Bayesian Variable Selection For Partial Linear Model With Nonignorably Missing Skew Normal Data

I propose skewed normal partial linear model with response variable of nonignorably missing at random in this paper,and discuss the parameter estimation and variable selection.Firstly,on the basis of the existing multivariate linear regression model,I consider partial linear semi-parametric model with response variable nonignorably missing at random.The nonlinear part of the model is fitted by second-order truncated basic splines.In order to increase the applicability and flexibility of the model,the random error is set as skewed normal distribution,and nonignorably missing at random mechanism is modeled based on Logistic regression model.Next there are many factors affecting a variable in real life.In order to find out which factors are significant,I use Bayesian Lasso method to select variables in this paper.I estimate and choose parameters simultaneously for linear partial variables and Logistic regression models.Next,I propose several simulation experiments in different situations in order to verify the effecti'veness of the proposed model.Simulation data are generated in R then WinBUGS is invoked to fill the missing values from posterior distribution sampling of missing values.And bayesian estimation is made from posterior sampling of unknown parameters.I use some commonly statistics to illustrate the applicability of the model and the effectiveness of the method.Finally,based on the model established in this paper,I studied the housing price data of King County in the United States in 2014 and draw the conclusion that the housing price belongs to nonignorably missing at random.I analyze the relationship between the missing price and other influencing factors,further verify effectiveness of the method.