In large-scale educational surveys, a latent regression model is used to compensate for the shortage of cognitive information. Conventionally, the covariates in the latent regression model are principal components extracted from background data. This operational method has several important disadvantages, such as the handling of missing data and…

This article describes an exploration of the distinction between typological and factorial latent variables in the domain of personality theory. Traditionally, many personality variables have been considered to be factorial in nature, even though there are examples of typological constructs dating back to Hippocrates. Recently, some…

Multidimensional item response models can be based on multivariate normal ability distributions or on multivariate polytomous ability distributions. For the case of simple structure in which each item corresponds to a unique dimension of the ability vector, some applications of the two-parameter logistic model to empirical data are employed to…

This paper introduces multilevel extensions for the general diagnostic model (GDM) following recent developments on extensions of latent class analysis (LCA) to hierarchical models. The GDM is based on LCA as well as discrete latent trait models and may be viewed as a general modeling framework for conrmatory multidimensional item response models.…

Probabilistic models with more than one latent variable are designed to report profiles of skills or cognitive attributes. Testing programs want to offer additional information beyond what a single test score can provide using these skill profiles. Many recent approaches to skill profile models are limited to dichotomous data and have made use of…