Treating random effects as observed versus latent predictors: The bias–variance tradeoff in small samples

Abstract

Random effects in longitudinal multilevel models represent individuals’ deviations from population means and are indicators of individual differences. Researchers are often interested in examining how these random effects predict outcome variables that vary across individuals. This can be done via a two-step approach in which empirical Bayes (EB) estimates of the random effects are extracted and then treated as observed predictor variables in follow-up regression analyses. This approach ignores the unreliability of EB estimates, leading to underestimation of regression coefficients. As such, previous studies have recommended a multilevel structural equation modeling (ML-SEM) approach that treats random effects as latent variables. The current study uses simulation and empirical data to show that a bias–variance tradeoff exists when selecting between the two approaches. ML-SEM produces generally unbiased regression coefficient estimates but also larger standard errors, which can lead to lower power than the two-step approach. Implications of the results for model selection and alternative solutions are discussed.