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A Second-Order Conditionally Linear Mixed Effects Model With Observed and Latent Variable Covariates.

Jeffrey R Harring1, Nidhi Kohli, Rebecca D Silverman

  • 1Department of Measurement, Statistics, and Evaluation, University of Maryland.

Structural Equation Modeling : a Multidisciplinary Journal
|August 24, 2012
PubMed
Summary

This study introduces a flexible mixed-effects model for analyzing nonlinear changes in repeated measurements. The model effectively uses the Michaelis-Menten function to explain individual differences in growth trajectories.

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Area of Science:

  • Statistics
  • Developmental Psychology
  • Quantitative Psychology

Background:

  • Repeatedly measured continuous latent variables often exhibit nonlinear change over time.
  • Traditional linear mixed effects models may not adequately capture complex nonlinear growth patterns.
  • A flexible modeling framework is needed to investigate individual differences in nonlinear trajectories.

Purpose of the Study:

  • To describe the application of a conditionally linear mixed effects model for nonlinear latent variable growth.
  • To demonstrate fitting a variant of the Michaelis-Menten function within this framework using Mplus 6.0.
  • To illustrate the incorporation of covariates for explaining individual differences in growth.

Main Methods:

  • Utilizing a conditionally linear mixed effects model to analyze nonlinear change in latent variables.
  • Implementing a modified Michaelis-Menten function to model the time-response function.
  • Employing Mplus 6.0 software for model fitting and analysis.
  • Incorporating observed and latent covariates to explain heterogeneity in growth.

Main Results:

  • The conditionally linear mixed effects model successfully fits nonlinear growth trajectories.
  • The Michaelis-Menten function variant provides a viable approach for modeling specific nonlinear patterns.
  • Observed and latent covariates significantly explain individual differences in growth characteristics.
  • Longitudinal reading data analysis demonstrates the model's practical application.

Conclusions:

  • Conditionally linear mixed effects models offer a powerful framework for studying nonlinear latent variable change.
  • The Michaelis-Menten function can be effectively integrated into this framework for growth modeling.
  • This approach enhances understanding of individual differences in developmental trajectories.
  • The provided Mplus code facilitates accessibility for researchers.