A Weighting Mean Score Estimation For A Random Effect Logistic Regression With Auxiliary Variables

A generalized linear mixed model(GLMM)is a special type of mixed model as well as an important extension of generalized linear model.In this model structure,instead of fixed effects,the linear predictor contains random effects,which usually have normal distributions.A random effect logistic regression is a special case of the generalized linear mixed model(GLMM),mainly used in epidemiology.This article first introduces the random effects logistic regression model,a new Method is proposed.We first propose a center-specific estimation based on the quasi-likelihood function using mean score method to deal with missing data,we use auxiliary variables,next we estimates the first step estimator in the specific data center,and then construct a two-step estimator using an optimal weighted version of the first step estimators.Finally a simulation study is also provided,showing that the estimation works properly.A real case of the risks of male birth defects is also studied,indicates that our proposed method works properly on real data.This paper first provides an overview of the related background and the significance of the survey,and analyzes the deficiencies of likelihood function in the estimation procedure,proposed a new method.Then we collected the existing literature of the random effects logistic model,missing data and male birth defects at home and aboard,we propose the research thesis of this article.Finally,the paper summarizes works and innovation.Second,this chapter describe basic idea and principle of the Mean Score Method,after that,we introduce the estimated method of the random effects logistic regression based on the Mean Score Method.In the end of this chapter,we provided the asymptotic property of the two-step estimator.Third,in this section,we carry out Monte Carlo simulations to study the performance of the proposed two-step estimator and the validation estimator.Furthermore,by contrast with true value,we appraise the two method.Fourth,this chapter builds the random effect logistic regression model and apply it in the empirical research for influence factors of male birth defects.And the estimated result indicates that our proposed method works properly on real dataFinally,this part summarizes study's conclusions and puts forward the research prospects in the field considering the limitation of Mean Score Method.