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A Note on Improving Variational Estimation for Multidimensional Item Response Theory

Published online by Cambridge University Press:  01 January 2025

Chenchen Ma ,
Jing Ouyang ,
Chun Wang  and
Gongjun Xu Open the ORCID record for Gongjun Xu [Opens in a new window]
Chenchen Ma
Affiliation:
University of Michigan
Jing Ouyang
Affiliation:
University of Michigan
Chun Wang*
Affiliation:
University of Washington
Gongjun Xu*
Affiliation:
University of Michigan
*
Correspondence should be made to Chun Wang, College of Education, University of Washington, 312 E Miller Hall, 2012 Skagit Lane, Seattle, WA98105, USA. Email: [email protected]
Correspondence should be made to Gongjun Xu, Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, MI 48109, USA. Email: [email protected]
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Abstract

Survey instruments and assessments are frequently used in many domains of social science. When the constructs that these assessments try to measure become multifaceted, multidimensional item response theory (MIRT) provides a unified framework and convenient statistical tool for item analysis, calibration, and scoring. However, the computational challenge of estimating MIRT models prohibits its wide use because many of the extant methods can hardly provide results in a realistic time frame when the number of dimensions, sample size, and test length are large. Instead, variational estimation methods, such as Gaussian variational expectation–maximization (GVEM) algorithm, have been recently proposed to solve the estimation challenge by providing a fast and accurate solution. However, results have shown that variational estimation methods may produce some bias on discrimination parameters during confirmatory model estimation, and this note proposes an importance-weighted version of GVEM (i.e., IW-GVEM) to correct for such bias under MIRT models. We also use the adaptive moment estimation method to update the learning rate for gradient descent automatically. Our simulations show that IW-GVEM can effectively correct bias with modest increase of computation time, compared with GVEM. The proposed method may also shed light on improving the variational estimation for other psychometrics models.

Keywords

multidimensional item response theoryGaussian variational emimportance sampling
Type
Theory & Methods
Information
Psychometrika , Volume 89 , Issue 1 , March 2024 , pp. 172 - 204
Copyright
Copyright © 2023 The Author(s), under exclusive licence to The Psychometric Society.

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