Nonlinear Growth Mixture Models With Fractional Polynomials: An Illustration With Early Childhood Mathematics Ability

Ji Hoon Ryoo, Timothy R. Konold, Jeffrey D. Long, Victoria J. Molfese, Xin Zhou

Research output: Contribution to journalArticle

2 Scopus citations


Applications of growth mixture modeling have become widespread in the fields of medicine, public health, and the social sciences for modeling linear and nonlinear patterns of change in longitudinal data with presumed heterogeneity with respect to latent group membership. However, in contrast to linear approaches, there has been relatively less focus on methods for modeling nonlinear change. We introduce a nonlinear mixture modeling approach for estimating change trajectories that rely on the use of fractional polynomials within a growth mixture modeling framework. Fractional polynomials allow for more parsimonious and flexible models in comparison to conventional polynomial models. The procedures are illustrated through the use of math ability scores obtained from 499 children over a period of 3 years, with 4 measurement occasions. Techniques for identifying the best empirically derived growth mixture model solution are also described and illustrated by way of substantive example and a simulation.

Original languageEnglish (US)
Pages (from-to)897-910
Number of pages14
JournalStructural Equation Modeling
Issue number6
StatePublished - Nov 2 2017



  • early childhood mathematics achievement
  • fractional polynomials
  • growth mixture models

ASJC Scopus subject areas

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

Cite this