The Impact of Free vs. Fixed Factor Correlations on Parameter Recovery in Multidimensional IRT Models

Authors

• Stephanie LeRoyFollow

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

ORCID

https://orcid.org/0000-0001-9098-4805

Date of Graduation

5-14-2026

Semester of Graduation

Spring

Degree Name

Doctor of Philosophy (PhD)

Department

Department of Graduate Psychology

First Advisor

Christine DeMars

Abstract

This dissertation investigated how cross-loading specification and factor-correlation treatment influence parameter recovery in multidimensional item response theory (MIRT) models. Two simulation studies extended Hosseinzadeh and Cole (2024) by examining whether freely estimating factor correlations improves recovery of item parameters, factor correlations, and latent traits. Study 1 used a compensatory multidimensional two-parameter logistic (M2PL) model with two correlated dimensions and 20 dichotomous items. Manipulated conditions included cross-loading specification (correctly specified vs. ignored), proportion of cross-loaded items, magnitude of cross-loadings, true factor correlation, and factor-correlation treatment during estimation (freely estimated vs. fixed to zero). Study 2 extended the design to a multidimensional three-parameter logistic (M3PL) model and added test length (10 vs. 50 items per factor). In both studies, 500 successful replications were retained per condition, and parameter recovery was evaluated using bias and root mean squared error (RMSE). Results showed that when cross-loadings were correctly specified, recovery of discrimination parameters and factor correlations was generally accurate. When cross-loadings were ignored, discrimination recovery worsened substantially, and freeing the factor correlation did not meaningfully reduce this error. In Study 2, the general findings from Study 1 replicated under the M3PL model and longer tests improved estimation precision but did not eliminate the effects of cross-loading misspecification. The findings indicate that accurate specification of both cross-loadings and correlations is important in applied MIRT. Freely estimating factor correlations may improve recovery in some conditions, but it is not a substitute for correctly specified cross-loading structure.