Bayesian Logistic Regression Analysis

Abstract

This thesis addresses the Bayesian Analysis of three binary logistic regress ion models i.e. binary logistic regression model without intercept, with intercept and with two explanatory variables. One informative (Normal) and three noninformative pnors are assumed for the parameters of three models. All the analysis is carried out in SAS package. We have sel ected , the hyperparameters for informative prior on basis of expert opinion and use for further analysis. We have used the data set of Erythrocyte Sedimentation Rate (ESR) form Cengiz et al. (200 I), that is binary in nature and coded [0 , 1] with two explana tory variables: Fibrinogen and Y-globulin that are blood plasma proteins. We have used the logistic link for logistic regression analys is. We proceed with Bayesian analysis foi' all the logistic regression models, the noninformative priors are derived, then based on posterior di stribution we have obtained the posterior modes, posterior means, posterior standard deviation and Karl Pearson Coefficient of Skewness to say about the shape of the distribution of parameters and the results are further compared with classical results. To check the significance of parameters we have developed programs in SAS package to fi nd posterior probabiliti es. the Bayesian approach to hypothescs testing has been carried out. The comparison of Bayesian and Classical res ults is also presented. We have also suggested the appropri ate model. Proposed SAS package plays major role for completion of this dissertation.