Identification And Estimation Of Generalized Additive Partial Linear Models With Nonignorable Missing Response

Missing data refers to the data that were not obtained due to various factors during the process of data collection and sorting.In practice,missing data occurs frequently in studies across different disciplines,including economics,medicine,public health,and social sciences.Rubin classified the missing data mechanisms into the following three main categories:missing completely at random,missing at random and not missing at random.Not missing at random is also called nonignorable missing.When modeling according to the characteristics of a data set,in order to combine the advantages of parametric and nonparametric models,we plan to use a semiparametric model to fit the data.In statistical research,generalized additive partially linear models have been extensively studied.Since the model can not only fit data with different response types,including linear regression with normal response,logistic regression with binary response,and log-linear regression with Poisson response,etc.,but also combines the easy interpretability of the linear part and the flexibility of the nonlinear part,so it is widely used in practice.In this paper,we promote the generalized additive partial linear model to the case of nonignorable missing data or the case of non-compliance data,respectively.In the case of nonignorable missing data,if the missing data is simply ignored and the model is fitted only on the observed data,the resulting estimates may be biased.The existence of non-compliance data invalidates the gold standard of randomization,which makes the estimates of randomization-based models can also seriously bias.Our main research contents and conclusions include the following three aspects:(1)The identification and estimation of generalized additive partial linear models are discussed when the response variable is nonignorable and missing.Three types of monotone missing data mechanism are assumed,including logistic model,probit model and complementary log-log model.In this situation,likelihood based on observed data may not be identifiable.In this article we show that the parameters of interest are identifiable under very mild conditions,and then construct the estimators of the unknown parameters and unknown functions based on a likelihood-based approach by expanding the unknown functions as a linear combination of polynomial spline functions.We establish asymptotic normality for the estimators of the parametric components.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to the household income dataset from the Chinese Household Income Project Survey 2013.(2)The identification and estimation of generalized additive partial linear models are discussed when the response variable is nonignorable and missing and the distribution of the response is unknown.Three types of monotone missing data mechanism are assumed,including logistic model,probit model and complementary log-log model.In this article we show that the parameters of interest are identifiable under very mild conditions.Drawing on the idea of single-index model,we propose a method for estimating parameters in the missing model,and prove that the obtained estimate satisfies consistency and asymptotic normality.We use the inverse probability weighting method to express the unknown function as a linear combination of polynomial spline functions,and construct a generalized estimating equation based on the quasi-likelihood method,and then obtain the estimation of the unknown parameters and unknown nonparametric functions and obtain Asymptotic normality of parameter estimates in regression models.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to the household income dataset from the Chinese Household Income Project Survey 2013.(3)The identification and estimation of generalized additive partial linear models based on grouped data is discussed when non-compliance data exists.Based on the Rubin causal model,we can obtain the interaction effects between the treatment and the covariates in the compliance sub-population by estimating the complier average causal effect.we construct the estimators of the unknown parameters and unknown functions based on a likelihood-based approach by expanding the unknown functions as a linear combination of polynomial spline functions.Simulation studies demonstrate that the proposed inference procedure performs well in many settings.We apply the proposed method to the 2013 data of the rural residents and the migrant residents in China,and use Mincer earnings function to evaluate the impact of migrant work on the rate of return to education.