Commimication Eficient Distributed Statistical Computation In Generalized Linear Mixed Model

In real application,widely used regression models,among others,include linear mixed model(LMMs),generalized linear model(GLMs)and generalized linear mixed model(GLMMs)to fit a range of real data.In particular,there are many potential applications of generalized linear mixed model in insurance,actuarial science,medical science,ecology,infectious diseases and other fields.However,the estimation of the generalized linear mixed model involves the problem of high-dimensional integration as compared to other models,so its practical calculation is more difficult.In the existing literature,Breslow and Clayton(1993)[3]first discussed how to use Laplace method to calculate the related Quasi Likelihood Estimation quickly,and proposed a kind of calculation method based on penalty Quasi Likelihood(PQL,penalized Quasi Likelihood),and deduced the theoretical properties of the related method.Then,with the data collection becoming increasingly convenient,massive data gradually appearing in past decade,which brings great challenges to the practical application of related models.Jordan et al.(2018)[18] proposed an effective inferential method for communication based on the linear model and generalized linear model in the case of Big data.In the light of the fact that Jordan et al.(2018)[18]related methods cannot be applied directly to generalized linear mixed model,this paper focuses on how to carry out the distributed calculation of generalized linear mixed model,and compiles the program implementation based on R,C + +,armadillo and other tools.Similar to Jordan et al.(2018)[18],the method in this paper adopts the effective communication processing method,and sets the part of the Hessian matrix involved in the optimization process for reuse,so it can effectively improve the calculation speed of related methods.Finally,simulation confirms the efficacy of the proposed method,and one example approves the performance of the new algorithm.In this paper,we expect to discuss the effective distributed computing method of communication in the generalized linear mixed model,which can help the real application in the future.