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Correction for Item Response Theory Latent Trait Measurement Error in Linear Mixed Effects Models

Published online by Cambridge University Press:  01 January 2025

Chun Wang Open the ORCID record for Chun Wang [Opens in a new window] ,
Gongjun Xu  and
Xue Zhang
Chun Wang*
Affiliation:
University of Washington
Gongjun Xu
Affiliation:
University of Michigan
Xue Zhang
Affiliation:
Northeast Normal University
*
Correspondence should be made to Chun Wang, Measurement and Statistics, College of Education, University of Washington, 312E Miller Hall, Box 353600, Seattle, WA 98195-3600, USA. Email: wang4066@uw.edu
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Abstract

When latent variables are used as outcomes in regression analysis, a common approach that is used to solve the ignored measurement error issue is to take a multilevel perspective on item response modeling (IRT). Although recent computational advancement allows efficient and accurate estimation of multilevel IRT models, we argue that a two-stage divide-and-conquer strategy still has its unique advantages. Within the two-stage framework, three methods that take into account heteroscedastic measurement errors of the dependent variable in stage II analysis are introduced; they are the closed-form marginal MLE, the expectation maximization algorithm, and the moment estimation method. They are compared to the naïve two-stage estimation and the one-stage MCMC estimation. A simulation study is conducted to compare the five methods in terms of model parameter recovery and their standard error estimation. The pros and cons of each method are also discussed to provide guidelines for practitioners. Finally, a real data example is given to illustrate the applications of various methods using the National Educational Longitudinal Survey data (NELS 88).

Keywords

item response theorymeasurement errormarginal maximum likelihood estimationexpectation–maximization estimationtwo-stage estimation

Information

Type
Original Research
Information
Psychometrika , Volume 84 , Issue 3 , September 2019 , pp. 673 - 700
Copyright
Copyright © 2019 The Psychometric Society

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