Comparative Study Of The Parameter Estimation Methods Of The Logistic Regression Model With Mixed Effects

Recently,generalized linear mixed-effects models have received much attention in addressing statistical problems in different domains.As a special form of generalized linear model,Logistic regression model plays a crucial role in statistics,and it is also one of the key issues.In the actual statistical research,in order to better study the statistical analysis of large sample data sets,usually by grouping the sample method,so not only produce the difference between samples,also produced the difference between groups,therefore,need to introduce random effects to help solve practical problems,make the difference between groups to find a balance.Logistic regression models with both fixed and random effects are called Logistic regression models with mixed effects.This thesis focuses on comparative studies of parameter estimation of Logistic regression model with mixed effects.We conclude that we summarize and evaluate these parameter estimation methods using four parameter estimation methods,Laplace approximation,Gauss-Hermite quadrature,adaptive Gauss-Hermite quadrature,and penalized quasi-likelihood methods.In this thesis,we mainly consider two-level mixed effects Logistic regression models,conduct simulations and use four parameter estimation methods to obtain the parameter estimation results.In the simulation,considering the simplicity,the number of repeated observations per individual was set to 5 times,and the trial simulation operation was repeated 1,000 times.In order to obtain a more universal conclusion,by changing the sample size of 100,200,500 and 1000,we fitted the model to obtain more experimental results and analyzed the advantages and disadvantages of the four parameter estimation methods to find a relatively excellent parameter estimation method to estimate the Logistic regression model with mixed effects.Through the comprehensive comparison,it is found that the Laplace approximation method and the adaptive Gauss-Hermite quadrature method are excellent in the accuracy,significance and convergence rate.Finally,the four parameter estimation methods are applied to the real data set Affairs,and the Logistic regression model of random effect variables is obtained.Through analysis,it is found that Laplace approximation and adaptive Gauss-Hermite quadrature method are better than the other two parameter estimation methods,similar to the numerical simulation analysis results,and the advantages of the four parameter estimation methods are summarized and evaluated.