A Probit Latent State IRT Model With Latent Item-Effect Variables

Abstract

Abstract. We present a probit latent state model for dichotomous items with one latent state variable for each occasion of measurement and one latent item-effect variable for each item, except for a reference item. All latent variables are well defined in terms of conditional probabilities. The model offers the possibility to include explanatory variables for the latent states as well as for the latent item-effect variables. We illustrate the model by a data example with the life satisfaction scale of the Freiburg Personality Inventory (FPI-R; Fahrenberg, Hampel, & Selg, 1984 ) assessed at three time points. Allowing for item-effect variables improves model fit considerably and enhances our knowledge about the items. In some applications, this model opens new ways to investigate differential item functioning, and in others it allows to study response styles.