In this article, we extend Liao's test for across-group comparisons of the fixed effects from the generalized linear model to the fixed and random effects of the generalized linear mixed model (GLMM). Using as our basis the Wald statistic, we developed an asymptotic test statistic for across-group comparisons of these effects. The test can be…

Multidimensional item response theory (MIRT) models have generated increasing interest in the psychometrics literature. Efficient approaches for estimating MIRT models with dichotomous responses have been developed, but constructing an equally efficient and robust algorithm for polytomous models has received limited attention. To address this gap,…

A primary purpose of cognitive diagnosis models (CDMs) is to classify examinees based on their attribute patterns. The Q-matrix (Tatsuoka, 1985), a common component of all CDMs, specifies the relationship between the set of required dichotomous attributes and the test items. Since a Q-matrix is often developed by content-knowledge experts and can…

Second-order item response theory models have been used for assessments consisting of several domains, such as content areas. We extend the second-order model to a third-order model for assessments that include subdomains nested in domains. Using a graphical model framework, it is shown how the model does not suffer from the curse of…

It is a well-known problem in testing the fit of models to multinomial data that the full underlying contingency table will inevitably be sparse for tests of reasonable length and for realistic sample sizes. Under such conditions, full-information test statistics such as Pearson's X[superscript 2] and the likelihood ratio statistic G[superscript…

Despite the growing popularity of diagnostic classification models (e.g., Rupp, Templin, & Henson, 2010) in educational and psychological measurement, methods for testing their absolute goodness-of-fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full-information test statistics…

The article provides an overview of goodness-of-fit assessment methods for item response theory (IRT) models. It is now possible to obtain accurate "p"-values of the overall fit of the model if bivariate information statistics are used. Several alternative approaches are described. As the validity of inferences drawn on the fitted model…

A multilevel latent transition analysis (LTA) with a mixture IRT measurement model (MixIRTM) is described for investigating the effectiveness of an intervention. The addition of a MixIRTM to the multilevel LTA permits consideration of both potential heterogeneity in students' response to instructional intervention as well as a methodology for…

In this article some results are presented relating to the dimensionality of instruments containing polytomously scored as well as dichotomously scored items, concentrating on the 1992 National Assessment of Educational Progress' (NAEP) mathematics and reading assessment data and several simulated datasets. The maximum likelihood factor analytic…