Longitudinal item response modeling and posterior predictive checking in {R} and {Stan}

Abstract

Item response theory is widely used in a variety of research fields. Among others, it is the de facto standard for test development and calibration in educational large-scale assessments. In this context, longitudinal modeling is of great importance to examine developmental trajectories in competences and identify predictors of academic success. Therefore, this paper describes various multidimensional item response models that can be used in a longitudinal setting and how to estimate change in a Bayesian framework using the statistical software Stan. Moreover, model evaluation techniques such as the widely applicable information criterion and posterior predictive checking with several discrepancy measures suited for Bayesian item response modeling are presented. Finally, an empirical application is described that examines change in mathematical competence between grades 5 and 7 for $N = 1,371$ German students using a Bayesian longitudinal item response model.

Keywords

• longitudinal
• item response model
• posterior predictive checking
• Stan
• Bayes
• R, RStan