Steve Quinn

Menzies Research Institute, University of Tasmania

A comparison of logistic regression goodness-of-fit statistics when applied to the log link

Blizzard L & Hosmer DW (2006, Biometrical Journal, pp.5-22) contributed to the development of the log binomial regression model for binary outcomes that make it possible to directly estimate relative risk in follow-up studies, and prevalence ratios in cross-sectional studies, and to adjust for continuous covariates. There are several goodness-of-fit statistics that describe how well a logistic regression model fits a set of observations, but to date little work has been done that summarizes the discrepancy between observed and expected values for log link models. Through extensive simulations we compare the performance of several goodness-of-fit statistics via rejection rates, power to detect an incorrectly specified model, and power to detect an incorrectly specified link when applied to log link models.