Hosmer-Lemeshow Goodness-of-Fit Test for Multiply Imputed Data

• Activity Number: 186
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): Danielle Sullivan*+ and Rebecca Andridge
• Companies: and The Ohio State University
• Keywords: Multiple Imputation ; Hosmer-Lemeshow Goodness of Fit

Abstract

The Hosmer-Lemeshow (H-L) test is widely used for evaluating goodness of fit in logistic regression models. The H-L test first creates groups based on deciles of the estimated probabilities and then compares observed and expected event rates within these groups. Multiple imputation (MI) is growing in popularity as a method for handling missing data, and how to apply the H-L test after MI is not straightforward. In this paper we discuss complexities involved in applying the H-L test to multiply imputed data, related to which variables have missingness. When covariates have been imputed, predicted probabilities vary across imputed data sets, and thus the boundaries of the predicted probability groupings vary as well. When the outcome has been imputed, both predicted probabilities and "observed" event rates change from one data set to the next. We then propose several different methods for using the H-L test with multiply imputed data, and compare the methods through simulation.