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Obtaining Interpretable Parameters From Reparameterized Longitudinal Models: Transformation Matrices Between Growth Factors in Two Parameter Spaces

Author

Listed:
  • Jin Liu
  • Robert A. Perera
  • Le Kang
  • Roy T. Sabo

    (Department of Biostatistics, School of Medicine, Virginia Commonwealth University, Richmond, VA, USA)

  • Robert M. Kirkpatrick

    (Department of Psychiatry, School of Medicine, Virginia Commonwealth University, Richmond, VA, USA)

Abstract

This study proposes transformation functions and matrices between coefficients in the original and reparameterized parameter spaces for an existing linear-linear piecewise model to derive the interpretable coefficients directly related to the underlying change pattern. Additionally, the study extends the existing model to allow individual measurement occasions and investigates predictors for individual differences in change patterns. We present the proposed methods with simulation studies and a real-world data analysis. Our simulation study demonstrates that the method can generally provide an unbiased and accurate point estimate and appropriate confidence interval coverage for each parameter. The empirical analysis shows that the model can estimate the growth factor coefficients and path coefficients directly related to the underlying developmental process, thereby providing meaningful interpretation.

Suggested Citation

  • Jin Liu & Robert A. Perera & Le Kang & Roy T. Sabo & Robert M. Kirkpatrick, 2022. "Obtaining Interpretable Parameters From Reparameterized Longitudinal Models: Transformation Matrices Between Growth Factors in Two Parameter Spaces," Journal of Educational and Behavioral Statistics, , vol. 47(2), pages 167-201, April.
    • Handle: RePEc:sae:jedbes:v:47:y:2022:i:2:p:167-201
    DOI: 10.3102/10769986211052009
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    References listed on IDEAS

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    1. G. Muniz Terrera & A. van den Hout & F. E. Matthews, 2011. "Random change point models: investigating cognitive decline in the presence of missing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(4), pages 705-716, November.
    2. Eric F. Lock & Nidhi Kohli & Maitreyee Bose, 2018. "Detecting Multiple Random Changepoints in Bayesian Piecewise Growth Mixture Models," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 733-750, September.
    3. Stephen Toit & Robert Cudeck, 2009. "Estimation of the Nonlinear Random Coefficient Model when Some Random Effects Are Separable," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 65-82, March.
    4. Chou, Chih-Ping & Yang, Dongyun & Pentz, Mary Ann & Hser, Yih-Ing, 2004. "Piecewise growth curve modeling approach for longitudinal prevention study," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 213-225, June.
    5. Asher Tishler & Isreal Zang, 1981. "A Maximum Likelihood Method for Piecewise Regression Models with a Continuous Dependent Variable," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(2), pages 116-124, June.
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