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A Nonlinear Mixed Effects Model for Latent VariablesUniversity of Maryland
The nonlinear mixed effects model for continuous repeated measures data has become an increasingly popular and versatile tool for investigating nonlinear longitudinal change in observed variables. In practice, for each individual subject, multiple measurements are obtained on a single response variable over time or condition. This structure can be adapted to examine the change in latent variables rather than modeling change in manifest variables. This article considers a nonlinear mixed effects model for describing nonlinear change of a latent construct over time, where the latent construct of interest is measured by multiple indicators gathered at each measurement occasion. To accomplish this, the nonlinear mixed effects model is modified to include a measurement model that explicitly expresses the relationship of the observed variables to the latent constructs. A method for marginal maximum likelihood estimation of this model is presented and discussed. An example using education data is provided to illustrate the utility of the model.
Key Words: nonlinear regression • mixed effects model • latent variable models • latent growth curve models
This version was published on September
1, 2009 Journal of Educational and Behavioral Statistics, Vol. 34, No. 3,
293-318 (2009) 
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