The Construction And Application Of Robust Semiparametric Regression Model For Binary Response

BackgroundBinary data with covariate is omnipresent in practice.Methods for their analysis have relied on subjectively specified models although existing semiparametric models have improved upon parametric models by trying to account for potential nonlinear effects of the covariates.Yuan et al.(2020)proposed a broadly applicable robust semiparametric ordinal regression model,in which the response is a nonparametric monotone increasing function of the parametrically specified covariates for robustness This model is more flexible than existing semiparametric models but more robustObjectiveIn this study,we proposed a Robust Semiparametric Binary Regression Model(Robust SBRM)based on the model Yuan et al.(2020)proposed,and compare it's parameter estimation,type ? error and power with Logistic regression model.MethodsYuan et al(2020)'s model is for ordinal data,in order to apply it to deal with binary data,we need to rebuild it with reducing the ordinal parameters.Then we construct the log-likelihood function and estimate the unknown parameters with isotonic regression and pool adjacent violators algorithm(PAVA).Though Monte Carlo simulation,we compare SBRM and Logistic regression model in the mean and standard deviation of parameter estimates,type ? error,and power of models based on data generated from different sample size and different distributions(Normal distribution,Beta distribution,and Exponential distribution).ResultIn the aspect of parameter estimation,the model we proposed SBRM has a better performance than Logistic model with smaller standard deviation and biasIn the aspect of parameter estimation,when the response variable is based on the normal distribution,Logistic model has the best performance of controlling the type ?error,the Probit model and SBRS perform not very well.What' more,in the cases of the response variable is based on the Beta distribution,and Exponential distribution,SBRM and Logistic regression model can control type ? error well.In the aspect of power,the power of both SBRM and Logistic regression model are above 80%,and the power of SBRM is higher than Logistic regression modelConclusionThe new model our study proposed(SBRM)has a better performance on parameter estimation than the classical Logistic regression model,and it can be applied to the data of different kind of distribution.The power of SBRM is high and without assuming a fixed link function so that SBRM is robust and flexible.