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

Sarfaraz Serang, Zhiyong Zhang, Jonathan Helm, Joel S. Steele, Kevin Grimm

Research output: Contribution to journalArticle

7 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)202-215
Number of pages14
JournalStructural Equation Modeling
Volume22
Issue number2
DOIs
StatePublished - Apr 3 2015

Fingerprint

Mixed Effects
Nonlinear Effects
Mixture Model
Bayesian Approach
Growth Model
Maximum Likelihood Estimation
Maximum likelihood estimation
Taylor Series Expansion
Evaluation
evaluation
Taylor series
Adaptive Quadrature
Latent Class
Structural Equation Modeling
Evaluate
Bayesian Estimation
EM Algorithm
Trajectory
Model-based
Polynomial

Keywords

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

ASJC Scopus subject areas

  • Modeling and Simulation
  • Decision Sciences(all)
  • Economics, Econometrics and Finance(all)
  • Sociology and Political Science

Cite this

Evaluation of a Bayesian Approach to Estimating Nonlinear Mixed-Effects Mixture Models. / Serang, Sarfaraz; Zhang, Zhiyong; Helm, Jonathan; Steele, Joel S.; Grimm, Kevin.

In: Structural Equation Modeling, Vol. 22, No. 2, 03.04.2015, p. 202-215.

Research output: Contribution to journalArticle

Serang, Sarfaraz ; Zhang, Zhiyong ; Helm, Jonathan ; Steele, Joel S. ; Grimm, Kevin. / Evaluation of a Bayesian Approach to Estimating Nonlinear Mixed-Effects Mixture Models. In: Structural Equation Modeling. 2015 ; Vol. 22, No. 2. pp. 202-215.
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