Noncompliance to treatment assignment is widespread in randomized trials and presents challenges in causal inference. In the presence of noncompliance, the most commonly estimated effect of treatment assignment, also known as the intent-to-treat (ITT) effect, is biased. Of interest in this setting is the complier average causal effect (CACE), the…

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

Explanatory item response models (EIRMs) have been applied to investigate the effects of person covariates, item covariates, and their interactions in the fields of reading education and psycholinguistics. In practice, it is often assumed that the relationships between the covariates and the logit transformation of item response probability are…

New statistical methods are being added to the literature as a result of scientific developments each and every day. This study aims at investigating one of these, Maximum Likelihood Score Estimation with Fences (MLEF) method, in ca-MST. The results obtained from this study will contribute to both national and international literature since there…

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…

In this article, the authors suggest a profile-likelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be…

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…

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian…

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]),…

The reporting methods used in large scale assessments such as the National Assessment of Educational Progress (NAEP) rely on a "latent regression model." The first component of the model consists of a "p"-scale IRT measurement model that defines the response probabilities on a set of cognitive items in "p" scales…