Approximated Perfect Values in Logistic Regression for Prediction and Outlier Detection

Abstract

A method to compute perfect values is developed for use with a weighted likelihood approach. It allows to obtain a direct one-iteration approximation for the parameter estimates. We study approximated perfect values applied to logistic regression and demonstrate their usefulness for predictive purposes when the response is missing. We also show that statistics for single-case outlier detection can be deduced. An empirical analysis to determine participation in a federal food-stamp program is presented to illustrate outlier detection and alternatives for estimating the probability of participation in the program. We compare results obtained with the new approach and those obtained maximizing the penalized log-likelihood function.