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Score‐based measurement invariance checks for Bayesian maximum‐a‐posteriori estimates in item response theory


Debelak, Rudolf; Pawel, Samuel; Strobl, Carolin; Merkle, Edgar C (2022). Score‐based measurement invariance checks for Bayesian maximum‐a‐posteriori estimates in item response theory. British Journal of Mathematical and Statistical Psychology, 75(3):728-752.

Abstract

A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-a-posteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be useful in practice with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

Abstract

A family of score-based tests has been proposed in recent years for assessing the invariance of model parameters in several models of item response theory (IRT). These tests were originally developed in a maximum likelihood framework. This study discusses analogous tests for Bayesian maximum-a-posteriori estimates and multiple-group IRT models. We propose two families of statistical tests, which are based on an approximation using a pooled variance method, or on a simulation approach based on asymptotic results. The resulting tests were evaluated by a simulation study, which investigated their sensitivity against differential item functioning with respect to a categorical or continuous person covariate in the two- and three-parametric logistic models. Whereas the method based on pooled variance was found to be useful in practice with maximum likelihood as well as maximum-a-posteriori estimates, the simulation-based approach was found to require large sample sizes to lead to satisfactory results.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:06 Faculty of Arts > Institute of Psychology
04 Faculty of Medicine > Epidemiology, Biostatistics and Prevention Institute (EBPI)
Dewey Decimal Classification:150 Psychology
610 Medicine & health
Scopus Subject Areas:Physical Sciences > Statistics and Probability
Social Sciences & Humanities > Arts and Humanities (miscellaneous)
Social Sciences & Humanities > General Psychology
Uncontrolled Keywords:General Psychology, Arts and Humanities (miscellaneous), General Medicine, Statistics and Probability
Language:English
Date:1 November 2022
Deposited On:29 Nov 2022 15:33
Last Modified:27 Jun 2024 01:42
Publisher:Wiley-Blackwell Publishing, Inc.
ISSN:0007-1102
OA Status:Green
Free access at:PubMed ID. An embargo period may apply.
Publisher DOI:https://doi.org/10.1111/bmsp.12275
PubMed ID:35670000
  • Content: Published Version
  • Language: English
  • Licence: Creative Commons: Attribution 4.0 International (CC BY 4.0)