Evaluation of a Bayesian Approach to Estimating Nonlinear Mixed-Effects Mixture Models

Abstract

The growth mixture model has become increasingly popular, given the willingness to acknowledge developmental heterogeneity in populations. Typically, linear growth mixture models, based on polynomials or piecewise functions, are used in substantive applications and evaluated quantitatively through simulation. Growth mixture models that follow inherently nonlinear trajectories, referred to as nonlinear mixed-effects mixture models, have received comparatively little attention—likely due to estimation complexity. Previous work on the estimation of these models has involved multistep routines (Kelley, 2008), maximum likelihood estimation (MLE) via the E-M algorithm (Harring, 2005, 2012), Taylor series expansion and MLE within the structural equation modeling framework (Grimm, Ram, & Estabrook, 2010), and MLE by adaptive Gauss–Hermite quadrature (Codd & Cudeck, 2014). This article proposes and evaluates the use of Bayesian estimation with OpenBUGS (Lunn, Spiegelhalter, Thomas, & Best, 2009), a free program, and compares its performance with the Taylor series expansion approach. Finally, these estimation routines are used to evaluate the need for multiple latent classes to account for between-child differences in the development of reading ability.

Keywords:

• change
• development
• growth mixture model
• latent growth models
• longitudinal
• mixed-effects models
• nonlinear models

Notes

¹ Example plots of simulated data are available along with additional supplemental materials (e.g., programming scripts and tables) on the last author’s Web page (https://sites.google.com/site/longitudinalmethods/people/kevin-grimm/downloads).

² The Lo–Mendell–Rubin likelihood ratio test, a commonly used comparative fit index, is unavailable in Mplus when the MODEL CONSTRAINT command is used.