Nonlinear Structured Growth Mixture Models in Mplus and OpenMx

Abstract

Growth mixture models (GMMs; B. O. Muthén & Muthén, 2000; B. O. Muthén & Shedden, 1999) are a combination of latent curve models (LCMs) and finite mixture models to examine the existence of latent classes that follow distinct developmental patterns. GMMs are often fit with linear, latent basis, multiphase, or polynomial change models because of their common use, flexibility in modeling many types of change patterns, the availability of statistical programs to fit such models, and the ease of programming. In this article, we present additional ways of modeling nonlinear change patterns with GMMs. Specifically, we show how LCMs that follow specific nonlinear functions can be extended to examine the presence of multiple latent classes using the Mplus and OpenMx computer programs. These models are fit to longitudinal reading data from the Early Childhood Longitudinal Study–Kindergarten Cohort to illustrate their use.

Notes

¹Age at assessment can vary widely over children in the ECLS-K. If age was the desired time metric, data could be collated into variables reflective of a specific number of discrete ages. For example, an age 5 variable may include anyone who was assessed between the ages of 4.75 and 5.25. Alternatively, the exact age at assessment can be used in both Mplus and OpenMx and placed into the model constraints for the factor loading pattern.

^a Latent variable covariance matrix was not positive definite.

^b Best log-likelihood was not replicated (from Mplus with multiple sets of starting values).

^c Bootstrap LRT p value may not be trustworthy.

^a Indicates value not contained with α matrix but estimated through the factor loadings.

*Indicates a significant parameter at p < .01.