Nonlinear Growth Models in Mplus and SAS

Nonlinear growth curves or growth curves that follow a specified nonlinear function in time enable researchers to model complex developmental patterns with parameters that are easily interpretable. In this article we describe how a variety of sigmoid curves can be fit using the Mplus structural modeling program and the nonlinear mixed-effects modeling procedure NLMIXED in SAS. Using longitudinal achievement data, collected as part of a study examining the effects of preschool instruction on academic gain, we illustrate the procedures for fitting growth models of logistic, Gompertz, and Richards functions. Brief notes regarding the practical benefits, limitations, and choices faced in the fitting and estimation of such models are included.