Regularization in Generalized Semiparametric Mixed-Effects Model for Longitudinal Data
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This paper considers the problem of simultaneous variable selection and estimation in the generalized semiparametric mixed-effects model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is proposed while using regression spline to approximate the nonparametric component. Our approach applies SCAD to the estimating equation objective function in order to simultaneously estimate parameters and select the important variables. The proposed procedure involves the specification of the posterior distribution of the random effects, which cannot be evaluated in a closed form. However, it is possible to approximate this posterior distribution by producing random draws from the distribution using a Metropolis algorithm, which does not require the specification of the posterior distribution. For practical implementation, we develop an appropriate iterative algorithm to select the significant variables and estimate the nonzero coefficient functions. Under some regularity conditions, the resulting estimators enjoy the oracle properties, under a high-dimensional regime. Simulation studies are carried out to assess the performance of our proposed method, and a real data set is analyzed to illustrate the procedure.
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