This article proposes a class of cognitive diagnosis models (CDMs) for polytomously scored items with different link functions. Many existing polytomous CDMs can be considered as special cases of the proposed class of polytomous CDMs. Simulation studies were carried out to investigate the feasibility of the proposed CDMs and the performance of…

There has been increasing interest in exploring heterogeneous treatment effects using machine learning (ML) methods such as causal forests, Bayesian additive regression trees, and targeted maximum likelihood estimation. However, there is little work on applying these methods to estimate treatment effects in latent classes defined by…

When nonrandom treatments occur across sites, within-site matching (WM) is often desirable. This approach, however, can significantly reduce treatment group sample size and exclude substantively important subgroups. To limit these drawbacks, we extend a matching approach developed by Stuart and Rubin to a multisite study. We demonstrate the…

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…

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…

In longitudinal education studies, assuming that dropout and missing data occur completely at random is often unrealistic. When the probability of dropout depends on covariates and observed responses (called "missing at random" [MAR]), or on values of responses that are missing (called "informative" or "not missing at random" [NMAR]),…

There has been considerable interest in nonlinear latent variable models specifying interaction between latent variables. Although it seems to be only slightly more complex than linear regression without the interaction, the model that includes a product of latent variables cannot be estimated by maximum likelihood assuming normality.…

To find population proficiency distributions, a two-level hierarchical linear model may be applied to large-scale survey assessments such as the National Assessment of Educational Progress (NAEP). The model and parameter estimation are developed and a simulation was carried out to evaluate parameter recovery. Subsequently, both a hierarchical and…

In this article, a heterogeneous latent growth curve model for modeling heterogeneity of growth rates is proposed. The suggested model is an extension of a conventional growth curve model and a complementary tool to mixed growth modeling. It allows the modeling of heterogeneity of growth rates as a continuous function of latent initial status and…