This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

Recent research has shown that over-extraction of latent classes can be observed in the Bayesian estimation of the mixed Rasch model when the distribution of ability is non-normal. This study examined the effect of non-normal ability distributions on the number of latent classes in the mixed Rasch model when estimated with maximum likelihood…

General diagnostic models (GDMs) and Bayesian networks are mathematical frameworks that cover a wide variety of psychometric models. Both extend latent class models, and while GDMs also extend item response theory (IRT) models, Bayesian networks can be parameterized using discretized IRT. The purpose of this study is to examine similarities and…

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…

This study examines model selection indices for use with dichotomous mixture item response theory (IRT) models. Five indices are considered: Akaike's information coefficient (AIC), Bayesian information coefficient (BIC), deviance information coefficient (DIC), pseudo-Bayes factor (PsBF), and posterior predictive model checks (PPMC). The five…

Estimating item parameters from a two-parameter normal ogive model is considered using Gibbs sampling to simulate draws from the joint posterior distribution of ability and item parameters. The method gives marginal posterior density estimates for any parameter of interest, as illustrated using data from a 33-item mathematics placement…

The issue of test-item selection in support of decision making in adaptive testing is considered. The number of items needed to make a decision is compared for two approaches: selecting items from an item pool that are most informative at the decision point or selecting items that are most informative at the examinee's ability level. The first…