Time-specific Errors in Growth Curve Modeling: Type-1 Error Inflation and a Possible Solution with Mixed-Effects Models

Growth curve modeling (GCM) has been one of the most popular statistical methods to examine participants' growth trajectories using longitudinal data. In spite of the popularity of GCM, little attention has been paid to the possible influence of time-specific errors, which influence all participants at each timepoint. In this article, we demonstrate that the failure to take into account such time-specific errors in GCM produces considerable inflation of type-1 error rates in statistical tests of fixed effects (e.g., coefficients for the linear and quadratic terms). We propose a GCM that appropriately incorporates time-specific errors using mixed-effects models to address the problem. We also provide an applied example to illustrate that GCM with and without time-specific errors would lead to different substantive conclusions about the true growth trajectories. Comparisons with other models in longitudinal data analysis and potential issues of model misspecification are discussed.