Information about forthcoming Psychometrika manuscripts http://www.psychometricsociety.org/journal/submissions/accepted.html 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]]>