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Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates

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  • Xiao-Feng Wang
  • Bo Hu
  • Bin Wang
  • Kuangnan Fang

Abstract

This paper is motivated from a neurophysiological study of muscle fatigue, in which biomedical researchers are interested in understanding the time-dependent relationships of handgrip force and electromyography measures. A varying coefficient model is appealing here to investigate the dynamic pattern in the longitudinal data. The response variable in the study is continuous but bounded on the standard unit interval (0, 1) over time, while the longitudinal covariates are contaminated with measurement errors. We propose a generalization of varying coefficient models for the longitudinal proportional data with errors-in-covariates. We describe two estimation methods with penalized splines, which are formalized under a Bayesian inferential perspective. The first method is an adaptation of the popular regression calibration approach. The second method is based on a joint likelihood under the hierarchical Bayesian model. A simulation study is conducted to evaluate the efficacy of the proposed methods under different scenarios. The analysis of the neurophysiological data is presented to demonstrate the use of the methods.

Suggested Citation

  • Xiao-Feng Wang & Bo Hu & Bin Wang & Kuangnan Fang, 2014. "Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(6), pages 1342-1357, June.
    • Handle: RePEc:taf:japsta:v:41:y:2014:i:6:p:1342-1357
    DOI: 10.1080/02664763.2013.868870
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    References listed on IDEAS

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    1. Damla Şentürk & Hans-Georg Müller, 2008. "Generalized varying coefficient models for longitudinal data," Biometrika, Biometrika Trust, vol. 95(3), pages 653-666.
    2. Patricia Espinheira & Silvia Ferrari & Francisco Cribari-Neto, 2008. "On beta regression residuals," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(4), pages 407-419.
    3. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506, October.
    4. Chiang C-T. & Rice J. A & Wu C. O, 2001. "Smoothing Spline Estimation for Varying Coefficient Models With Repeatedly Measured Dependent Variables," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 605-619, June.
    5. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    6. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167, October.
    7. Zhao, Peixin & Xue, Liugen, 2010. "Variable selection for semiparametric varying coefficient partially linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1872-1883, September.
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    Cited by:

    1. Taining Wang & Jinjing Tian & Feng Yao, 2021. "Does high debt ratio influence Chinese firms’ performance? A semiparametric stochastic frontier approach with zero inefficiency," Empirical Economics, Springer, vol. 61(2), pages 587-636, August.

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