Spearman's factor-analytic model has been proposed as a unidimensional linear item response theory (IRT) model for continuous item responses. This article first proposes a reexpression of the model that leads to a form similar to that of standard IRT models for binary responses and discusses the item indices of difficulty discrimination and…

This study linked nonlinear profile analysis (NPA) of dichotomous responses with an existing family of item response theory models and generalized latent variable models (GLVM). The NPA method offers several benefits over previous internal profile analysis methods: (a) NPA is estimated with maximum likelihood in a GLVM framework rather than…

A loglinear item response theory (IRT) model is proposed that relates polytomously scored item responses to a multidimensional latent space. The analyst may specify a response function for each response, and each item may have a different number of response categories. Conditional maximum likelihood estimates are derived. (SLD)

Formula score theory (FST) associates each multiple choice test with a linear operator and expresses all of the real functions of item response theory as linear combinations of the operator's eigenfunctions. Hard measurement problems can then often be reformulated as easier, standard mathematical problems. For example, the problem of estimating…

A loglinear item response theory (IRT) model is proposed that relates polytomously scored item responses to a multidimensional latent space. Each item may have a different response function where each item response may be explained by one or more latent traits. Item response functions may follow a partial credit model (D. Andrich, 1978; and G. N.…