We propose the use of the latent change and latent acceleration frameworks for modeling nonlinear growth in structural equation models. Moving to these frameworks allows for the direct identification of rates of change and acceleration in latent growth curves-information available indirectly through traditional growth curve models when change patterns are nonlinear with respect to time. To illustrate this approach, exponential growth models in the three frameworks are fit to longitudinal response time data from the Math Skills Development Project (Mazzocco & Meyers, 2002, 2003). We highlight the additional information gained from fitting growth curves in these frameworks as well as limitations and extensions of these approaches.
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The authors would like to thank Jack McArdle, John Nesselroade, Nilam Ram, and Jonathan Helm for their helpful comments. Kevin J. Grimm was supported by a National Science Foundation REESE Program Grant DRL-0815787 and the National Center for Research in Early Childhood Education, Institute of Education Sciences, US Department of Education (R305A06021). Michèle Mazzocco was supported by National Institutes of Health award R01-HD34061-01-09. The opinions expressed are those of the authors and do not represent views of the US Department of Education.
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