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…

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…

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…

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…

The generalized logit-linear item response model (GLLIRM) is a linearly constrained nominal categories model (NCM) that computes the scale and intercept parameters for categories as a weighted sum of basic parameters. This paper addresses the problems of the identifiability of the basic parameters and the equivalence between different GLLIRM…

With reference to a questionnaire aimed at assessing the performance of Italian nursing homes on the basis of the health conditions 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…

A Bayesian nonparametric model is introduced for score equating. It is applicable to all major equating designs, and has advantages over previous equating models. Unlike the previous models, the Bayesian model accounts for positive dependence between distributions of scores from two tests. The Bayesian model and the previous equating models are…

Eight different variable selection techniques for model-based and non-model-based clustering are evaluated across a wide range of cluster structures. It is shown that several methods have difficulties when non-informative variables (i.e., random noise) are included in the model. Furthermore, the distribution of the random noise greatly impacts the…

In a recent paper, Hessen ("Psychometrika" 70(3):497-516, 2005) introduces the class of constant latent odds-ratios models as an extension of the Rasch model for which the sum score is still the sufficient statistic for ability. In this paper the relation between both the general and the general parametric constant latent odds-ratios model and the…

A method is presented for marginal maximum likelihood estimation of the nonlinear random coefficient model when the response function has some linear parameters. This is done by writing the marginal distribution of the repeated measures as a conditional distribution of the response given the nonlinear random effects. The resulting distribution…

We propose a coefficient of agreement to assess the degree of concordance between two independent groups of raters classifying items on a nominal scale. This coefficient, defined on a population-based model, extends the classical Cohen's kappa coefficient for quantifying agreement between two raters. Weighted and intraclass versions of the…

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for…

This paper analyzes the sum score based (SSB) formulation of the Rasch model, where items and sum scores of persons are considered as factors in a logit model. After reviewing the evolution leading to the equality between their maximum likelihood estimates, the SSB model is then discussed from the point of view of pseudo-likelihood and of…

In psychological research, one often aims at explaining individual differences in S-R profiles, that is, individual differences in the responses (R) with which people react to specific stimuli (S). To this end, researchers often postulate an underlying sequential process, which boils down to the specification of a set of mediating variables (M)…

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…