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Consequences of misspecifying the random effect distribution in a linear mixed-effects model for experimental data
Journal of the Korean Data & Information Science Society 2023;34:811-21
Published online September 30, 2023;
© 2023 Korean Data and Information Science Society.

Wooyeol Lee1

1Department of Psychology, Chungbuk National University
Correspondence to: 1 Associate professor, Department of Psychology, Chungbuk National University, Chungbuk 28644, Korea. E-mail:
Received July 5, 2023; Revised August 13, 2023; Accepted August 21, 2023.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License ( which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
This study examined the consequences of misspecifying the distribution of random effects on inferences about random and fixed effects when a linear mixed-effects model with crossed random effects is used to analyze experimental data. In a simulation study, we manipulated the type and magnitude of the variance of the participant random effects and observed the biases in the covariance matrix of the random effects and fixed effects coefficients and the detection rate of the fixed effects. The results showed that the linear mixed-effects model is robust to the distributional assumptions, as no bias was found in the estimates of the fixed effects when the distribution of the random effects was not normally distributed. In contrast, biases in the estimates of the covariance of the random effects, decreases in the precision of the standard error estimates of the fixed effects, and reductions in the power of the fixed effects were found under certain circumstances. The implications of our findings for empirical researchers were discussed.
Keywords : Distributional assumptions, experimental data, linear mixed-effects models, robustness, simulation study