Semiparametric Regression for Clustered Data Using Generalized Estimating Equations
نویسندگان
چکیده
We consider estimation in a semiparametric generalized linear model for clustered data using estimating equations. Our results apply to the case where the number of observations per cluster is nite, whereas the number of clusters is large. The mean of the outcome variable Œ is of the form g4Œ5 D X‚C ˆ4T 5, where g4¢5 is a link function, X and T are covariates, ‚ is an unknown parameter vector, and ˆ4t5 is an unknown smooth function. Kernel estimating equations proposed previously in the literature are used to estimate the in nitedimensional nonparametric function ˆ4t5, and a pro le-based estimating equation is used to estimate the nite-dimensional parameter vector ‚. We show that for clustered data, this conventional pro le-kernel method often fails to yield a p n-consistent estimator of ‚ along with appropriate inference unless working independence is assumed or ˆ4t5 is arti cially undersmoothed, in which case asymptotic inference is possible. To gain insight into these results, we derive the semiparametric ef cient score of ‚, which is found to have a complicated form, and show that, unlike for independent data, the pro le-kernel method does not yield a score function asymptotically equivalent to the semiparametric ef cient score of ‚, even when the true correlation is assumed and ˆ4t5 is undersmoothed. We illustrate the methods with an application to infectious disease data and evaluate their nite-sample performance through a simulation study.
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