Bayesian Explanatory Additive IRT Models

Patrick Mair*, Kathrin Gruber

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

In this article we extend the framework of explanatory mixed IRT models to a more general class called explanatory additive IRT models. We do this by augmenting the linear predictors in terms of smooth functions. This development offers many new modeling options such as the inclusion of nonlinear covariate effects, the specification of various temporal and spatial dependency patterns, and parameter partitioning across covariates. We use integrated nested Laplace approximation (INLA) for accurate and computationally efficient estimation of the parameters. Uninformative, weakly informative, and informative prior settings for the hyperparameters are discussed. Running time experiments and Monte Carlo parameter recovery simulations are performed in order to study the accuracy and computational efficiency of INLA when applied to the proposed explanatory additive IRT model class. Using a real-life dataset, a variety of application scenarios is explored, and the results are compared with classical maximum likelihood estimation when possible. R code is included in the supplemental materials to allow readers to fully reproduce the examples computed in the paper.

Original languageEnglish
Pages (from-to)59-87
Number of pages29
JournalBritish Journal of Mathematical and Statistical Psychology
Volume75
Issue number1
Early online date5 Jun 2021
DOIs
Publication statusPublished - Feb 2022

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