A Nonlinear Mixed Effects Model for Latent Variables

• Published in: Journal of educational and behavioral statistics Vol. 34; no. 3; pp. 293 - 318
• Main Author: Harring, Jeffrey R.
• Format: Journal Article
• Language: English
• Published: Los Angeles, CA SAGE Publications 01.09.2009; American Educational Research Association
• Subjects: Ability; Coefficients; Computation; Covariance matrices; Economic models; Factor analysis; Grade 5; Latent Variables; Longitudinal Studies; Mathematical independent variables; Maximum likelihood estimation; Maximum likelihood estimators; Maximum Likelihood Statistics; Measurement; Modeling; Nonlinear systems; Parametric models; Polynomials; Regression (Statistics); School and College Ability Tests; Sequential Tests of Educational Progress; Statistical variance; Tests; Variables; nonlinear regression; latent variable models; latent growth curve models; mixed effects model
• ISSN: 1076-9986; 1935-1054
• DOI: 10.3102/1076998609332750

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.