This study proposes a Bayesian method for diagnostic classification models (DCMs) for a partially known Q-matrix setting between exploratory and confirmatory DCMs. This Q-matrix setting is practical and useful because test experts have pre-knowledge of the Q-matrix but cannot readily specify it completely. The proposed method employs priors for…

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response…

With this article, we propose using a Bayesian multilevel latent class (BMLC; or mixture) model for the multiple imputation of nested categorical data. Unlike recently developed methods that can only pick up associations between pairs of variables, the multilevel mixture model we propose is flexible enough to automatically deal with complex…

This article proposes a novel approach to detect differential item functioning (DIF) among dichotomously scored items. Unlike standard DIF methods that perform an item-by-item analysis, we propose the "LR lasso DIF method": logistic regression (LR) model is formulated for all item responses. The model contains item-specific intercepts,…

Empirical Bayes's (EB) estimation has become a popular procedure used to calculate teacher value added, often as a way to make imprecise estimates more reliable. In this article, we review the theory of EB estimation and use simulated and real student achievement data to study the ability of EB estimators to properly rank teachers. We compare the…

Many standardized tests are now administered via computer rather than paper-and-pencil format. In a computer-based testing environment, it is possible to record not only the test taker's response to each question (item) but also the amount of time spent by the test taker in considering and answering each item. Response times (RTs) provide…

Mixed-effects models (MEMs) and latent growth models (LGMs) are often considered interchangeable save the discipline-specific nomenclature. Software implementations of these models, however, are not interchangeable, particularly with small sample sizes. Restricted maximum likelihood estimation that mitigates small sample bias in MEMs has not been…

Imputation methods are popular for the handling of missing data in psychology. The methods generally consist of predicting missing data based on observed data, yielding a complete data set that is amiable to standard statistical analyses. In the context of Bayesian factor analysis, this article compares imputation under an unrestricted…

The purpose of this study is to compare the maximum likelihood (ML) and Bayesian estimation methods for polychoric correlation (PCC) under diverse conditions using a Monte Carlo simulation. Two new Bayesian estimates, maximum a posteriori (MAP) and expected a posteriori (EAP), are compared to ML, the classic solution, to estimate PCC. Different…

Two procedures for classifying examinees into categories, one based on the sequential probability ratio test (SPRT) and the other on sequential Bayes methodology, were compared to determine which required fewer items for classification. Results showed that the SPRT procedure requires fewer items to achieve the same accuracy level. (SLD)