Parametric Bootstrapping Predictive Estimator for Logistic Regression
Kunio Takezawa *
Division of Informatics and Inventory, Institute for Agro-Environmental Sciences, National Agriculture and Food Research Organization, Kannondai 3-1-3, Tsukuba, Ibaraki 305-8604, Japan.
*Author to whom correspondence should be addressed.
Abstract
This paper proposes a method for constructing a predictive estimator for logistic regression. We make a provisional assumption that the predictive estimator is given by multiplying the maximum likelihood estimators by constants, which are estimated using a parametric bootstrap method. The relative merits of the maximum likelihood estimator and the predictive estimator produced by this method are determined by cross-validation. The results show that the predictive
estimators derived by this method lead to a smaller deviance than that obtained by the maximum likelihood estimator in many instances.
Keywords: Log-likelihood, future data, predictive estimator, logistic regression, maximum likelihood estimator, parametric bootstrap method.