Generalized Partially linear models with missing data

Abstract

In multivariate data with binary outcome, having some of explanatory variable missing, generalized linear models are sometimes hard to be applied. Among the covariates, some behave linearly and the others do nonlinearly when having effect on the outcome variable, which is the variable to be expected statistically. In this case, the generalized partially linear models, which considers the aspects of both generalized linear model and generalized additive model, is one of the ways to deal with. Especially, under the existence of missing data, WEE(weighted estimating equation) method can be employed in order to estimate the function of interest. It is interesting that the probability of missing covariates does not affect the biasedness of the estimator. This is because the inverse probability weighting method gives weights to another data of near values of missing, to complement missing portion. Also, we apply the kernel regression to estimate nonparametric term. Since the bandwidth h is necessary, we also check that how critical bandwidth selection is by making several simulation and computing biasedness of estimates.