Simultaneous Confidence Bands For Logistic Regression With Covariates Constrained In Intervals

The focus of this article is on simultaneous confidence bands over a rectangular covariate region for mean of Logistic regression model,based on the theory and methods for simultaneous confidence bands of linear regression model.The main work is to build hyperbolic bands of binomial dependent variable's probability p(x).Then,through a multi-factor design,simulate the coverage probability of simple Logistic regression,and conduct comprehensive comparison analysis.Formulas of the simulation method on hyperbolic bands with k ?1 covariates and a given simultaneous confidence level 1-? are provided.For simple Logistic regression,the formulas and steps of solving the critical value c by exact and simulation methods are given.Based on these two methods,simulating the coverage probability of simple Logistic regression of 48 kinds of designed structures and three confidence levels.Then,analyze and compare the simulation results.Finally,it is pointed out that using the critical value c generated by the method of linear regression for Logistic regression shows good results.At the same time,for a specific set of data,according to the confidence level,limited range of covariates,model requirements to choose an appropriate method to build simultaneous confidence bands for Logistic regression model.