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A Finite Mixture of Nonlinear Random Coefficient Models for Continuous Repeated Measures Data.

Nidhi Kohli1, Jeffrey R Harring2, Cengiz Zopluoglu3

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This study introduces a finite mixture of nonlinear random coefficient models (NRCMs) to analyze complex developmental patterns. The model effectively captures within-person variability, between-person differences, and subpopulation heterogeneity in longitudinal data.

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Area of Science:

  • Statistics
  • Biostatistics
  • Psychometrics

Background:

  • Nonlinear random coefficient models (NRCMs) analyze individual nonlinear developmental trajectories.
  • Finite mixture models identify unobserved subpopulations.
  • Integrating these models offers advanced longitudinal data analysis.

Purpose of the Study:

  • To introduce and evaluate a finite mixture of NRCMs for continuous longitudinal data.
  • To simultaneously investigate intra-individual variability, inter-individual variability, and subpopulation heterogeneity.
  • To assess the model's performance under realistic data conditions.

Main Methods:

  • A Monte Carlo simulation study was conducted.
  • An R routine utilizing maximum likelihood and the expectation-maximization algorithm was developed.
  • The simulation design mimicked a two-class mixture model applied to task completion data.

Main Results:

  • The finite mixture of NRCMs demonstrated efficacy in analyzing data with unobserved subpopulations.
  • The model successfully integrated nonlinear functions to capture developmental patterns.
  • Simulation results indicated the model's effectiveness under various data analytic conditions.

Conclusions:

  • Finite mixture of NRCMs provide a robust framework for analyzing complex longitudinal data with heterogeneity.
  • This approach enhances the understanding of individual development by accounting for unobserved group structures.
  • The developed R routine facilitates the application of this advanced statistical model.