Diagnostics for the Complementary Log-Log Regression Model

• Activity Number: 73
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Health Policy Statistics Section
• Author(s): Stephen Quinn* and Leigh Blizzard and Jana Canary and David W. Hosmer
• Companies: Flinders University and Menzies Institute of Medical Research and Menzies Institute of Medical Research and University of Massachusetts
• Keywords: Goodness of fit ; complmentary log-log ; logistic ; regression ; diagnostics

Abstract

The complementary log-log model has been used in various research applications. It is closely related to continuous-time models for the occurrence of events and has a direct interpretation in terms of hazards ratios in discrete time models (Fadem, 2014). It has been used to calculate prevalence ratios (Bhattacharya, 2014) in preference to prevalence odds ratios via logistic regression. In other situations investigators have chosen to use complementary log-log regression in preference to binomial regression with another link function, based on a biological expectation of a non-symmetrical relationship between the conditional probability of success and failure when the coding for the outcome is reversed (Gyimah, 2012). Assessing the goodness-of fit of the final model obtained is an essential step in the analytic process because the validity of any conclusions drawn depends on how well the model fits the data. Through extensive simulations, we compare the performance of several goodness-of-fit statistics via rejection rates, power to detect an incorrectly model, and power to detect an incorrectly specified link when applied to complementary log-log models.