Fitting an item response theory model with random item effects across groups by a variational approximation method

Abstract

Purpose. Data from international educational assessments conducted in many countries are mostly analyzed using item response theory. The assumption that all items behave the same in all countries is often not tenable. The variability of item parameters across countries can be taken into account by assuming that the item parameters are random effects (De Jong et al. in J. Consum. Res. 34:260–278, 2007; De Jong and Steenkamp in Psychometrika 75:3–32, 2010). However, the complex latent structure of such a model, with latent variables both at the item and the person level, renders maximum likelihood estimation computationally challenging. We describe a variational estimation technique that consists of approximating the likelihood function by a computationally tractable lower bound.