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Generalized Quasi-Likelihood Ratio Tests for Semiparametric Analysis of Covariance Models in Longitudinal Data

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  • Jin Tang
  • Yehua Li
  • Yongtao Guan

Abstract

We model generalized longitudinal data from multiple treatment groups by a class of semiparametric analysis of covariance models, which take into account the parametric effects of time dependent covariates and the nonparametric time effects. In these models, the treatment effects are represented by nonparametric functions of time and we propose a generalized quasi-likelihood ratio test procedure to test if these functions are identical. Our estimation procedure is based on profile estimating equations combined with local linear smoothers. We find that the much celebrated Wilks phenomenon which is well established for independent data still holds for longitudinal data if a working independence correlation structure is assumed in the test statistic. However, this property does not hold in general, especially when the working variance function is misspecified. Our empirical study also shows that incorporating correlation into the test statistic does not necessarily improve the power of the test. The proposed methods are illustrated with simulation studies and a real application from opioid dependence treatments. Supplementary materials for this article are available online.

Suggested Citation

  • Jin Tang & Yehua Li & Yongtao Guan, 2016. "Generalized Quasi-Likelihood Ratio Tests for Semiparametric Analysis of Covariance Models in Longitudinal Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 736-747, April.
    • Handle: RePEc:taf:jnlasa:v:111:y:2016:i:514:p:736-747
    DOI: 10.1080/01621459.2015.1036995
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    Cited by:

    1. Bai, Yansong & Zhang, Yong & Liu, Congmin, 2023. "Moderate deviation principle for likelihood ratio test in multivariate linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    2. Li, Yehua & Qiu, Yumou & Xu, Yuhang, 2022. "From multivariate to functional data analysis: Fundamentals, recent developments, and emerging areas," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    3. Weicheng Zhu & Sheng Xu & Catherine C. Liu & Yehua Li, 2023. "Minimax powerful functional analysis of covariance tests with application to longitudinal genome‐wide association studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(1), pages 266-295, March.

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