Work

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

Year: 2024

Type: article

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.

Source: Journal of Educational and Behavioral Statistics

DOI: 10.3102/10769986241283687

Authors: Mia Johanna Katharina Kornely, Maria Kateri

Institution: RWTH Aachen University

Language: English

Topic: Psychometric Methodologies and Testing

Subfield: Management Science and Operations Research

Field: Decision Sciences

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $2,500

OpenAlex ID: W4403659702

FWCI:

Cites: 13

Cited by:

Related to: 10