Although most item response theory (IRT) applications and related methodologies involve
model fitting within a single parametric IRT (PIRT) family [eg, the Rasch (1960) model or the …

We analyze the problem of maximum likelihood estimation for Gaussian distributions that
are multivariate totally positive of order two (MTP_2). By exploiting connections to …

We discuss properties of distributions that are multivariate totally positive of order two
(MTP2) related to conditional independence. In particular, we show that any independence …

One of the goals of probabilistic inference is to decide whether an empirically observed
distribution is compatible with a candidate Bayesian network. However, Bayesian networks …

Multivariate categorical data, such as binary or multiple choice individual responses to a set
of questions, are abundant in the social sciences. These data can be recorded in a multi …

Given a set of discrete response variables, some of which are ordinal, and an arbitrary set of
discrete explanatory variables, we propose a simple matrix formulation for parameterising …

For a class of latent Markov models for discrete variables having a longitudinal structure, we
introduce an approach for formulating and testing linear hypotheses on the transition …

This chapter reviews some of the important research in nonparametric and parametric item
response theory (IRT) today, and considers some current measurement challenges in …

We study nonparametric maximum likelihood estimation for two classes of multivariate
distributions that imply strong forms of positive dependence; namely log‐supermodular …

The goodness-of-fit of the unidimensional monotone latent variable model can be assessed
using the empirical conditions of nonnegative correlations (Mokken in A theory and …