Growth Curve Modeling for Nonnormal Data: A Two-Stage Robust Approach Versus a Semiparametric Bayesian Approach

Growth curve models are often used to investigate growth and change phenomena in social, behavioral, and educational sciences and are one of the fundamental tools for dealing with longitudinal data. Many studies have demonstrated that normally distributed data in practice are rather an exception, especially when data are collected longitudinally. Estimating a model without considering the nonnormality of data may lead to inefficient or even incorrect parameter estimates, or misleading statistical inferences. Therefore, robust methods become important in growth curve modeling. Among the existing robust methods, the two-stage robust approach from the frequentist perspective and the semiparametric Bayesian approach from the Bayesian perspective are promising. We propose to use these two approaches for growth curve modeling when the nonnormality is suspected. An example about the development of mathematical abilities is used to illustrate the application of the two approaches, using school children's Peabody Individual Achievement Test mathematical test scores from the National Longitudinal Survey of Youth 1997 Cohort.