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Goodness-of-fit measures of R2 for repeated measures mixed effect models

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  • Honghu Liu
  • Yan Zheng
  • Jie Shen

Abstract

Linear mixed effects model (LMEM) is efficient in modeling repeated measures longitudinal data. However, little research has been done in developing goodness-of-fit measures that can evaluate the models, particularly those that can be interpreted in an absolute sense without referencing a null model. This paper proposes three coefficient of determination (R2) as goodness-of-fit measures for LMEM with repeated measures longitudinal data. Theorems are presented describing the properties of R2 and relationships between the R2 statistics. A simulation study was conducted to evaluate and compare the R2 along with other criteria from literature. Finally, we applied the proposed R2 to a real virologic response data of an HIV-patient cohort. We conclude that our proposed R2 statistics have more advantages than other goodness-of-fit measures in the literature, in terms of robustness to sample size, intuitive interpretation, well-defined range, and unnecessary to determine a null model.

Suggested Citation

  • Honghu Liu & Yan Zheng & Jie Shen, 2008. "Goodness-of-fit measures of R2 for repeated measures mixed effect models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(10), pages 1081-1092.
    • Handle: RePEc:taf:japsta:v:35:y:2008:i:10:p:1081-1092
    DOI: 10.1080/02664760802124422
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    References listed on IDEAS

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    1. Estrella, Arturo, 1998. "A New Measure of Fit for Equations with Dichotomous Dependent Variables," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 198-205, April.
    2. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. Colin Cameron, A. & Windmeijer, Frank A. G., 1997. "An R-squared measure of goodness of fit for some common nonlinear regression models," Journal of Econometrics, Elsevier, vol. 77(2), pages 329-342, April.
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    Cited by:

    1. Ziyue Liu & Anne R. Cappola & Leslie J. Crofford & Wensheng Guo, 2014. "Modeling Bivariate Longitudinal Hormone Profiles by Hierarchical State Space Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(505), pages 108-118, March.
    2. Yan Meng & Xueyan Zhao & Xibin Zhang & Jiti Gao, 2017. "A panel data analysis of hospital variations in length of stay for hip replacements: Private versus public," Monash Econometrics and Business Statistics Working Papers 20/17, Monash University, Department of Econometrics and Business Statistics.
    3. Cantoni, Eva & Jacot, Nadège & Ghisletta, Paolo, 2024. "Review and comparison of measures of explained variation and model selection in linear mixed-effects models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 150-168.

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