Abstract:

Item response theory (IRT) is a modern measurement theory for accurately estimating individuals’ ability, and latent class analysis (LCA) is a statistical technique used to identify subtypes of individuals, which is based on statistic models. Mixture item response theory (Mixture IRT) combining LCA and IRT is able to classify the subjects as well as quantifying their traits. The concept and principle of Mixture IRT is elaborated in this paper. Besides, several common mixed models are introduced here, such as the mixed Rasch model (MRM), a mixture version of the nominal response model (mNRM) and a mixture version of the partial credit model (mPCM). Furthermore, different parameter estimation methods are described and the application traces in psychological test of Mixture IRT is evaluated from the perspectives of classifying psychological or behavioral traits, detecting differential item functioning and estimating test validity.

Key words: item response theory (IRT), latent class analysis (LCA), Mixture IRT, latent structure