Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

An extension of the latent Markov Rasch model is described for the analysis of binary longitudinal data with covariates when subjects are collected in clusters, such as students clustered in classes. For each subject, a latent process is used to represent the characteristic of interest (e.g., ability) conditional on the effect of the cluster to…

Doubly bounded continuous data are common in the social and behavioral sciences. Examples include judged probabilities, confidence ratings, derived proportions such as percent time on task, and bounded scale scores. Dependent variables of this kind are often difficult to analyze using normal theory models because their distributions may be quite…