A Note on the Asymptotic Posterior Normality of Multivariate Latent Traits in an IRT Model for Polytomous Items of Mixed Format

Abstract

The asymptotic posterior normality (APN) of the latent vector in an item response theory model is an important argument in modeling and inference. For a single latent trait, Chang and Stout proved its APN for binary items under general conditions, which generalized Chang for polytomous data and Kornely and Kateri for multivariate latent traits (MLT) and binary items. As MLT and polytomous items are nowadays common in psychometry, an APN-theory covering both simultaneously remains an open and ongoing problem. We generalize the APN-theory accordingly, providing thus a broader foundation for developments relying on APN. We also prove consistency of common estimators for the MLT, extending the according results of Chang and Kornely and Kateri.