Bayes-Type Tests For Constancy Of Parameters In Logistic Regression Models

Change-point problems arise in a variety of practical situations including engineering and health science applications. There are generally two approaches for these problems. One is the likelihood approach, and the other is the Bayesian approach. The Bayes-type test statistics, which are derived as the marginal likelihood ratio with appropriate prior distributions on the nuisance parameters, have been shown to provide higher power than likelihood ratio tests in linear regression models and first order autoregressive models. The change-point problem in logistic models has not been investigated extensively. The aim of this thesis is to provide a unified approach of Bayes-type and Rao's Score test to the problem of testing for constancy of parameters in logistic regression models, and explore the connection between Bayes-type tests and Rao's Score tests. Test Statistics are derived for changes at unknown times in the parameters of a logistic regression model. Asymptotic distribution theory for the tests is discussed. Simulations are carried out to compare the power with other options from the literature. An application of the test procedure on a real data set has been discussed.