The issue of measurement invariance commonly arises in factor-analytic contexts, with methods for assessment including likelihood ratio tests, Lagrange multiplier tests, and Wald tests. These tests all require advance definition of the number of groups, group membership, and offending model parameters. In this paper, we study tests of measurement…

We investigate the performance of three statistics, R [subscript 1], R [subscript 2] (Glas in "Psychometrika" 53:525-546, 1988), and M [subscript 2] (Maydeu-Olivares & Joe in "J. Am. Stat. Assoc." 100:1009-1020, 2005, "Psychometrika" 71:713-732, 2006) to assess the overall fit of a one-parameter logistic model…

Bi-factor analysis is a form of confirmatory factor analysis originally introduced by Holzinger and Swineford ("Psychometrika" 47:41-54, 1937). The bi-factor model has a general factor, a number of group factors, and an explicit bi-factor structure. Jennrich and Bentler ("Psychometrika" 76:537-549, 2011) introduced an exploratory form of bi-factor…

In some popular test designs (including computerized adaptive testing and multistage testing), many item pairs are not administered to any test takers, which may result in some complications during dimensionality analyses. In this paper, a modified DETECT index is proposed in order to perform dimensionality analyses for response data from such…

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…

This paper presents a noncompensatory latent trait model, the multicomponent latent trait model for diagnosis (MLTM-D), for cognitive diagnosis. In MLTM-D, a hierarchical relationship between components and attributes is specified to be applicable to permit diagnosis at two levels. MLTM-D is a generalization of the multicomponent latent trait…

A new class of parametric models that generalize the multivariate probit model and the errors-in-variables model is developed to model and analyze ordinal data. A general model structure is assumed to accommodate the information that is obtained via surrogate variables. A hybrid Gibbs sampler is developed to estimate the model parameters. To…

Measures of agreement are used in a wide range of behavioral, biomedical, psychosocial, and health-care related research to assess reliability of diagnostic test, psychometric properties of instrument, fidelity of psychosocial intervention, and accuracy of proxy outcome. The concordance correlation coefficient (CCC) is a popular measure of…

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…

Nested logit item response models for multiple-choice data are presented. Relative to previous models, the new models are suggested to provide a better approximation to multiple-choice items where the application of a solution strategy precedes consideration of response options. In practice, the models also accommodate collapsibility across all…

Recent advances in data recording technology have given researchers new ways of collecting on-line and continuous data for analyzing input-output systems. For example, continuous response digital interfaces are increasingly used in psychophysics. The statistical problem related to these input-output systems reduces to linking time-varying…

Methods of incorporating a ridge type of regularization into partial redundancy analysis (PRA), constrained redundancy analysis (CRA), and partial and constrained redundancy analysis (PCRA) were discussed. The usefulness of ridge estimation in reducing mean square error (MSE) has been recognized in multiple regression analysis for some time,…

It is common practice in IRT to consider items as fixed and persons as random. Both, continuous and categorical person parameters are most often random variables, whereas for items only continuous parameters are used and they are commonly of the fixed type, although exceptions occur. It is shown in the present article that random item parameters…

The Candecomp/Parafac (CP) method decomposes a three-way array into a prespecified number R of rank-1 arrays, by minimizing the sum of squares of the residual array. The practical use of CP is sometimes complicated by the occurrence of so-called degenerate sequences of solutions, in which several rank-1 arrays become highly correlated in all three…

Hierarchical classes models are quasi-order retaining Boolean decomposition models for N-way N-mode binary data. To fit these models to data, rationally started alternating least squares (or, equivalently, alternating least absolute deviations) algorithms have been proposed. Extensive simulation studies showed that these algorithms succeed quite…