A realistic perspective on pattern representation in growth data: comment on Bauer and Curran (2003)

D. J. Bauer and P. J. Curran (2003) cautioned that results obtained from growth mixture models may sometimes be inaccurate. The problem they addressed occurs when a growth mixture model is applied to a single, general population of individuals but findings incorrectly support the conclusion that there are 2 subpopulations. In an artificial sampling experiment, they showed that this can occur when the variables in the population have a nonnormal distribution. A realistic perspective is that although a healthy skepticism to complex statistical results is appropriate, there are no true models to discover. Consequently, the issue of model misspecification is irrelevant in practical terms. The purpose of a mathematical model is to summarize data, to formalize the dynamics of a behavioral process, and to make predictions. All of this is scientifically valuable and can be accomplished with a carefully developed model, even though the model is false.