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Nonparametric estimation for time-varying transformation models with longitudinal data

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  • Colin Wu
  • Xin Tian
  • Jarvis Yu

Abstract

Regression methods for longitudinal analyses have traditionally focused on conditional-mean-based models. In many situations, the relevant scientific questions could be better studied by modelling the conditional distributions of the outcome variables as a function of time and other covariates. In this paper, we propose a class of time-varying transformation models for modelling the cumulative distribution function of a response variable conditioning on a set of covariates, and develop a two-step smoothing method for estimating the time-varying parameters. Applications and finite sample properties of our models and smoothing estimators are demonstrated through a cohort study of childhood obesity and cardiovascular risk factors, and a simulation study. Theoretical properties are developed for the two-step local polynomial estimators. Our approach provides a useful statistical tool in longitudinal analysis when the conditional-mean-based methods are inappropriate.

Suggested Citation

  • Colin Wu & Xin Tian & Jarvis Yu, 2010. "Nonparametric estimation for time-varying transformation models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 133-147.
    • Handle: RePEc:taf:gnstxx:v:22:y:2010:i:2:p:133-147
    DOI: 10.1080/10485250903160988
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    References listed on IDEAS

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    Cited by:

    1. Minjung Kwak, 2017. "Estimation and inference of the joint conditional distribution for multivariate longitudinal data using nonparametric copulas," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 491-514, July.
    2. Lin Liu & Jianbo Li & Riquan Zhang, 2014. "General partially linear additive transformation model with right-censored data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(10), pages 2257-2269, October.
    3. Mohammed Chowdhury & Colin Wu & Reza Modarres, 2018. "Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 61-83, January.
    4. Colin O. Wu & Xin Tian, 2013. "Nonparametric Estimation of Conditional Distributions and Rank-Tracking Probabilities With Time-Varying Transformation Models in Longitudinal Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 971-982, September.

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