Impact of Serial Correlation Misspecification with the Linear Mixed Model

Abstract

Linear mixed models are popular models for use with clustered and longitudinal data due to their ability to model variation at different levels of clustering. A Monte Carlo study was used to explore the impact of assumption violations on the bias of parameter estimates and the empirical type I error rates. Simulated conditions included in this study are: simulated serial correlation structure, fitted serial correlation structure, random effect distribution, cluster sample size, and number of measurement occasions. Results showed that the fixed effects are unbiased, but the random components tend to be overestimated and the empirical Type I error rates tend to be inflated. Implications for applied researchers were discussed.

Misspecification of the random effect structure: Implications for the linear mixed model

“…However, there was evidence of bias in the variance components and simulation conditions did explain significant variation in the average relative bias. This is similar to previous research when serial correlation was not modeled (Kwok et al, 2007;LeBeau, 2016;Murphy & Pituch, 2009). Similar to prior work, even correctly modeling the serial correlation structure tended to produce biased random components (Kwok et al, 2007;LeBeau, 2016;Murphy & Pituch, 2009).…”

“…This is similar to previous research when serial correlation was not modeled (Kwok et al, 2007;LeBeau, 2016;Murphy & Pituch, 2009). Similar to prior work, even correctly modeling the serial correlation structure tended to produce biased random components (Kwok et al, 2007;LeBeau, 2016;Murphy & Pituch, 2009). This suggests that adding serial correlation can not significantly overcome bias in the random effects when the random effect structure is misspecified.…”

“…The results showed that the relative bias for the fixed effects were not affected by any of the simulation conditions studied, including the generated or fitted serial correlation structures, random effect distribution, sample size considerations, or missing a random effect. These results are similar to other Monte Carlo studies with the linear mixed model (Ferron et al, 2002;Kasim & Raudenbush, 1998;Kwok et al, 2007;LeBeau, 2016;Maas & Hox, 2004a;Murphy & Pituch, 2009). This recommendation level likely has the fewest number of applied researchers in it.…”

Creating a Developmental Scale to Account for Heterotypic Continuity in Development: A Simulation Study

“…We used analysis of variance (ANOVA) to determine which simulation conditions explained variation in the estimated standardized linear slopes, consistent with generalizability theory (Shavelson, Webb, & Rawley, 1989). This approach has been used by prior studies (Kwok et al, 2007;LeBeau, 2016LeBeau, , 2018 and is helpful for exploring interactions among the simulation conditions. In the ANOVA model, the standardized linear slopes served as the outcome, and the simulation conditions were the predictors.…”

“…We did not model random slopes due to convergence issues resulting from small variances of the slopes across people. If there is variation in the slopes across people (i.e., the variance of the slopes across people does not equal 0 in the population), prior simulation evidence indicates that the fixed effect estimates will be unbiased (Kwok, West, & Green, 2007; LeBeau, 2016), however, the standard errors for the linear slope may be biased, resulting in inflated Type I errors (LeBeau, 2018; LeBeau, Song, & Liu, 2018). Because the primary interest in this study was the direction and magnitude of the slope estimates (rather than tests of whether the slopes differed reliably from 0), we deemed this approach satisfactory.…”