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Parametric variable selection in generalized partially linear models with an application to assess condom use by HIV‐infected patients
Author(s) -
Leng Chenlei,
Liang Hua,
Martinson Neil
Publication year - 2011
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.4233
Subject(s) - logistic regression , covariate , condom , mathematics , monte carlo method , model selection , parametric statistics , statistics , computer science , human immunodeficiency virus (hiv) , mathematical optimization , medicine , syphilis , family medicine
To study significant predictors of condom use in HIV‐infected adults, we propose the use of generalized partially linear models and develop a variable selection procedure incorporating a least squares approximation. Local polynomial regression and spline smoothing techniques are used to estimate the baseline nonparametric function. The asymptotic normality of the resulting estimate is established. We further demonstrate that, with the proper choice of the penalty functions and the regularization parameter, the resulting estimate performs as well as an oracle procedure. Finite sample performance of the proposed inference procedure is assessed by Monte Carlo simulation studies. An application to assess condom use by HIV‐infected patients gains some interesting results, which cannot be obtained when an ordinary logistic model is used. Copyright © 2011 John Wiley & Sons, Ltd.