Models of Nonlinear Growth
Methods of Research
Statistical Methods
Patrick Coulombe,
James P. Selig,
Patrick Coulombe
University of New Mexico, Albuquerque, New Mexico, USA
Search for more papers by this authorJames P. Selig
University of New Mexico, Albuquerque, New Mexico, USA
Search for more papers by this authorPatrick Coulombe,
James P. Selig,
Patrick Coulombe
University of New Mexico, Albuquerque, New Mexico, USA
Search for more papers by this authorJames P. Selig
University of New Mexico, Albuquerque, New Mexico, USA
Search for more papers by this authorFirst published: 15 May 2015
Abstract
Models for nonlinear growth are not new, but have not been widely applied in the social and behavioral sciences. In this essay, we describe the fundamental issues relevant to choosing and using a nonlinear growth model. We discuss how researchers can go about choosing a model and then focus on the application of two specific nonlinear models: the fractional polynomial model and the piecewise model. We highlight recent work in reparameterization that allows researchers to choose models with parameters tailored specifically to research questions. We also review recent work on the topic of growth rates in nonlinear models that will allow researchers to obtain richer information from the application of nonlinear models. We conclude by pointing out some of the unresolved issues in the use of nonlinear growth models.
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Further Reading
- Cudeck, R., & Harring, J. R. (2007). Analysis of nonlinear patterns of change with random coefficient models. Annual Review of Psychology, 58, 615–637.
- Grimm, K. J., & Ram, N. (2009). Nonlinear growth models in Mplus and SAS. Structural Equation Modeling, 16, 676–701.
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Kamata, A., Nese, J. F., Patarapichayatham, C., & Lai, C. F. (2012). Modeling nonlinear growth with three data points: Illustration with benchmarking data. Assessment for Effective Intervention, 38, 105–116.
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- Long, J., & Ryoo, J. (2010). Using fractional polynomials to model non-linear trends in longitudinal data. British Journal of Mathematical and Statistical Psychology, 63(1), 177–203.
- Preacher, K. J., & Hancock, G. R. (in press). On interpretable reparameterizations of linear and nonlinear latent growth curve models. In J. R. Harring, & G. R. Hancock, Advances in longitudinal methods in the social and behavioral sciences (pp. 25–58). Charlotte, NC: Information Age Publishing.
- Ram, N., & Grimm, K. (2007). Using simple and complex growth models to articulate developmental change: Matching theory to method. International Journal of Behavioral Development, 31, 303–316.
- Zhang, Z., McArdle, J. J., & Nesselroade, J. R. (2012). Growth rate models: Emphasizing growth rate analysis through growth curve modeling. Journal of Applied Statistics, 39, 1241–1262.
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