• SIZE AND POWER OF GOODNESS-OF-FIT TESTS FOR LOGISTIC REGRESSION MODEL WITH MISSING INTERACTION TERMS

Abstract

An assessment of model fit and an evaluation of how well model-based predicted outcomes coincide with the observed data is an important component of any modeling procedure. When at least one continuous predictor is present, classical Pearson and deviance goodness-of-fit tests for logistic regression model are invalid. The Hosmer–Lemeshow test can be used in these situations. However, it does not have desirable power in many cases and provides no further information on the source of any detectable lack of fit. We propose a new method for goodness-of-fit testing that uses partitioning in the covariate space using the estimated probabilities from the assumed model. Properties of the proposed statistics are discussed, and a simulation study demonstrates increased power to detect omission of interaction terms in a variety of settings controlling type I error rates.