Bayesian inference with spike-and-slab priors for differential item functioning detection in a multiple-group IRT tree model

Abstract

Group differences have practical implications in analysing data from achievement tests or questionnaires. In the current study, we develop a model that accounts for between-group differences, differential item functioning (DIF), latent factors, and missing item response data simultaneously. Different from most of the present DIF studies where one has to iteratively select anchor items and detect DIF items, we achieve DIF detection and parameter estimation simultaneously by properly reparameterizing model parameters and applying some spike-and-slab priors (Ishwaran & Rao, Spike and slab variable selection: frequentist and Bayesian strategies. Ann Stat. 2005a;33:730–773; Ročková & George, The spike-and-slab LASSO. J Am Stat Assoc. 2018;113:431–444) in Bayesian estimation. Simulation studies are conducted to illustrate the validation of the proposed estimation procedure and the efficiency of DIF detection. The proposed method is further applied to a real dataset for illustration.