Bayesian Variable Selection for Semiparametric Logistic Regression

Lasso variable selection is an attractive approach to improve the prediction accuracy. Bayesian lasso approach is suggested to estimate and select the important variables for single index logistic regression model. Laplace distribution is set as prior to the coefficients vector and prior to the unknown link function (Gaussian process). A hierarchical Bayesian lasso semiparametric logistic regression model is constructed and MCMC algorithm is adopted for posterior inference. To evaluate the performance of the proposed method BSLLR is through comparing it to three existing methods BLR, BPR and BBQR. Simulation examples and numerical data are to be considered. The results indicate that the proposed method get the smallest bias, SD, MSE and MAE in simulation and real data. The proposed method BSLLR performs better than other methods.

A More Accurate Estimation of Semiparametric Logistic Regression

Growing interest in genomics research has called for new semiparametric models based on kernel machine regression for modeling health outcomes. Models containing redundant predictors often show unsatisfactory prediction performance. Thus, our task is to construct a method which can guarantee the estimation accuracy by removing redundant variables. Specifically, in this paper, based on the regularization method and an innovative class of garrotized kernel functions, we propose a novel penalized kernel machine method for a semiparametric logistic model. Our method can promise us high prediction accuracies, due to its capability of flexibly describing the complicated relationship between responses and predictors and its compatibility of the interactions among the predictors. In addition, our method can also remove the redundant variables. Our numerical experiments demonstrate that our method yields higher prediction accuracies compared to competing approaches.