Heinz Holling, Ulrike Grasshoff and Rainer SchwabeAbstract:In this paper, optimal designs will be derived for estimating the ability parameters of the Rasch model, when difficulty parameters are known. It is well established that a design is locally D-optimal if the ability and difficulty coincide. But locally optimal designs require that the ability parameters to be estimated are known. To attenuate this very restrictive assumption, prior knowledge on the ability parameter may be incorporated within a Bayesian approach. Several symmetric weight distributions, e. g. uniform, normal and logistic distributions will be considered. Furthermore, maximin efficient designs are developed where the minimal efficiency is maximized over a specified range of ability parameters. Keywords:optimal design;Bayesian design;maximin efficient design;item response theory;Rasch model]]> Section:Theory & MethodsArticle Title:The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses related to Skewed Item Category FunctionsAuthor(s):Dylan Molenaar, Conor V. Dolan and Paul De BoeckAbstract:The Graded Response Model (GRM; Samejima, 1969) can be derived by assuming a linear regression of a continuous variable, Z, on the trait, ?, to underlie the ordinal item scores (Takane & de Leeuw, 1987). Traditionally, a normal distribution is specified for Z implying homoscedastic error variances and a normally distributed ?. In this paper we present the Heteroscedastic GRM with Skewed Latent Trait, which extends the traditional GRM by incorporation of heteroscedastic error variances and a skew-normal latent trait. An appealing property of the extended GRM is that it includes the traditional GRM as a special case. This enables specific tests on the normality assumption of Z. We show how violations of normality in Z can lead to asymmetrical category response functions. The ability to test this normality assumption is beneficial from both a statistical and substantive perspective. In a simulation study, we show the viability of the model and investigate the specificity of the effects. We apply the model to a dataset on affect and a dataset on alexithymia. Keywords:Graded response model, Normal distribution, Heteroscedasticity, Skew-Normal distribution, Non-normality.]]> Section:Theory & MethodsArticle Title:Speed-Accuracy Response Models: Scoring Rules based on Response Time and AccuracyAuthor(s):Gunter Maris and Han L.J. Van der MaasAbstract:Starting from an explicit scoring rule for time limit tasks incorporating both response time and accuracy, and a definite trade-off between speed and accuracy, a response model is derived. Since the scoring rule is interpreted as a sufficient statistic, the model belongs to the exponential family. The various marginal and conditional distributions for response accuracy and response time are derived, and it is shown how the model parameters can be estimated. The model for response accuracy is found to be the two-parameter logistic model. It is found that the time limit determines the item discrimination, and this effect is illustrated with the Amsterdam Chess Test II. Keywords:item response theory;Response times;two-parameter logistic model;scoring rule]]> Section:Theory & MethodsArticle Title:Modeling Associations among Multivariate Longitudinal Categorical Variables in Survey Data: a Semiparametric Bayesian ApproachAuthor(s):Sylvie Tchumtchoua and Dipak K. DeyAbstract:This paper proposes a semiparametric Bayesian framework for the analysis of associations among multivariate longitudinal categorical variables in high-dimensional data settings. This type of data is frequent, especially in the social and behavioral sciences. A semiparametric hierarchical factor analysis model is developed in which the distributions of the factors are modeled nonparametrically through a dynamic hierarchical Dirichlet process prior. A Markov chain Monte Carlo algorithm is developed for fitting the model, and the methodology is exemplified through a study of the dynamics of public attitudes toward science and technology in the United States over the period 1992-2001.Keywords:Dynamic hierarchical Dirichlet process;Factor Analysis;Hierarchical factor analysis;High-dimensional data;Longitudinal categorical variables]]> Section:Theory & MethodsArticle Title:Functional Extended Redundancy AnalysisAuthor(s):Heungsun Hwang, Hye Won Suk, Jang-Han Lee and Debbie S. MoskowitzAbstract:We propose a functional version of extended redundancy analysis that examines directional relationships among several sets of multivariate variables. As in extended redundancy analysis, the proposed method posits that a weighed composite of each set of exogenous variables influences a set of endogenous variables. It further considers endogenous and/or exogenous variables functional, varying over time, space, or other continua. Computationally, the method reduces to minimizing a penalized least squares criterion through the adoption of a basis function expansion approach to approximating functions. We develop an alternating regularized least squares algorithm to minimize this criterion. We apply the proposed method to real datasets to illustrate the empirical feasibility of the proposed method. Keywords:Functional data;extended redundancy analysis;penalized least squares;alternating regularized least squares algorithm]]> Section:Theory & MethodsArticle Title:An isotonic model for ordering subjects on the basis of their sum scoresAuthor(s):Rudy LigtvoetAbstract:In practice, the sum of the item scores is often used as a basis for comparing subjects. For items that have more than two ordered score categories, only the partial credit model (PCM) and special cases of this model, imply that the subjects are stochastically ordered on the common latent variable. However, the PCM is very restrictive with respect to the constraints that it imposes on the data. In this paper, sufficient conditions for the stochastic ordering of subjects by their sum score are obtained. These conditions define the isotonic (nonparametric) PCM model. The isotonic PCM is more flexible than the PCM, which makes it useful for a wider variety of tests. Also, observable properties of the isotonic PCM are derived in the form of inequality constraints. It is shown how to obtain estimates of the score distribution under these constraints by using the Gibbs sampling algorithm. A small simulation study shows that the Bayesian p-values based on the log-likelihood ratio statistic can be used to assess the fit of the isotonic PCM to the data, where model-data fit can be taken as a justification of the use of the sum score to order subjects. Keywords:Item response theory;monotone likelihood ratio;ordinal inferences;Partial Credit Model;polytomously scored items;stochastic ordering;sum score]]> Section:Theory & MethodsArticle Title:Exploratory Bi-factor Analysis: The Oblique caseAuthor(s):Robert I. Jennrich and Peter BentlerAbstract:Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford (1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler (2011) introduced an exploratory form of bi-factor analysis that does not require one to provide an explicit bi-factor structure a priori. They use exploratory factor analysis and a bi-factor rotation criterion designed to produce a rotated loading matrix that has an approximate bi-factor structure. Among other things this can be used as an aid in finding an explicit bi-factor structure for use in a confirmatory bi-factor analysis. They considered only orthogonal rotation. The purpose of this paper is to consider oblique rotation and to compare it to orthogonal rotation. Because there are many more oblique rotations of an initial loading matrix than orthogonal rotations, one expects the oblique results to approximate a bi-factor structure better than orthogonal rotations and this is indeed the case. A surprising result arises when oblique bi-factor rotation methods are applied to ideal data. Keywords:Bi-factor rotation, general factor, group factor, gradient projection algorithms, oblique rotation, orthogonal rotation.]]> Section:Theory & MethodsArticle Title:A Multinormal Partial Credit Model for Item Factor AnalysisAuthor(s):David J. HessenAbstract:A multinormal partial credit model for factor analysis of polytomously scored items with ordered response categories is derived using an extension of the Dutch Identity (Holland, 1990). In the model, latent variables are assumed to have a multivariate normal distribution conditional on unweighted sums of item scores, which are sufficient statistics. Attention is paid to maximum likelihood estimation of item parameters, multivariate moments of latent variables, and person parameters. It is shown that the maximum likelihood estimates can be found without the use of numerical integration techniques. More general models are discussed which can be used for testing the model and it is shown how models with different numbers of latent variables can be tested against each other. In addition, multi-group extensions are proposed, which can be used for testing both measurement invariance and latent population differences. Models and procedures discussed are demonstrated in an empirical data example. Keywords:Partial Credit Model;multivariate normal distribution;Factor Analysis;multi-group model;measurement invariance.]]> description>Section:Book ReviewsArticleTitle:Review of Projection Matrices, Generalized Inverse Matrices, And Singular Value Decomposition by H. Yanai, K. Takeuchi, & Y Takane.Author(s):Jos ten BergeAbstract:Keywords:]]> Section:Book ReviewsArticleTitle:Review of Negative Binomial Regression by J. M. Hilbe.Author(s):Timothy R. JohnsonAbstract:Keywords:]]> Section:Theory & MethodsArticleTitle:Confidence Bounds and Power for the Reliability of Observational Measures on the Quality of a Social SettingAuthor(s):Yongyun Shin and Stephen RaudenbushAbstract:Social scientists are frequently interested in assessing the qualities of social settings such as classrooms, schools, neighborhoods, or day care centers. The most common procedure requires observers to rate social interactions within these settings on multiple items and then to combine the item responses to obtain a summary measure of setting quality. A key aspect of the quality of such a summary measure is its reliability. In this paper we derive a confidence interval for reliability, a test for the hypothesis that the reliability meets a minimum standard, and the power of this test against alternative hypotheses. Next, we consider the problem of using data from a preliminary field study of the measurement procedure to inform the design of a later study that will test substantive hypotheses about the correlates of setting quality. The preliminary study is typically called the "generalizability study" or "G-study" while the later, substantive study is called the "decision study" or "D-study." We show how to use data from the G study to estimate reliability, a confidence interval for the reliability, and the power of tests for the reliability of measurement produced under alternative designs for the D study. We conclude with a discussion of sample size requirements for G studies. Keywords:confidence interval;D Study;G Study;Power;Reliability;Teaching Quality]]> Section:Theory & MethodsArticleTitle:Multidimensional CAT item selection methods for domain scores and composite scores: Theory and ApplicationsAuthor(s):Lihua YaoAbstract:Multidimensional computer adaptive testing (MCAT) can provide higher precision and reliability or reduce test length when compared with unidimensional CAT or the paper and pencil test. This study compared five item selection procedures in the MCAT framework for both domain scores and overall scores through simulation by varying the structure of item pools, the population distribution of the simulees, the number of items selected, and the content area. The existing procedures such as Volume (Segall, 1996), Kullback-Leibler information (Veldkamp & van der Linden, 2002), Minimize the error variance of the linear combination (van der Linden, 1999), and Minimum Angle (Reckase, 2009) are compared to a new procedure, Minimize the variance of the composite score with the optimized weight, proposed for the first time in this study. The intent is to find an item selection procedure that yields higher precisions for both the domain and composite abilities and a higher percentage of selected items. The comparision is performed by examining the absolute bias, correlation, test reliability, and item usage. Three sets of item pools are used with the item parameters estimated from real live CAT data. Results show that Volume and Minimum Angle performed similarly, balancing informaion for all content areas, while the other three procedures performed similarly, with a high precision for both domain and overall scores when selecting items alternatively with the required number of items for each domain. The new item selection procedure has the highest percentage of item usage. Moreover, for the overall score, it produces similar or even better results compared to those from the method that selects items favoring the general dimension using the general model (Segall, 2001); the general dimension method has low precision for the domain scores. Besides the simulation study, the mathematical theory for some procedures are derived. The theories are confirmed by the simulation applications. Keywords: BMIRT, CAT, Domain scores, Kullback-Leibler, MCAT, Multidimensional Item Response Theory, Multidimensional Information, Overall scores]]> Section:Theory & MethodsArticleTitle:A composite likelihood inference in latent variable models for ordinal longitudinal responsesAuthor(s):Vassilis Vasdekis, Silvia Cagnone and Irini MoustakiAbstract:The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate ordinal items. Time-dependent latent variables are linked with an autoregressive model. Simulation results have shown estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood. Model selection criteria developed for composite likelihood estimation are used in the applications. Furthermore, lower-order residuals are used as measures-of-fit for the selected models. Keywords: composite likelihood;longitudinal;ordinal data;Latent variables;goodness-of-fit test]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:A Two-Step Bayesian Approach for Propensity Score Analysis: Simulations and Case StudyAuthor(s):David Kaplan and Jianshen ChenAbstract:A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for three methods of implementation: propensity score stratification, weighting, and optimal full matching. Three simulation studies and one case study are presented to elaborate the proposed two-step Bayesian propensity score approach. Results of the simulation studies reveal that greater precision in the propensity score equation yields better recovery of the frequentist-based treatment effect. A slight advantage is shown for the Bayesian approach in small samples. Results also reveal that greater precision around the wrong treatment effect can lead to seriously distorted results. However, greater precision around the correct treatment effect parameter yields quite good results, with slight improvement seen with greater precision in the propensity score equation. A comparison of coverage rates for the conventional frequentist approach and proposed Bayesian approach is also provided. The case study reveals that credible intervals are wider than frequentist confidence intervals when priors are non-informative. Keywords:Propensity score analysis;Bayesian inference]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:Application of a Multidimensional Nested Logit Model to Multiple-Choice TestsAuthor(s):Daniel M. Bolt, Youngsuk Suh and James A. WollackAbstract:Nested logit models have been presented as an alternative to multinomial logistic models for multiple-choice test items (Suh \& Bolt, 2010) and possess a mathematical structure that naturally lends to evaluating the incremental information provided by attending to distractor selection in scoring. One potential concern in attending to distractors is the possibility that distractor selection reflects a different trait/ability than that underlying the correct response. This paper illustrates a multidimensional extension of a nested logit item response model that can be used to evaluate such distinctions and also defines a new framework for incorporating collateral information from distractor selection when differences exist. The approach is demonstrated in application to questions faced by a university testing center over whether to incorporate distractor selection into the scoring of its multiple-choice tests. Several empirical examples are presented.Keywords:multidimensionality, multiple-choice items, item response theory]]> Section:Theory & MethodsArticleTitle:Some paradoxical results for the quadratically weighted kappaAuthor(s):Matthijs J. WarrensAbstract:The quadratically weighted kappa is the most commonly used weighted kappa statistic for summarizing interrater agreement on an ordinal scale. The paper present several properties of the quadratically weighted kappa that are paradoxical. For agreement tables with an odd number of categories n it is shown that if one of the raters uses the same base rates for categories 1 and $n$, categories 2 and n-1, and so on, then the value of quadratically weighted kappa does not depend on the value of the center cell of the agreement table. Since the center cell reflects the exact agreement of the two raters on the middle category, this result questions the applicability of the quadratically weighted kappa to agreement studies. If one wants to report a single index of agreement for an ordinal scale, it is recommended that the linearly weighted kappa instead of the quadratically weighted kappa is used. Keywords:Cohen''s kappa;Weighted kappa;Nominal agreement;Ordinal agreement;Agreement studies;Radiology;Quadratic weights.]]> Section:Theory & MethodsArticleTitle:On-line Calibration Methods in Cognitive Diagnostic Computerized Adaptive TestingAuthor(s):Ping Chen, Tao Xin, Chun Wang and Hua-Hua ChangAbstract:Item replenishing is essential for item bank maintenance in cognitive diagnostic computerized adaptive testing (CD-CAT). In regular CAT, on-line calibration is commonly used to calibrate the new items continuously. However, until now no reference is publicly available about on-line calibration for CD-CAT. Thus, this study investigates the possibility to extend some current strategies used in CAT to CD-CAT. Three representative on-line calibration methods are under investigation: Method A (Stocking, 1988), marginal maximum likelihood estimate with one EM cycle (OEM) method (Wainer & Mislevy, 1990) and marginal maximum likelihood estimate with multiple EM cycles (MEM) method (Ban, Hanson, Wang, Yi, & Harris, 2001). The objective of the current paper is to generalize these methods to the CD-CAT context under certain theoretical justifications and the new methods are denoted as CD-Method A, CD-OEM and CD-MEM, respectively. Simulation studies are conducted to compare the performance of the three methods in terms of item-parameter recovery, and the results show that all three methods are able to recover item parameters accurately and CD-Method A performs best when the items have smaller slipping and guessing parameters. This research is a starting point of introducing online calibration in CD-CAT, and further studies are proposed for investigations such as different sample sizes, cognitive diagnostic models, and attribute-hierarchical structures. Keywords: cognitive diagnostic computerized adaptive testing;on-line calibration;DINA model;independent attribute;new item]]> Section:Theory & MethodsArticleTitle:The SIMCLAS model: Simultaneous analysis of coupled binary data matrices with noise heterogeneity between and within data blocksAuthor(s):Tom Wilderjans, Eva Ceulemans and Iven Van MechelenAbstract:In many research domains different pieces of information are collected regarding the same set of objects. Each piece of information constitutes a data block, and all these (coupled) blocks have the object mode in common. When analyzing such data, an important aim is to obtain an overall picture of the structure underlying the whole set of coupled data blocks. A further challenge consists of accounting for the differences in information value that exist between and within (i.e., between the objects of a single block) data blocks. To tackle these issues, analysis techniques may be useful in which all available pieces of information are integrated and in which at the same time noise heterogeneity is taken into account. For the case of binary coupled data, however, only methods exist that go for a simultaneous analysis of all data blocks, but that do not account for noise heterogeneity. Therefore, in this paper, the SIMCLAS model, being a Hierarchical Classes model for the simultaneous analysis of coupled binary two-way matrices, is presented. In this model, noise heterogeneity between and within the data blocks is accounted for by downweighting entries from noisy blocks/objects within a block. In a simulation study it is shown (1) that the SIMCLAS technique recovers the underlying structure of coupled data to a very large extent, and (2) that the SIMCLAS technique outperforms a Hierarchical Classes technique in which all entries contribute equally to the analysis (i.e., noise homogeneity within and between blocks). The latter is also demonstrated in an application of both techniques to empirical data on categorization of semantic concepts. Keywords:data fusion;coupled data;multi-set data;noise heterogeneity;simultaneous clusterings;Hierarchical Classes Analysis;overlapping clustering;hierarchical relations;multivariate binary data]]> Section:Theory & MethodsArticleTitle:A Heterogeneous Bayesian Regression Model for Cross Sectional Data Involving a Single Observation per Response UnitAuthor(s):Duncan K.H. Fong, Peter Ebbes and Wayne DeSarboAbstract:Multiple regression is frequently used across the various social sciences to analyze cross-sectional data. However, it can often times be challenging to justify the assumption of common regression coefficients across all respondents. This manuscript presents a heterogeneous Bayesian regression model that enables the estimation of individual level regression coefficients in cross sectional data involving a single observation per response unit. A Gibbs sampling algorithm is developed to implement the proposed Bayesian methodology. A Monte Carlo simulation study is constructed to assess the performance of the proposed methodology across a number of experimental factors. We then apply the proposed method to analyze data collected from a consumer psychology study that examines the differential importance of price and quality in determining perceived value evaluations. Keywords:Bayesian estimation;Cross Sectional Analysis;Heterogeneity;Consumer Psychology.]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:Regime switching state-space models applied to psychological processes: Handling missing data and making inferencesAuthor(s):Ellen Hamaker and Raoul GrasmanAbstract:Many psychological processes are characterized by recurrent shifts between distinct regimes or states. Examples that are considered in this paper are the switches between different states associated with premenstrual syndrome, hourly fluctuations in affect during a major depressive episode, and shifts between a "hot hand'' and a "cold hand'' in a top athlete. We model these processes with the regime switching state-space model proposed by Kim (1994), which results in both maximum likelihood estimates for the model parameters and estimates of the latent variables and the discrete states of the process. However, the current algorithm cannot handle missing data, which limits its applicability to psychological data. Moreover, the performance of standard errors for the purpose of making inferences about the parameter estimates is yet unknown. In this paper we modify Kim's algorithm so it can handle missing data and we perform a simulation study to investigate its performance in (relatively) short time series in case of different kinds of missing data and in case of complete data. Finally, we apply the regime switching state-space model to the three empirical data sets described above. Keywords: Kalman filter;regime switching;state-space model;Missing data]]> Section:Theory & MethodsArticleTitle:Identification of a Semiparametric Item Response ModelAuthor(s):Michael PeressAbstract:We consider the identification of a semiparametric multidimensional fixed effects item response model. Item response models are typically estimated under parametric assumptions about the shape of the Item Characteristic Curves (ICCs), and existing results suggest difficulties in recovering the distribution of individual characteristics under nonparametric assumptions. We show that if the shape of the ICCs are unrestricted, but the shape is common across individuals and items, the individual characteristics are identified. If the shape of the ICCs are allowed to differ over items, the individual characteristics are identified in the multidimensional linear compensatory case but only identified up to a monotonic transformation in the unidimensional case. Our results suggest the development of two new semiparametric estimators for the item response model. Keywords:item response theory;Nonparametric Identification]]> Section:Theory & MethodsArticleTitle:Rotational Uniqueness Conditions Under Oblique Factor Correlation MetricAuthor(s):Carel Frederik Wilhelm PeetersAbstract:In an addendum to his seminal 1969 article Jöreskog stated two sets of conditions for rotational identification of the oblique factor solution under utilization of fixed zero elements in the factor loadings matrix (Jöreskog, 1979). These condition sets, formulated under factor correlation and factor covariance metric respectively, were claimed to be equivalent and to lead to global rotational uniqueness of the factor solution. It is shown here that the conditions for the oblique factor correlation structure need to be amended for global rotational uniqueness, and hence, that the condition sets are not equivalent in terms of unicity of the solution.Keywords:Factor analysis; Oblique rotation; Rotational uniqueness; Unrestricted factor model]]> Section:Book ReviewsArticleTitle:FITZMAURICE, G., M. DAVIDIAN, G. VERBEKE & G. MOLENBERGHS (Eds). (2008) Longitudinal Data Analysis: A Handbook of Modern Statistical Methods Boca Raton, FL: Chapman & Hall/CRC. 632 pages. US$89.95. ISBN: 978-1584886587.Author(s):Ji Hoon RyooAbstract:Keywords:]]> Section:Theory & MethodsArticleTitle:Predicting Latent Class Memberships for Subsequent AnalysisAuthor(s):Janne Petersen, Karen Bandeen-Roche, Esben Budtz-Jorgensen and Klaus LarsenAbstract:Latent Class Regression models relate covariates and latent constructs such as psychiatric disorders. Though full maximum likelihood estimation is available, estimation is often in three steps: (i) a latent class model is fitted without covariates; (ii) latent class scores are predicted; and (iii) the scores are regressed on covariates. We propose a new method for predicting class scores, that in contrast to posterior probability-based methods, yields consistent estimators of theKeywords:classification; latent class regression; Least Squares Class; three-step procedure; latent class model; latent class scores]]> Section:Theory & MethodsArticleTitle:A New Heterogeneous Multidimensional Unfolding ProcedureAuthor(s):Joonwook Park, Priyali Rajagopal and Wayne DeSarboAbstract:A variety of joint space multidimensional scaling (MDS) methods have been utilized for the spatial analysis of two or three-way dominance data involving subjects' preferences, choices, considerations, intentions, etc. so as to provide a parsimonious spatial depiction of the underlying relevant dimensions, attributes, stimuli, and/or subjects' utility structures in the same joint space representation. We demonstrate that care must be taken with respect to a key assumption in existent joint space MDS models such that all estimated dimensions are utilized by each and every subject in the sample, as this assumption can lead to serious distortions with respect to the derived joint spaces. We develop a new Bayesian dimension selection methodology for the multidimensional unfolding model which accommodates heterogeneity with respect to such dimensional utilization at the individual subject level for the analysis of two or three-way dominance data. A consumer psychology application regarding the preference for over-the-counter (OTC) analgesics is provided. We conclude by discussing the practical implications of the results, as well as directions for future research.Keywords:Multidimensional Unfolding; Dimension Selection; Bayesian Multidimensional Scaling; Consumer Psychology; Heterogeneity]]> Section:Theory & MethodsArticleTitle:On Compensation in Multidimensional Response ModelingAuthor(s):Wim van der LindenAbstract:The issue of compensation in multidimensional response modeling is addressed. We show that multidimensional response models are compensatory in their ability parameters if and only if they are monotone. In addition, a minimal set of assumptions is presented under which the MLEs of the ability parameters are also compensatory. In a recent series of articles, beginning with Hooker, Finkelman, and Schwartzman (2009) in this journal, the second type of compensation was presented as a paradoxical result for certain multidimensional response models, leading to occasional unfairness in maximum-likelihood test scoring. First, it is indicated that the compensation is not unique and holds generally for any multiparameter likelihood with monotone score functions. Second, we analyze why, in spite of its generality, the compensation may give the impression of a paradox or unfairness.Keywords:Compensatory Model; Maximum-Likelihood Estimation; Monotone Score Function; Multidimensional Response Model.]]> Section:Theory & MethodsArticleTitle:Using the criterion-predictor factor model to compute the probability of detecting prediction bias with ordinary least squares regressionAuthor(s):Steven Andrew CulpepperAbstract:The study of prediction bias is important and the last five decades includes research studies that examined whether test scores differentially predict academic or employment performance. Previous studies used ordinary least squares (OLS) to assess whether groups differ in intercepts and slopes. This study shows that OLS yields inaccurate inferences for prediction bias hypotheses. This paper builds upon the criterion-predictor factor model by demonstrating the effect of selection, measurement error, and measurement bias on prediction bias studies that use OLS. The range restricted, criterion-predictor factor model is used to compute type I error and power rates associated with using regression to assess prediction bias hypotheses. In short, OLS is not capable of testing hypotheses about group differences in latent intercepts and slopes. Additionally, a theorem is presented which shows that researchers should not employ hierarchical regression to assess intercept differences with selected samples.Keywords:Selection, Prediction bias, Measurement bias, Type I error, Power]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:Parsimonious Structural Equation Models for Repeated Measures Data, With Application to the Study of Consumer PreferencesAuthor(s):Terry Elrod, Gerald Haubl and Steven W. TippsAbstract:Recent research reflects a growing awareness of the value of using structural equation models to analyze repeated measures data. However, such data, particularly in the presence of covariates, often lead to models that either fit the data poorly, are exceedingly general and hard to interpret, or are specified in a manner that is highly data dependent. This article introduces methods for developing parsimonious models for such data. The underlying technology uses reduced-rank representations of the variances, covariances and means of observed and latent variables. The value of this approach, which may be implemented using standard structural equation modeling software, is illustrated in an application study aimed at understanding heterogeneous consumer preferences. In this application, the parsimonious representations characterize systematic relationships among consumer demographics, attitudes and preferences that would otherwise be undetected. The result is a model that is parsimonious, illuminating, and fits the data well, while keeping data dependence to a minimum.Keywords:consumer preferences; random effects; random coefficients; structural equation models; multilevel models; multilevel latent variable models; matrix approximation; singular value decomposition; LU decomposition; second-order factor analysis; reduced-rank regression; conjoint analysis]]> Section:Theory & MethodsArticleTitle:A Note on the Reliability Coefficients for Item Response Model-Based Ability EstimatesAuthor(s):Seonghoon KimAbstract:Assuming item parameters on a test are known constants, the reliability coefficient for item response theory (IRT) ability estimates is defined for a population of examinees in two different ways: as (a) the product-moment correlation between ability estimates on two parallel forms of a test and (b) the squared correlation between the true abilities and estimates. Due to the bias of IRT ability estimates, the parallel-forms reliability coefficient is not generally equal to the squared-correlation reliability coefficient. It is shown algebraically that the parallel-forms reliability coefficient is expected to be greater than the squared-correlation reliability coefficient but the difference would be negligible in a practical sense.Keywords:reliability coefficient; ability estimates; item response theory]]> Section:Theory & MethodsArticleTitle:Likelihood Based Clustering of Meta-Analytic SROC CurvesAuthor(s):Heinz Holling, Walailuck Bohning and Dankmar BoehningAbstract:Meta-analysis of diagnostic studies experience the common problem that different studies might not be comparable since they have been using a different cut-off value for the continuous or ordered categorical diagnostic test value defining different regions for which the diagnostic test is defined to be positive. Hence specificities and sensitivities arising from different studies might vary just because the underlying cut-off value had been different. To cope with the cut-off value problem interest is usually directed towards the receiver-operating-characteristic (ROC) curve which consists of pairs of sensitivities and false-positive rate (1-specificity). In the context of meta-analysis one pair represents one study and the associated diagram is called SROC curve where the S stands for "summary". In meta-analysis of diagnostic studies emphasis has traditionally been placed on modelling this SROC curve with the intention of providing a summary measure of the diagnostic accuracy by means of an estimate of the summary ROC curve. Here, we focus instead on finding sub-groups or components in the data representing different diagnostic accuracies. The paper will consider modelling SROC curves with the Lehmann family which is characterized by one parameter only. Each single study can be represented by a specific value of that parameter. Hence we focus on the distribution of these parameter estimates and suggest to model a potential heterogeneous or cluster structure by a mixture of specifically parameterized normal densities. We point out that this mixture is completely nonparametric and the associated mixture likelihood is well-defined and globally bounded. We use the theory and algorithms of nonparametric mixture likelihood estimation to identify a potential cluster structure in the diagnostic accuracies of the collection of studies to be analyzed. Several meta-analytic applications on diagnostic studies including AUDIT and AUDIT-C for detection of unhealthy alcohol use, the mini-mental state examination for cognitive disorders as well as diagnostic accuracy inspection data on metal fatique of aircraft spare parts are discussed to illustrate the methodology.Keywords:C.A.MAN, diagnostic testing, meta--analysis, sensitivity, specificity, summary receiver operating characteristic (SROC), summary statistics approach]]> Section:Theory & MethodsArticleTitle:Generalizations of paradoxical resultsAuthor(s):Pascal Jordan and Martin SpiessAbstract:ML- and Bayesian ability estimation in multidimensional item response models can lead to paradoxical results as proven by Hooker et al. (2009): Changing a correct response on one item into an incorrect response may produce a higher ability estimate in one dimension. Furthermore, the conditions under which this paradox arises are very general, and may in fact be fullfilled by many of the multidimensional scales currently in use. This paper tries to emphasize and extend the generality of the results of Hooker et al. by (1) considering the paradox in a generalized class of IRT models, (2) giving a weaker sufficient condition for the occurence of the paradox with relations to an important concept of statistical association, and by (3) providing some additional specific results for linearly compensatory models with special emphasis on the factor analysis model.Keywords:multidimensional item response theory; paradoxical results; simple structure; reverse rule functions; multidimensional graded response model; factor analysis.]]> Section:Book ReviewsArticleTitle:Measuring latent quantities.Author(s):Rod McDonaldAbstract:A distinction is proposed between measures and predictors of latent variables. The discussion addresses the consequences of the distinction for the true-score model, the linear factor model, Structural Equation Models, longitudinal and multilevel models, and item response models. A distribution-free treatment of calibration and error-of-measurement is given, and the contrasting properties of measures and predictors are examined.Keywords: calibration; standard error of measurement; regression predictors; Bayes predictors.]]> Section:Theory & MethodsArticleTitle:Functional Multiple-set Canonical Correlation AnalysisAuthor(s):Heungsun Hwang, Kwanghee Jung, Yoshio Takane and Todd S. WoodwardAbstract:We propose functional multiple-set canonical correlation analysis for exploring associations among multiple sets of functions. The proposed method includes functional canonical correlation analysis as a special case when only two sets of functions are considered. As in classical multiple-set canonical correlation analysis, computationally, the method solves a matrix eigen-analysis problem through the adoption of a basis expansion approach to approximating data and weight functions. We apply the proposed method to functional magnetic resonance imaging (fMRI) data to identify networks of neural activity that are commonly activated across subjects while carrying out a working memory task.Keywords:Functional data; multiple-set canonical correlation analysis; functional canonical correlation analysis; functional magnetic resonance imaging data.; ]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:Detecting Treatment Effects with Small Samples: The Power of Some Tests Under the Randomization ModelAuthor(s):Bryan Sean KellerAbstract:Randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid. In addition to being exact, a randomization test may also be more powerful than its parametric counterpart. This was demonstrated in a simulation study which examined the conditional power of the randomization t test, the Wilcoxon-Mann-Whitney (WMW) test, and the parametric t test. When the treatment effect was skewed, with degree of skew correlated with the size of the effect, the randomization t test was systematically more powerful than the parametric t test. The relative power of the WMW test under the skewed treatment effect condition depended on the sample size ratio.Keywords: randomization test; permutation test; Wilcoxon-Mann-Whitney test; nonparametric; exact Type I error rate; conditional power]]> Section:Theory & MethodsArticleTitle:The CLASSI-N model for the study of sequential processesAuthor(s):Eva Vande Gaer, Eva Ceulemans, Iven Van Mechelen and Peter KuppensAbstract:In many psychological research domains stimulus-response profiles are explained by conjecturing a sequential process in which some variables mediate between stimuli and responses. Charting sequential processes is often a complex task because (1) many possible mediating variables may exist, and (2) interindividual differences may occur in the relationship between these mediating variables and the response. Recently, Ceulemans and Van Mechelen (2008) addressed these challenges by developing the CLASSI model. A major drawback of CLASSI is that it requires information about the same set of stimuli for all participants (i.e., crossed data), whereas recently a number of data gathering techniques have been proposed in which the set of stimuli differs across participants, yielding nested data. Therefore we present the CLASSI-N model which extends the CLASSI model to nested data. A simulated annealing algorithm is proposed. The results of a simulation study are discussed as well as an application to data concerning depression.Keywords:sequential processes; CLASSI; individual differences; binary data; clusterwise regression; clustering]]> Section:Theory & MethodsArticleTitle:Moment testing for interaction terms in structural equation modelingAuthor(s):Ab Mooijaart and Albert SatorraAbstract:Starting with Kenny and Judd (1984) several methods have been introduced for analyzing models with interaction terms. In all these methods more information from the data than just means and covariances is required. In this paper we also use more than just first- and second-order moments, but we are aiming for a selection of the third-order moments. The key issue in this paper is to develop theoretical results that will allow practitioners to evaluate the strength of different third-order moments in assessing interaction terms of the model. The procedure we propose is based on the power of the goodness-of-fit test of a model with no interactions when the moment analysis involves a selection of the third-order moments (in addition to the means and covariances). A theorem is presented that relates the power of the goodness of fit test to a moment test (on third-order moments) that does not involve fitting a model. The main conclusion is that evaluation of the power for selection of third-order moments can easily be done by multivariate analysis of third-order moments, and thus selection of third-order moments can be computationally simple. The paper gives an illustration of the method and argues for the need of refraining from adding an excess of higher-order moments.Keywords:structural equation modeling; testing model fit; nonlinear relations; interaction terms; equivalent models; saturated model; asymptotic robustness]]> Section:Theory & MethodsArticleTitle:On the Relation Between the Linear Factor Model and the Latent Profile ModelAuthor(s):Peter Francis Halpin, Conor V. Dolan, Raoul Grasman and Paul De BoeckAbstract:The relationship between linear factor models and latent profile models is addressed within the context of maximum likelihood estimation based on the joint distribution of the manifest variables. Although the two models are well known to imply equivalent covariance decompositions, in general they do not yield equivalent estimates of the unconditional covariances. In particular, a 2-class latent profile model with Gaussian components underestimates the observed covariances but not the variances, when the data are consistent with a unidimensional Gaussian factor model. In explanation of this phenomenon we provide some results relating the unconditional covariances to the goodness of fit of the latent profile model, and to its excess multivariate kurtosis. The analysis also leads to some useful parameter restrictions related to symmetry.Keywords:linear factor model; latent profile model; maximum likelihood; Kullback-Leibler divergence; multivariate kurtosis.]]> Section:Book ReviewsArticleTitle:A.A. RUPP, J. TEMPLIN, & R.A. HENSON. Diagnostic Measurement: Theory, Methods, and ApplicationsAuthor(s):Ali Unlu and Thomas KieferAbstract:Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model. The second stage then uses mixture modeling treating the class membership as known. The proposed approach is theoretically justifiable, directly checks the conditional independence assumption, and converges much faster than the full likelihood approach when analyzing high-dimensional data. This paper also develops a new classification rule based on latent variable models. The proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease, which makes it perfect for analyzing high-throughput genomic data. Simulation studies and real data analysis demonstrate the advantages of the proposed method.Keywords:classification; finite mixture; hierarchical clustering; high-dimensional data; k-means; microarray; two-stage approach.; ]]> Section:Theory & MethodsArticleTitle:Optimization-Based Model Fitting for Latent Class and Latent Profile AnalyeseAuthor(s):Guan-Hua Huang, Su-Mei Wang and Chung-Chu HsuAbstract:Statisticians typically estimate the parameters of latent class and latent profile models using the Expectation-Maximization algorithm. This paper proposes an alternative two-stage approach to model fitting. The first stage uses the modified k-means and hierarchical clustering algorithms to identify the latent classes that best satisfy the conditional independence assumption underlying the latent variable model. The second stage then uses mixture modeling treating the class membership as known. The proposed approach is theoretically justifiable, directly checks the conditional independence assumption, and converges much faster than the full likelihood approach when analyzing high-dimensional data. This paper also develops a new classification rule based on latent variable models. The proposed classification procedure reduces the dimensionality of measured data and explicitly recognizes the heterogeneous nature of the complex disease, which makes it perfect for analyzing high-throughput genomic data. Simulation studies and real data analysis demonstrate the advantages of the proposed method.Keywords:classification; finite mixture; hierarchical clustering; high-dimensional data; k-means; microarray; two-stage approach.; ]]> Section:Theory & MethodsArticleTitle:A flexible latent trait model for response times testsAuthor(s):Jochen Ranger and Jorg-Tobias KuhnAbstract:Latent trait models for response times in tests have become popular recently. One challenge for response time modeling is the fact that the distribution of response times can differ considerably even in similar tests. In order to reduce the need for tailor-made models, a model is proposed that unifies two popular approaches to response time modeling: Proportional hazard models and the accelerated failure time model with log-normally distributed response times. This is accomplished by resorting to discrete time. The categorization of response time allows the formulation of a response time model within the framework of generalized linear models by using a flexible link function. Item parameters of the proposed model can be estimated with marginal maximum likelihood estimation. Applicability of the proposed approach is demonstrated in a simulation study and an empirical application. Additionally, means for the evaluation of model fit are suggested.Keywords:Response time; Latent trait model; Generalized linear model;]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:The Cognitive-Miser Response Model: Testing for intuitive and deliberate reasoningAuthor(s):Ulf BoeckenholtAbstract:In a number of psychological studies, answers to reasoning vignettes have been shown to be a result of both intuitive and deliberate response processes. This paper utilizes a psychometric model to separate these two response tendencies. An experimental application shows that the proposed model facilitates the analysis of dual--process item responses and the assessment of individual-difference factors as well as conditions that favor one response tendency over another one.Keywords:local item dependencies; multiple-choice items; nominal response model; marginal maximum likelihood estimation;]]> Section:Theory & MethodsArticleTitle:A Geometric Analysis of When Fixed Weighting Schemes Will Outperform Ordinary Least SquaresAuthor(s):Clintin P. Davis-StoberAbstract:Many researchers have demonstrated that fixed, exogenously chosen weights can be useful alternatives to Ordinary Least Squares (OLS) estimation within the linear model (e.g., Dawes, 1979; Einhorn \& Hogarth, 1975; Wainer, 1976). Generalizing the approach of Davis-Stober, Dana, and Budescu (2010b), I present an analytic method to determine when a choice of fixed weights will incur less mean squared error than OLS as a function of sample size, error variance, and model predictability. Geometrically, I solve for the region of population $\boldsymbol{\beta}$ that favors a choice of fixed weights over OLS. I derive closed-form upper and lower bounds on the volume of this region, giving tight bounds on the proportion of population $\boldsymbol{\beta}$ favoring a choice of fixed weights. I illustrate this methodology with several examples and provide a MATLAB (The MathWorks, 2010) programming implementation of the major results.Keywords:Improper Models; Alternative Weights; Mean Squared Error; Equal Weights; Hyper-Cylinders;]]> Section:Theory & MethodsArticleTitle:The Geometry of Enhancement in Multiple RegressionAuthor(s):Niels G. WallerAbstract:In linear multiple regression, "enhancement" is said to occur when R^2 = b'r > r'r, where b is a p × 1 vector of standardized regression coefficients and r is a p × 1 vector of correlations between a criterion y and a set of standardized regressors, x. When p = 1 then b = r and enhancement cannot occur. When p = 2, for all full-rank Rxx ? I, Rxx = E[xx'] = V ?V ' (where V ?V ' denotes the eigen decomposition of Rxx; ?1 > ?2), the set B1 := {bi : R2 = b_i'r_i = r_i'r_i; 0 < R^2 = 1} contains four vectors; the set B2 := {bi : R^2 = b'iri > r'iri; 0 < R^2 = 1;R^2?_p = r_i'r_i < R2} contains an infinite number of vectors. When p = 3 (and ?_1 > ?_2 > ... > ?_p), both sets contain an uncountably infinite number of vectors. Geometrical arguments demonstrate that B1 occurs at the intersection of two hyper-ellipsoids in R^p. Equations are provided for populating the sets B1 and B2 and for demonstrating that maximum enhancement occurs when b is collinear with the eigenvector that is associated with ?p (the smallest eigenvalue of the predictor correlation matrix). These equations are used to illustrate the logic and the underlying geometry of enhancement in population multiple regression models. The Appendix includes R code for simulating regression models that exhibit enhancement of any degree and any number of predictors.Keywords:Suppression; suppressor variable; enhancement; multiple regression]]> Section:Theory & MethodsArticleTitle:Some Results on MaxbetAuthor(s):Vartan ChoulakianAbstract:The Maxbet method is a generalized principal components analysis of a dataset, where the group structure of the variables is taken into account. Similarly, 3-block[12,13] partial Maxdiff method is a generalization of covariance analysis, where only the covariances between blocks (1,2) and (1,3) are taken into account. The aim of this paper is to give the global maximum for the 2-block Maxbet and 3-block[12,13] partial Maxdiff problems by picking the best solution from the complete solution set for the multivariate eigenvalue problem involved. To do this we generalize the characteristic polynomial of a matrix to a system of 2 characteristic polynomials, and provide the complete solution set of the latter via Sylvester resultants. Examples are provided.Keywords:Principal components analysis; centroid method; Maxbet; Maxdiff; multi-block method; Sylvester resultant; Gröbner bases; algebraic statistics.; ]]> Section:Theory & MethodsArticleTitle:The K-INDSCAL Model for Heterogeneous Three-way Dissimilarity DataAuthor(s):Maurizio Vichi and Laura BocciAbstract:A weighted Euclidean distance model for analyzing three-way dissimilarity data (stimuli by stimuli by subjects) for heterogeneous subjects is proposed. First, it is shown that INDSCAL may fail to identify a common space representative of the observed data structure in presence of heterogeneity. A new model that removes the rotational invariance of the classical multidimensional scaling problem and specifies K common homogeneous spaces is proposed. The model, called mixture INDSCAL in K classes, or briefly K-INDSCAL, still includes individual saliencies. However, the large number of parameters in K-INDSCAL may produce instability of the estimates and therefore a parsimonious model will also be discussed. The parameters of the model are estimated in a least-squares fitting context and an efficient coordinate descent algorithm is given. The usefulness of K-INDSCAL is demonstrated by both artificial and real data analyses.Keywords:Three-way dissimilarity data; INDSCAL; heterogeneous dissimilarities data; mixture of INDSCAL models]]> Section:Theory & MethodsArticleTitle:A Tabu Search Heuristic for Two-Mode BlockmodelingAuthor(s):Michael J. Brusco and Douglas SteinleyAbstract:Two-mode binary data matrices arise in a variety of social network contexts, such as the attendance or non-attendance of individuals at events, the participation or lack of participation of groups in projects, and the votes of judges on cases. A popular method for analyzing such data is two-mode blockmodeling based on structural equivalence, where the goal is to identify partitions for the row and column objects such that the clusters of the row and column objects form blocks that are either complete (all 1s) or null (all 0s) to the greatest extent possible. Multiple restarts of an object relocation heuristic that seeks to minimize the number of inconsistencies (i.e., 1s in null blocks and 0s in complete blocks) with ideal block structure is the predominant approach for tackling this problem. As an alternative, we propose a fast and effective implementation of tabu search. Computational comparisons across a set of 48 large network matrices revealed that the new tabu search heuristic always provided objective function values that were better than those of the relocation heuristic when the two methods were constrained to the same amount of computation time.Keywords:Clustering; Two-mode networks, Blockmodeling; Tabu Search; Heuristics]]> Section:Theory & MethodsArticleTitle:Exploratory bi-factor analysisAuthor(s):Robert I. Jennrich and Peter BentlerAbstract:Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger. The bi-factor model has a general factor and a number of group factors. The purpose of this paper is to introduce an exploratory form of bi-factor analysis. An advantage of using exploratory bi-factor analysis is that one need not provide a specific bi-factor model a priori. The result of an exploratory bi-factor analysis, however, can be used as an aid in defining a specific bi-factor model. Our exploratory bi-factor analysis is simply exploratory factor analysis using a bi-factor rotation criterion. This is a criterion designed to produce perfect cluster structure in all but the first column of a rotated loading matrix. Examples are given to show how exploratory bi-factor analysis can be used with ideal and real data. The relation of exploratory bi-factor analysis to the Schmid-Leiman method is discussed.Keywords:Bi-factor rotation, general factor, group factor, gradient projection algorithms, Holzinger's bi-factor method, Schmid-Leiman method.; ]]> Section:Theory & MethodsArticleTitle:Factor Analysis via Components AnalysisAuthor(s):Peter Bentler and Jan de LeeuwAbstract:Under the null hypothesis, component loadings are linear combinations of factor loadings, and vice versa. This interrelation permits defining new optimization criteria and estimation methods for exploratory factor analysis. Although this note is primarily conceptual in nature, an illustrative example and a small simulation show the methodology to be promising.Keywords:factor loadings; factor scores; component loadings; component scores]]> Section:Book ReviewsArticleTitle:G. CLAESKENS & N. L. HJORT. Model Selection and Model AveragingAuthor(s):Alex KaragrigoriouAbstract:Keywords:]]> Section:Theory & MethodsArticleTitle:Statistical Significance of the Contribution of Variables to the PCA solution: An Alternative Permutation StrategyAuthor(s):Mariëlle Linting, Bart-Jan van Os and Jacqueline MeulmanAbstract:In this paper, the statistical significance of the contribution of variables to the principal components in principal components analysis (PCA) is assessed nonparametrically by the use of permutation tests. We compare a new strategy to a strategy used in previous research consisting of permuting the columns (variables) of a data matrix independently and concurrently, thus destroying the entire correlational structure of the data. This strategy is considered appropriate for assessing the significance of the PCA solution as a whole, but is not suitable for assessing the significance of the contribution of single variables. Alternatively, we propose a strategy involving permutation of one variable at a time, while keeping the other variables fixed. We compare the two approaches in a simulation study, considering proportions of Type I and Type II error. We use two corrections for multiple testing: the Bonferroni correction and controlling the False Discovery Rate (FDR). To assess the significance of the variance-accounted-for by the variables, permuting one variable at a time, combined with FDR correction, yields the most favorable results. This optimal strategy is applied to an empirical data set, and results are compared to bootstrap confidence intervals.Keywords: Principal components analysis; PCA; statistical significance; component loadings; p-values; permutation]]> Section:Theory & MethodsArticleTitle:Biases and Standard Errors of Standardized Regression CoefficientsAuthor(s):Ke-Hai Yuan and Wai ChanAbstract:The paper obtains consistent standard errors (SE) and biases at order $O(1/n)$ for the sample standardized regression coefficients with both random and given predictors. Analytical results indicate that the formulas for SEs given in popular text books are consistent only when the population value of the regression coefficient is zero. The sample standardized regression coefficients are also biased in general, although it should not be a concern in practice when the sample size is not too small. Monte Carlo results imply that, for both standardized and unstandardized sample regression coefficients, SE estimates based on asymptotics tend to under-predict the empirical ones at smaller sample sizes.Keywords:Asymptotics; bias; consistency; Monte Carlo]]> Section:Book ReviewsArticleTitle:Mark D. Reckase (2008). Multidimensional Item Response TheoryAuthor(s):Hua-Hua ChangAbstract:Keywords:]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:A Joint Modeling Approach for Reaction Time and Accuracy in Psycholinguistic ExperimentsAuthor(s):Tom Loeys, Yves Rosseel and Kristof BatenAbstract:In the psycholinguistic literature, reaction times and accuracy can be analyzed separately using mixed (logistic) effects models with crossed random effects for item and subject. Given the potential correlation between these 2 outcomes, a joint model for the reaction time and accuracy may provide further insight. In this paper, a Bayesian hierarchical framework is proposed that allows estimation of the correlation between time intensity and difficulty at the item level, and between speed and ability at the subject level. The framework is shown to be flexible in that reaction times can follow a (log) normal or (shifted) Weibull distribution. A simulation study reveals the reduction in bias gains possible when using joint models, and an analysis of an example from a Dutch-English word recognition study illustrates the proposed method.Keywords:Joint Modeling; Bayesian estimation; Reaction Time; Psycholinguistic Experiment; ]]> Section:Theory & MethodsArticleTitle:On the Bayesian nonparametric generalization of IRT-type modelsAuthor(s):Ernesto San Martin, Alejandro Jara, Jean-Marie Rolin and Michael MouchartAbstract:We study the identification and consistency of Bayesian semiparametric IRT-type models, where the uncertainty on the abilities' distribution is modeled using a prior distribution on the space of probability measures. We show that for the semiparametric Rasch Poisson counts model, simple restrictions ensure the identification of a general distribution generating the abilities, even for a finite number of probes. For the semiparametric Rasch model, only a finite number of properties of the general abilities' distribution can be identified by a finite number of items, which are completely characterized. The full identification of the semiparametric Rasch model can be only achieved when an infinite number of items is available. The results are illustrated using simulated data.Keywords:Bayesian identification; Bayesian consistency; Rasch model; Dirichlet processes; Polya tree processes.; Rasch Poisson counts model;]]>" Section:Theory & MethodsArticleTitle:Cohen's Linearly Weighted Kappa is a Weighted Average of 2x2 Kappas.Author(s):Matthijs J. WarrensAbstract:An agreement table with n>=3 ordered categories can be collapsed into n-1 distinct 2x2 tables by combining adjacent categories. Vanbelle and Albert (2009c) showed that the components of Cohen's weighted kappa with linear weights can be obtained from these n-1 collapsed 2x2 tables. In this paper we consider several consequences of this result. One is that the weighted kappa with linear weights can be interpreted as a weighted arithmetic mean of the kappas corresponding to the 2x2 tables, where the weights are denominators of the 2x2 kappas. In addition, it is shown that similar results and interpretations hold for linearly weighted kappas for multiple raters.Keywords:Cohen's kappa; Merging categories; Linear weights; Quadratic weights; Mielke, Berry and Johnston's weighted kappa; Hubert's weighted kappa.]]> Section:Theory & MethodsArticleTitle:Three-Way Tucker-2 Component Analysis Solutions of Stimuli x Responses x Individuals Data with Simple Structure and the Fewest Core DifferencesAuthor(s):Kohei AdachiAbstract:Multivariate stimulus-response designs can be described by a three-way array of stimuli by responses by individuals. Its underlying structure can be represented by a network based on the Tucker2 component model in which stimulus components are connected with response components by means of the links that differ between individuals. For each individual such links are represented in a slice of the extended core array. For a proper understanding of these links, it is desirable that [1] the individual core slices as well as the component matrices have simple structures and [2] the differences of core slices between individuals are as few as possible. For attaining [1] and [2] we propose a method in which both the component matrices and the core slices of a Tucker2 solution are transformed simultaneously in order that the component matrices match simple target matrices and the core slices are summarized by a simple target slice. The proposed method is evaluated in a simulation study and illustrated with a three-way data array of semantic differential ratings.Keywords:three-way component analysis; stimuli x responses x individuals data; simplimax; promax; joint Procrustes analysis; Tucker2 model;]]> Section:Theory & MethodsArticleTitle:Item Selection in Multidimensional Computerized Adaptive Testing -- Gaining Information from Different AnglesAuthor(s):Chun Wang and Hua-Hua ChangAbstract:Over the past thirty years, obtaining diagnostic information from examinees' item responses has become an increasingly important feature of educational and psychological testing. The objective can be achieved by sequentially selecting multidimensional items to fit the class of latent traits being assessed, and therefore Multidimensional Computerized Adaptive Testing (MCAT) is one reasonable approach to such task. This study conducts a rigorous investigation on the relationships among four promising item selection methods: D-optimality, KL information index, continuous entropy, and mutual information. Some theoretical connections among the methods are demonstrated to show how information about the unknown vector theta can be gained from different perspectives. Two simulation studies were carried out to compare the performance of the four methods. The simulation results showed that mutual information not only improved the overall estimation accuracy but also yielded the smallest conditional mean squared error in most region of theta . In the end, the overlap rates were calculated to empirically show the similarity and difference among the four methods.Keywords:Kullback-Leibler information, Fisher information, mutual information, multidimensional computerized adaptive test, continuous entropy; ]]> Section:Theory & MethodsArticleTitle:Investigating the Performance of Alternate Regression Weights by Studying All Possible Criteria in Regression Models with a Fixed Set of PredictorsAuthor(s):Niels G. Waller and Jeff A. JonesAbstract:We describe methods for assessing all possible criteria (i.e., dependent variables) and subsets of criteria for regression models with a fixed set of predictors, $\boldsymbol{x}$ (where $\boldsymbol{x}$ is an $n\times1$ vector of independent variables). Our methods build upon the geometry of regression coefficients (hereafter called regression weights) in $n$-dimensional space. For a full-rank predictor correlation matrix, $\boldsymbol{R_{xx}}$, of order \emph{n,} and for regression models with constant $R^{2}$ (coefficient of determination), the OLS weight vectors for all possible criteria terminate on the surface of an \emph{n}-dimensional ellipsoid. The population performance of alternate regression weights---such as equal weights, correlation weights, or rounded weights---can be modeled as a function of the Cartesian coordinates of the ellipsoid. These geometrical notions can be easily extended to assess the sampling performance of alternate regression weights in models with either fixed or random predictors and for models with any value of $R^2$. To illustrate these ideas, we describe algorithms and R (R Development Core Team, 2009) code for: (1) generating points that are uniformly distributed on the surface of an\emph{ n}-dimensional ellipsoid, (2) populating the set of regression (weight) vectors that define an elliptical arc in $\mathbb{R}^{n}$, and (3) populating the set of regression vectors that have constant cosine with a target vector in $\mathbb{R}^{n}$. Each algorithm is illustrated with real data. The examples demonstrate the usefulness of studying all possible criteria when evaluating alternate regression weights in regression models with a fixed set of predictors.Keywords:Monte Carlo; multiple regression; weighting]]> ]]> ]]> ]]> ]]> ]]> ]]> ]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:Modeling Rule-Based Item GenerationAuthor(s):Hanneke Geerlings, Wim van der Linden and Cees A.W. GlasAbstract:An application of a hierarchical IRT model for items in families generated through the application of different combinations of design rules is discussed. Within the families, the items are assumed to differ only in surface features. The parameters of the model are estimated in a Bayesian framework, using a data-augmented Gibbs sampler. An obvious application of the model is computerized algorithmic item generation. Such algorithms have the potential to increase the cost-effectiveness of item generation as well as the flexibility of item administration. The model is applied to data from a non-verbal intelligence test created using design rules. In addition, results from a simulation study conducted to evaluate parameter recovery are presented.Keywords:hierarchical modeling; item generation; item response theory; Markov chain Monte Carlo method.]]> Section:Theory & MethodsArticleTitle:A Boundary Mixture Approach to Violations of Conditional IndependenceAuthor(s):Johan BraekenAbstract:Conditional independence is a fundamental principle in latent variable modeling and item response theory. Violations of this principle, commonly known as local item dependencies, are put in a test information perspective, and sharp bounds on these violations are defined. A modeling approach is proposed that makes use of a mixture representation of these boundaries to account for the local dependence problem by finding a balance between independence on the one side and absolute dependence on the other side. In contrast to alternative approaches, the nature of the proposed boundary mixture model does not necessitate a change in formulation of the typical item characteristic curves used in item response theory. This has attractive interpretational advantages and can show useful for general test construction purposes.Keywords:frechet-hoeffding bounds; local item dependencies; conditional independence; copula function]]> Section:Theory & MethodsArticleTitle:Investigating the Impact of Uncertainty About Item Parameters on Ability EstimationAuthor(s):Jinming Zhang, Minge Xie, Xiaolan Song and Ting LuAbstract:Asymptotic expansions of the maximum likelihood estimator (MLE) and weighted likelihood estimator (WLE) of an examinee’s ability are derived while item parameter estimators are treated as covariates measured with error. The asymptotic formulae present the amount of bias of the ability estimators due to the uncertainty of item parameter estimators. A numerical example is presented to illustrate how to apply the formulae to evaluate the impact of uncertainty about item parameters on ability estimation and the appropriateness of estimating ability using the regular MLE or WLE method.Keywords:bias, item response theory (IRT), measurement error, maximum likelihood estimator (MLE), weighted likelihood estimator (WLE).]]> Section:Book ReviewsArticleTitle:R. R. WILCOX. Fundamentals of Modern Statistical Methods: Substantially Improving Power and Accuracy.Author(s):Tian Siva Tian]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:A Network Approach For Evaluating Coherence in Multivariate Systems: An Application to Psychophysiological Emotion DataAuthor(s):Fushing Hsieh, Emilio Ferrer, Shu-Chun Chen, Iris Mauss, James Gross and Oliver JohnAbstract:Indefinite symmetric matrices that are estimates of positive definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a matrix to achieve positive definiteness. As a contrast to recently developed ridge procedures, the proposed method does not need variables to contain measurement errors. When minimum trace factor analysis is used to implement the theory, only correlations that are associated with Heywood cases are shrunk.Keywords:indefinite matrix; eigenvalues; minimum trace factor analysis]]> Section:Theory & MethodsArticleTitle:Positive Definiteness via Offdiagonal Scaling of a Symmetric Indefinite MatrixAuthor(s):Peter Bentler and Ke-Hai YuanAbstract:Indefinite symmetric matrices that are estimates of positive definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based methods for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a matrix to achieve positive definiteness. As a contrast to recently developed ridge procedures, the proposed method does not need variables to contain measurement errors. When minimum trace factor analysis is used to implement the theory, only correlations that are associated with Heywood cases are shrunk.Keywords:indefinite matrix; eigenvalues; minimum trace factor analysis]]> Section:Book ReviewsArticleTitle:F. MOSTELLER. The Pleasures of Statistics: The Autobiography of Frederick Mosteller.Author(s):Howard Wainer]]> Section:Theory & MethodsArticleTitle:Kullback-Leibler Information and Its Applications in Multidimensional Adaptive TestingAuthor(s):Chun Wang, Hua-Hua Chang and Keith A. BoughtonAbstract:This paper first discusses the relationship between Kullback-Leibler information (KL) and Fisher information in the context of multidimensional item response theory and is further interpreted for the two-dimensional case, from a geometric perspective. This explication should allow for a better understanding of the various item selection methods in multidimensional adaptive tests (MAT) which are based on these two information measures. The KL information index (KI) method is then discussed and two theorems are derived to quantify the relationship between KI and item parameters. Due to the fact that most of the existing item selection algorithms for MAT bear severe computational complexity, which substantially lowers the applicability of MAT, two versions of simplified KL index (SKI), built from the analytical results, are proposed to mimic the behavior of KI, while reducing the overall computational intensity.Keywords:Kullback-Leibler information; Fisher information; multidimensional adaptive testing]]> Section:Theory & MethodsArticleTitle:Sample Size Determination for Rasch Model TestsAuthor(s):Clemens DraxlerAbstract:This paper is concerned with supplementing statistical tests for the Rasch Model so that additionally to the probability of the error of the first kind (Type I probability) the probability of the error of the second kind (Type II probability) can be controlled at predetermined level by basing the test on the appropriate number of observations. An approach to determining a practically meaningful extent of model deviation is proposed and the asymptotic distribution of the Wald test is derived under the extent of model deviation one is interested in.Keywords:Rasch Model; Wald test; sample size; error of the second kind (Type II error).]]> Section:Book ReviewsArticleTitle:ROBERT W LISSITZ (Ed.). The Concept of Validity. Revisions, New Directions, and Applications.Author(s):Klaas Sijtsma]]> Section:Theory & MethodsArticleTitle:On Separable Tests, Correlated Priors and Paradoxical Results in Multidimensional Item Response TheoryAuthor(s):Giles HookerAbstract:This paper presents a study of the impact of prior structure on paradoxical results in multidimensional item response theory. Paradoxical results refer to the possibility that an incorrect response could be beneficial to an examinee. We demonstrate that when three or more ability dimensions are being used, paradoxical results can be induced by using priors in which all abilities are positively correlated where they would not occur if the abilities were modeled as being independent. In the case of separable tests, we demonstrate the mathematical causes of paradoxical results, develop a computationally feasible means to check whether they can occur in any given test and demonstrate a class of prior covariance matrices that can be guaranteed to avoid them.Keywords:multidimensional item response theory; maximum a posteriori estimate; paradoxical results; separable tests]]> Section:Theory & MethodsArticleTitle:A Bayesian Multi-Level Factor Analytic Model of Consumer Price Sensitivities Across CategoriesAuthor(s):Sri Devi Duvvuri and Thomas S. GrucaAbstract:Identifying price sensitive consumers is an important problem in marketing. We develop a Bayesian multi-level factor analytic model of the covariation among household-level price sensitivities across product categories that are substitutes. Based on a multivariate probit model of category incidence, this framework also allows the researcher to model overall price sensitivity (i.e. indicated by higher order factor scores) as a function of household-level covariates. All model parameters are estimated simultaneously to circumvent the downward bias resulting from two-stage estimation. The modeling framework is illustrated using scanner panel data from multiple categories of instant coffee.Keywords:Cross Category Analysis, Related Categories, Price Sensitivity, Multivariate Probit, Bayesian Factor Analysis, Heterogeneity, MCMC Procedures, Metropolis-Hastings Algorithm.]]> Section:Theory & MethodsArticleTitle:Bayesian Semiparametric Structural Equation Models with Latent VariablesAuthor(s):Mingan Yang and David B. DunsonAbstract:Structural equation models (SEMs) with latent variables are widely useful for sparse covariance structure modeling and for inferring relationships among latent variables. Bayesian SEMs are appealing in allowing for the incorporation of prior information and in providing exact posterior distributions of unknowns, including the latent variables. In this article, we propose a broad class of semiparametric Bayesian SEMs, which allow mixed categorical and continuous manifest variables while also allowing the latent variables to have unknown distributions. In order to include typical identi ability restrictions on the latent variable distributions, we rely on centered Dirichlet process (CDP) and CDP mixture (CDPM) models. The CDP will induce a latent class model with an unknown number of classes, while the CDPM will induce a latent trait model with unknown densities for the latent traits. A simple and e cient Markov chain Monte Carlo algorithm is developed for posterior computation, and the methods are illustrated using simulated examples, and several applications.Keywords:Dirichlet process; Factor analysis; Latent class; Latent trait; Mixture model; Nonparametric Bayes; Parameter expansion.]]> Section:Theory & MethodsArticleTitle:Modeling Noisy Data with Differential Equations using Observed and Expected MatricesAuthor(s):Pascal R. Deboeck and Steven M. BokerAbstract:Complex intraindividual variability observed in psychology may be well described using differential equations. It is difficult, however, to apply differential equation models in psychological contexts, as time series are frequently short, poorly sampled, and have large proportions of measurement and dynamic error. Furthermore, current methods for differential equation modeling usually consider data that are atypical of many psychological applications. Using embedded and observed data matrices, a statistical approach to differential equation modeling is presented. This approach appears robust to many characteristics common to psychological time series.Keywords:Intraindividual Variability, Di erential Equation Model(s)(ing), Time Series, Damped Linear Oscillator, Analytic Solution(s)]]> Section:Theory & MethodsArticleTitle:Determinants of Standard Errors of MLEs in Confirmatory Factor AnalysisAuthor(s):Ke-Hai Yuan, Ying (Alison) Cheng and Wei ZhangAbstract:This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found. Conditions under which monotonic relationships do not exist are also identified. Such functional relationships allow researchers to better understand the problem when significant factor loading estimates are expected but not obtained, and vice versa. What will affect the likelihood for Heywood cases (negative unique variance estimates) is also explicit through these relationships. Empirical findings in the literature are discussed using the obtained results.Keywords:Standard error, confirmatory factor analysis, maximum likelihood, improper solution.]]> Section:Theory & MethodsArticleTitle:New Equating Methods and Their Relationships with Levine Observed Score Linear Equating under the Kernel Equating FrameworkAuthor(s):Haiwen Chen and Paul W. HollandAbstract:In this paper, we develop a new curvilinear equating for the nonequivalent groups with anchor test (NEAT) design under the assumption of the classical test theory model, that we name curvilinear Levine observed score equating. In fact, by applying both the kernel equating framework and the mean preserving linear transformation of post-stratification equating, we obtain a family of observed score equipercentile equating functions, which also includes the classical Levine observed score linear equating and the Tucker linear equating as special cases.Keywords:NEAT design, curvilinear Levine observed score equating (CLOSE), Levine observed score linear equating (LOSLE), Tucker linear equating (TLE), kernel equating (KE), Mean preserving linear transformation (MPLT), Post-stratification equating (PSE)]]> Section:Theory & MethodsArticleTitle:HIERARCHICAL BAYES MODELS FOR RESPONSE TIME DATAAuthor(s):Peter F. Craigmile, Mario Peruggia and Patricia Van ZandtAbstract:Human response time (RT) data are widely used in experimental psychology to evaluate theories of mental processing. Typically, the data constitute the times taken by a subject to react to a succession of stimuli under varying experimental conditions. Because of the sequential nature of the experiments there are trends (due to learning, fatigue, fluctuations in attentional state, etc.) and serial dependencies in the data. The data also exhibit extreme observations that can be attributed to lapses, intrusions from outside the experiment, and errors occurring during the experiment. Any adequate analysis should account for these features and quantify them accurately. Recognizing that Bayesian hierarchical models are an excellent modeling tool, we focus on the elaboration of a realistic likelihood for the data and on a careful assessment of the quality of fit that it provides. We judge quality of fit in terms of the predictive performance of the model evaluated using predictive diagnostics. We demonstrate how simple Bayesian hierarchical models can be built for several RT sequences, differentiating between subject-specific and condition-specific effects.Keywords:Extreme observations; long tails; mixture models; reaction times; sequential dependencies; time series modeling; wavelet-based trend.]]> Section:Book ReviewsArticleTitle:Review of Applied Nonparametric Statistical Methods by SPRENT, P. & N. C. SMEETON. Author(s):Laura M. Schultz]]> Section:Book ReviewsArticleTitle:Review of Multivariable Modeling and Multivariate Analysis for the Behavioral Sciences by EVERITT, B. S. Author(s):Paul M. W. Hackett]]> Section:Theory & MethodsArticleTitle:Tests of homoscedasticity, multivariate normality, and missing completely at random for multivariate data with missing valuesAuthor(s):Mortaza Jamshidian and Siavash JalalAbstract:Test of homogeneity of covariances (or homoscedasticity) among several groups has many applications in statistical analysis. In the context of incomplete data analysis, tests of homoscedasticity among groups of cases with identical missing data patterns have been proposed to test whether data are missing completely at random (MCAR). These tests of MCAR require large sample sizes $n$ and/or large group sample sizes $n_i$, and they usually fail when applied to non-normal data. Hawkins (1981) proposed a test of multivariate normality and homoscedasticity that is an exact test for complete data when $n_i$ are small. This paper proposes a modification of this test for complete data to improve its performance, and extends its application to test of homoscedasticity and MCAR when data are multivariate normal and incomplete. Moreover, it is shown that the statistic used in the Hawkins test in conjunction with a nonparametric $k$-sample test can be used to obtain a nonparametric test of homoscedasticity that works well for both normal and non-normal data. It is explained how a combination of the proposed normal-theory Hawkins test and the nonparametric test can be employed to test for homoscedasticity, MCAR, and multivariate normality.
Simulation studies show that the newly proposed tests generally outperform their existing competitors in terms of type I error rejection rates. Also, a power study of the proposed tests indicates good power. The proposed methods use appropriate missing data imputations to impute missing data. Methods of multiple imputation are described and one of the methods is employed to confirm the result of our single imputation methods. Examples are provided where multiple imputation enables one to identify group or groups whose covariance matrices differ from the majority of other groups.Keywords:Covariance Structures; $k$-Sample Test; Missing Data; Multiple Imputation; Nonparametric Test; Structural Equations; Test of Homogeneity of Covariances.]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:Using State-Space Model with Regime Switching to Represent the Dynamics of Facial Electromyography (EMG) DataAuthor(s):Manshu Yang and Sy Miin ChowAbstract:Facial electromyography (EMG) is a useful physiological measure for detecting subtle affective changes in real time. A time series of EMG data contains bursts of electrical activity that increase in magnitude when the pertinent facial muscles are activated. Whereas previous methods for detecting EMG activation are often based on deterministic or externally imposed thresholds, we used regime-switching models to probabilistically classify each individual's time series into latent "regimes" characterized by similar error variance and dynamic patterns. We also allowed the association between EMG signals and self-reported affect ratings to vary between regimes and found that the relationship between these two markers did in fact vary over time. The potential utility of using regime-switching models to detect activation patterns in EMG data and to summarize the temporal characteristics of EMG activities is discussed.Keywords:state-space model, regime-switching, time series, electromyography]]> Section:Theory & MethodsArticleTitle:A Sandwich-Type Standard Error Estimator of SEM Models with Multivariate Time SeriesAuthor(s):Guangjian Zhang, Sy Miin Chow and Anthony OngAbstract:Structural equation models are increasingly used as a modeling tool for multivariate time series data in the social and behavioral sciences. Standard error estimators of SEM models, originally developed for independent data, require modifications to accommodate the fact that time series data are inherently dependent. In this article, we extend a sandwich-type standard error estimator of independent data to multivariate time series data. One required element of this estimator is the asymptotic covariance matrix of concurrent and lagged correlations among manifest variables, whose closed--form expression has not been presented in the literature. The performance of the adapted sandwich-type standard error estimator is evaluated using a simulation study and further illustrated using an empirical example.]]> Section:Book ReviewsArticleTitle:Review of Propensity Score Analysis: Statistical Methods and Applications by GUO, S. & M. W. FRASER. Author(s):Peter M. Steiner]]> Section:Application Reviews & Case Studies (ARCS)ArticleTitle:Multidimensional latent Markov models in a developmental study of inhibitory control and attentional flexibility in early childhoodAuthor(s):Francesco Bartolucci and Ivonne L. Solis-TrapalaAbstract:We demonstrate the use of a multidimensional extension of the latent Markov model to analyse data from studies with correlated binary responses in developmental psychology. In particular, we consider an experiment based on a battery of tests which was administered to pre-school children, at three time periods, in order to measure their inhibitory control (IC) and attentional flexibility (AF) abilities. Our model represents these abilities by two latent traits which are associated to each state of a latent Markov chain. The conditional distribution of the test outcomes given the latent process depends on these abilities through a multidimensional twoparameter logistic parameterisation. We outline an EM algorithm to conduct likelihood inference on the model parameters; we also focus on likelihood ratio testing of hypotheses on the dimensionality of the model and on the transition matrices of the latent process. Through the approach based on the proposed model, we find evidence that supports that IC and AF can be conceptualised as distinct constructs. Furthermore, we outline developmental aspects of participants' performance on these abilities based on inspection of the estimated transition matrices.Keywords:dimensionality assessment; executive function; item response theory; latent Markov model; Rasch model; two-parameter logistic parameterisation]]> Section:Book ReviewsArticleTitle:Review of The Theory and Practice of Item Response Theory by DE AYALA, R. J. Author(s):Adam E. Wyse]]> Section:Theory & MethodsArticleTitle:A Two-tier Full-information Item Factor Analysis Model with ApplicationsAuthor(s):Li CaiAbstract:A two-tier item factor analysis model is proposed. The modeling framework subsumes standard multidimensional IRT models, bifactor IRT models, and testlet response theory models as special cases. Features of the model lead to a reduction in the dimensionality of the latent variable space and consequently significant computational savings. An EM algorithm for full-information maximum marginal likelihood estimation is developed. Simulations and real data demonstrations confirm the accuracy and efficiency of the proposed methods. Three real data sets from a large-scale educational assessment, a longitudinal public health survey, and a scale development study measuring patient reported quality of life outcomes are analyzed as illustrations of the model's broad range of applicability.Keywords:Multidimensional item response theory, factor analysis, bifactor model, testlet response model, patient reported outcomes, latent variable modeling]]>