A new test for detecting specification errors in Gaussian linear mixed-effects models

Linear mixed-effects models (LMEMs) are widely used in medical, engineering, and social applications. The accurate specification of the covariance matrix structure within the error term is known to impact the estimation and inference procedures. Thus, it is crucial to detect the source of errors in LMEMs specifications. In this study, we propose combining a user-friendly computational test with an analytical method to visualize the source of errors. Through statistical simulations under different scenarios, we evaluate the performance of the proposed test in terms of the Power and Type I error rate. Our findings indicate that as the sample size $n$ increases, the proposed test effectively detects misspecification in the systematic component, the number of random effects, the within-subject covariance structure, and the covariance structure of the error term in the LMEM with high Power while maintaining the nominal Type I error rate. Finally, we show the practical usefulness of our proposed test with a real-world application.