Nonlinear Growth Models in Mplus and SAS

Abstract

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.

Notes

¹In version 4.0 and more recent versions of Mplus the phantom variable could be specified without a manifest variable, such as

phantom BY;

In version 5.0, the parameters of the nonlinear equations can simply be added in the MODEL CONSTRAINT command. Therefore creating phantom variables is unnecessary. This addition of parameters can be programmed as

MODEL CONSTRAINT:

NEW(alpha∗.5 lambda∗5);

∗ p < .05.

∗p < .05.

²Available on request from Michael Browne, Department of Psychology, Ohio State University, Columbus, OH 43210-1222.

³Growth models with individually varying measurement occasions can be fit in Mplus using the multilevel (TYPE = TWOLEVEL RANDOM) or TSCORES with the AT option. However, these options can only be used to fit polynomial (e.g., linear, quadratic, cubic) growth models. The multilevel option can fit growth models in a similar manner as linear multilevel modeling software (e.g., PROC MIXED) with data in the long format.