In the context of Bayesian factor analysis, it is possible to compute plausible values, which might be used as covariates or predictors or to provide individual scores for the Bayesian latent variables. Previous simulation studies ascertained the validity of mean plausible values by the mean squared difference of the mean plausible values and the…

The computerized adaptive tests (CAT) apply an adaptive process in which the items are tailored to individuals' ability scores. The multidimensional CAT (MCAT) designs differ in terms of different item selection, ability estimation, and termination methods being used. This study aims at investigating the performance of the MCAT designs used to…

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…

Bayesian alternatives to frequentist propensity score approaches have recently been proposed. However, few studies have investigated their covariate balancing properties. This article compares a recently developed two-step Bayesian propensity score approach to the frequentist approach with respect to covariate balance. The effects of different…

Simulation or game-based assessments produce outcome data and process data. In this article, some statistical models that can potentially be used to analyze data from simulation or game-based assessments are introduced. Specifically, cognitive diagnostic models that can be used to estimate latent skills from outcome data so as to scale these…

A two-step Bayesian propensity score approach is introduced that incorporates prior information in the propensity score equation and outcome equation without the problems associated with simultaneous Bayesian propensity score approaches. The corresponding variance estimators are also provided. The two-step Bayesian propensity score is provided for…

Causal inference in observational studies typically requires making comparisons between groups that are dissimilar. For instance, researchers investigating the role of a prolonged duration of breastfeeding on child outcomes may be forced to make comparisons between women with substantially different characteristics on average. In the extreme there…

In practice, the sum of the item scores is often used as a basis for comparing subjects. For items that have more than two ordered score categories, only the partial credit model (PCM) and special cases of this model imply that the subjects are stochastically ordered on the common latent variable. However, the PCM is very restrictive with respect…

In studies of change in education and numerous other fields, interest often centers on how differences in the status of individuals at the start of a period of substantive interest relate to differences in subsequent change. In this article, the authors present a fully Bayesian approach to estimating three-level Hierarchical Models in which latent…

Bayesian inference on multinomial probabilities is conducted based on data collected from the game Pass the Pigs[R]. Prior information on these probabilities is readily available from the instruction manual, and is easily incorporated in a Dirichlet prior. Posterior analysis of the scoring probabilities quantifies the discrepancy between empirical…

Explores posterior analysis in estimating factor score in a confirmatory factor analysis model with polytomous, censored or truncated data, and studies the accuracy of Bayesian estimates through simulation. Results support these Bayesian estimates for statistical inference. (SLD)

Four monte carlo simulation studies of Owen's Bayesian sequential procedure for adaptive mental testing were conducted. Whereas previous simulation studies of this procedure have concentrated on evaluating it in terms of the correlation of its test scores with simulated ability in a normal population, these four studies explored a number of…

A computerized flexilevel test was implemented and its ability estimates were compared with those of a Bayesian estimation based computerized adaptive test (CAT) as well as with known true ability estimates. Results showed that when the flexilevel test was terminated according to Lord's criterion, its ability estimates were highly and…

Monte Carlo simulation was used to investigate score bias and information characteristics of Owen's Bayesian adaptive testing strategy, and to examine possible causes of score bias. Factors investigated in three related studies included effects of item discrimination, effects of fixed vs. variable test length, and effects of an accurate prior…