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Consistent model selection and data‐driven smooth tests for longitudinal data in the estimating equations approach

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  • Lan Wang
  • Annie Qu

Abstract

Summary. Model selection for marginal regression analysis of longitudinal data is challenging owing to the presence of correlation and the difficulty of specifying the full likelihood, particularly for correlated categorical data. The paper introduces a novel Bayesian information criterion type model selection procedure based on the quadratic inference function, which does not require the full likelihood or quasi‐likelihood. With probability approaching 1, the criterion selects the most parsimonious correct model. Although a working correlation matrix is assumed, there is no need to estimate the nuisance parameters in the working correlation matrix; moreover, the model selection procedure is robust against the misspecification of the working correlation matrix. The criterion proposed can also be used to construct a data‐driven Neyman smooth test for checking the goodness of fit of a postulated model. This test is especially useful and often yields much higher power in situations where the classical directional test behaves poorly. The finite sample performance of the model selection and model checking procedures is demonstrated through Monte Carlo studies and analysis of a clinical trial data set.

Suggested Citation

  • Lan Wang & Annie Qu, 2009. "Consistent model selection and data‐driven smooth tests for longitudinal data in the estimating equations approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 177-190, January.
  • Handle: RePEc:bla:jorssb:v:71:y:2009:i:1:p:177-190
    DOI: 10.1111/j.1467-9868.2008.00679.x
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    References listed on IDEAS

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    Cited by:

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    2. Lv, Jing & Guo, Chaohui & Yang, Hu & Li, Yalian, 2017. "A moving average Cholesky factor model in covariance modeling for composite quantile regression with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 112(C), pages 129-144.
    3. Lan Wang & Jianhui Zhou & Annie Qu, 2012. "Penalized Generalized Estimating Equations for High-Dimensional Longitudinal Data Analysis," Biometrics, The International Biometric Society, vol. 68(2), pages 353-360, June.
    4. Tsubasa Ito & Shonosuke Sugasawa, 2023. "Grouped generalized estimating equations for longitudinal data analysis," Biometrics, The International Biometric Society, vol. 79(3), pages 1868-1879, September.
    5. Li, Gaorong & Lian, Heng & Feng, Sanying & Zhu, Lixing, 2013. "Automatic variable selection for longitudinal generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 61(C), pages 174-186.
    6. Song Liu & Yuhong Yang, 2012. "Combining models in longitudinal data analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 233-254, April.
    7. Tang, Yanlin & Wang, Huixia Judy & Zhu, Zhongyi, 2013. "Variable selection in quantile varying coefficient models with longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 435-449.
    8. Alexander Knobel & Alexey Mironov, 2014. "Оценка Готовности Стран СНГ к Созданию Валютного Союза c Россией (Readiness Assessment of the CIS Member States to Create a Monetary Union with Russia)," Working Papers 136, Gaidar Institute for Economic Policy, revised 2015.
    9. Kari R. Hart & Teng Fei & John J. Hanfelt, 2021. "Scalable and robust latent trajectory class analysis using artificial likelihood," Biometrics, The International Biometric Society, vol. 77(3), pages 1118-1128, September.
    10. Denis Heng-Yan Leung & Dylan S. Small & Jing Qin & Min Zhu, 2013. "Shrinkage Empirical Likelihood Estimator in Longitudinal Analysis with Time-Dependent Covariates—Application to Modeling the Health of Filipino Children," Biometrics, The International Biometric Society, vol. 69(3), pages 624-632, September.

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