Regularized Bayesian calibration and scoring of the WD-FAB IRT model improves predictive performance over marginal maximum likelihood

Abstract

Item response theory (IRT) is the statistical paradigm underlying a dominant family of generative probabilistic models for test responses, used to quantify traits in individuals relative to target populations. The graded response model (GRM) is a particular IRT model that is used for ordered polytomous test responses. Both the development and the application of the GRM and other IRT models require statistical decisions. For formulating these models (calibration), one needs to decide on methodologies for item selection, inference, and regularization. For applying these models (test scoring), one needs to make similar decisions, often prioritizing computational tractability and/or interpretability. In many applications, such as in the Work Disability Functional Assessment Battery (WD-FAB), tractability implies approximating an individual's score distribution using estimates of mean and variance, and obtaining that score conditional on only point estimates of the calibrated model. In this manuscript, we evaluate the calibration and scoring of models under this common use-case using Bayesian cross-validation. Applied to the WD-FAB responses collected for the National Institutes of Health, we assess the predictive power of implementations of the GRM based on their ability to yield, on validation sets of respondents, estimates of latent ability with uncertainty that are most predictive of patterns of item responses. IRT models in-general have the concrete interpretation of latent abilities, combining with item parameters, to produce predictions of response patterns. Our main finding is that regularized Bayesian calibration of the GRM outperforms the prior-free empirical Bayesian procedure of maximum marginal likelihood. We also motivate the use of compactly supported priors in test scoring.