The Use of Restricted Latent Class Models for Defining and Testing Nonparametric and Parametric Item Response Theory Models

Abstract

A general class of ordinal logit models is presented that specifies equality and inequality constraints on sums of conditional response probabilities. Using these constraints in latent class analysis, models are obtained that are similar to parametric and nonparametric item response models. Maximum likelihood is used to estimate these models, making their assumptions testable with likelihood-ratio statistics. Because of the intractability of the asymptotic distribution of the goodness-of-fit measure when imposing inequality constraints, parametric bootstrapping is used to obtain estimates of p values. The proposed restricted latent class models are illustrated by an example using reported adult crying behavior.