Journal of Educational and Behavioral Statistics, Ahead of Print.
Item-level count data frequently arise in cognitive, educational, and psychological assessments. Correctly handling different dispersion levels in count data is crucial for accurate statistical inference. This research proposes a Quasi-Poisson item response theory model that accommodates overdispersion, underdispersion, and equidispersion in count data, aiming to explicitly model the connection between the mean and variance parameters, providing a method that is both computationally efficient and statistically robust. This semiparametric model specifies the first two conditional moments for the count variables and derives marginal moments to estimate model parameters. Simulation studies demonstrate the Quasi-Poisson model’s efficacy in parameter recovery across different dispersion scenarios and its negligible computation time. Empirical data analysis further underscores the model’s superior fit and computational efficiency in a real-world setting.

Journal of Educational and Behavioral Statistics, Volume 50, Issue 1, Page 3-4, February 2025.

Journal of Educational and Behavioral Statistics, Volume 50, Issue 1, Page 180-182, February 2025.

Journal of Educational and Behavioral Statistics, Ahead of Print.
We study an Expectation-Maximization (EM) algorithm for estimating product-term regression models with missing data. The study of such problems in the frequentist tradition has thus far been restricted to an EM algorithm method using full numerical integration. However, under most missing data patterns, we show that this problem can be solved analytically, and numerical approximations are only needed under specific conditions. Thus we propose a hybrid EM algorithm, which uses analytic solutions when available and approximate solutions only when needed. The theoretical framework of our algorithm is described herein, along with three empirical experiments using both simulated and real data. We demonstrate that our algorithm provides greater estimation accuracy, exhibits robustness to distributional violations, and confers higher power to detect interaction effects. We conclude with a discussion of extensions and topics of further research.

Journal of Educational and Behavioral Statistics, Ahead of Print.
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 Bayesian variable selection to simultaneously estimate the effects of active and nonactive attributes, and the simulations lead to appropriate attribute recovery rates. Furthermore, the proposed method recovers the attribute mastery of individuals at the same as for a fully known Q-matrix. In addition, the proposed methods can be used to estimate the unknown Q-matrix part. A real data example indicates that the proposed Bayesian estimation method for the partially known Q-matrix fits better than a fully specified Q-matrix. Finally, extensions and future research directions are discussed.

Journal of Educational and Behavioral Statistics, Ahead of Print.
Observed-score test equating is a vital part of every testing program, aiming to make test scores across test administrations comparable. Central to this process is the equating function, typically estimated by composing distribution functions of the scores to be equated. An integral part of this estimation is presmoothing, where statistical models are fit to observed score frequencies to mitigate sampling variability. This study evaluates the impact of commonly used model fit indices on bivariate presmoothing model-selection accuracy in both item response theory (IRT) and non-IRT settings. It also introduces a new model-selection criterion that directly targets the equating function in contrast to existing methods. The study focuses on the framework of non-equivalent groups with anchor test design, estimating bivariate score distributions based on real and simulated data. Results show that the choice of presmoothing model and model fit criterion influences the equated scores. In non-IRT contexts, a combination of the proposed model-selection criterion and the Bayesian information criterion exhibited superior performance, balancing bias, and variance of the equated scores. For IRT models, high selection accuracy and minimal equating error were achieved across all scenarios.

Journal of Educational and Behavioral Statistics, Ahead of Print.
In cognitive diagnosis, attribute hierarchies are considered important structural features of cognitive diagnostic models, as they provide auxiliary information about the nature of attributes. In this article, the idea of ordering theory is applied to cognitive diagnosis, and a new approach to identify attribute hierarchy based on the attribute correlation intensity matrix is proposed. This approach attempts to identify attribute hierarchy in data with a small sample size while ensuring a high accuracy rate. The results of simulation studies and empirical data analysis show that the proposed approach can be used to identify attribute hierarchy in diagnostic tests, especially in small samples, making it worth popularizing.