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Missing covariate data in generalized linear mixed models with distribution-free random effects

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  • Liu, Li
  • Xiang, Liming

Abstract

We consider generalized linear mixed models in which random effects are free of parametric distributions and missing at random data are present in some covariates. To overcome the problem of missing data, we propose two novel methods relying on auxiliary variables: a penalized conditional likelihood method when covariates are independent of random effects, and a two-step procedure consisting of a pairwise likelihood for estimating fixed effects in the first step and a penalized conditional likelihood for estimating random effects in the second step while covariates can be related to random effects. Our methods allow a nonparametric structure for the missing covariate data and do not rely on distribution assumptions for random effects, which are not observed in the data, thus providing great flexibility in capturing a board range of the missingness mechanism and behaviors of random effects. We show that the proposed estimators enjoy desirable theoretical properties by relaxing the conditions for a finite number of clusters or finite cluster size imposed in the literature. The finite sample performance of the estimators is assessed through extensive simulations. We illustrate the application of the methods using a longitudinal data set on forest health monitoring.

Suggested Citation

  • Liu, Li & Xiang, Liming, 2019. "Missing covariate data in generalized linear mixed models with distribution-free random effects," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 1-16.
    • Handle: RePEc:eee:csdana:v:134:y:2019:i:c:p:1-16
    DOI: 10.1016/j.csda.2018.10.011
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    References listed on IDEAS

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    1. Anthony Y. C. Kuk, 2007. "A Hybrid Pairwise Likelihood Method," Biometrika, Biometrika Trust, vol. 94(4), pages 939-952.
    2. Nicholas J. Horton & Nan M. Laird, 2001. "Maximum Likelihood Analysis of Logistic Regression Models with Incomplete Covariate Data and Auxiliary Information," Biometrics, The International Biometric Society, vol. 57(1), pages 34-42, March.
    3. Kuk, Anthony Y. C. & Nott, David J., 2000. "A pairwise likelihood approach to analyzing correlated binary data," Statistics & Probability Letters, Elsevier, vol. 47(4), pages 329-335, May.
    4. C.-Y. Huang & J. Qin & M.-C. Wang, 2010. "Semiparametric Analysis for Recurrent Event Data with Time-Dependent Covariates and Informative Censoring," Biometrics, The International Biometric Society, vol. 66(1), pages 39-49, March.
    5. Francis K. C. Hui & Samuel Müller & A. H. Welsh, 2017. "Joint Selection in Mixed Models using Regularized PQL," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1323-1333, July.
    6. Haibo Zhou & Jianwei Chen & Jianwen Cai, 2002. "Random Effects Logistic Regression Analysis with Auxiliary Covariates," Biometrics, The International Biometric Society, vol. 58(2), pages 352-360, June.
    7. Thomas Kneib & Torsten Hothorn & Gerhard Tutz, 2009. "Variable Selection and Model Choice in Geoadditive Regression Models," Biometrics, The International Biometric Society, vol. 65(2), pages 626-634, June.
    8. Li Liu & Liming Xiang, 2014. "Semiparametric estimation in generalized linear mixed models with auxiliary covariates: A pairwise likelihood approach," Biometrics, The International Biometric Society, vol. 70(4), pages 910-919, December.
    9. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    10. Kathryn M. Aloisio & Sonja A. Swanson & Nadia Micali & Alison Field & Nicholas J. Horton, 2014. "Analysis of partially observed clustered data using generalized estimating equations and multiple imputation," Stata Journal, StataCorp LLC, vol. 14(4), pages 863-883, December.
    11. Agresti, Alan & Caffo, Brian & Ohman-Strickland, Pamela, 2004. "Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 639-653, October.
    12. Peng Wang & Guei-feng Tsai & Annie Qu, 2012. "Conditional Inference Functions for Mixed-Effects Models With Unspecified Random-Effects Distribution," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 725-736, June.
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