An Improved Goodness-of-Fit Test for Logistic Regression Models Based on Case-Control Data by Random Partition

Abstract

Zhang (1999) proposed a chi-squared goodness-of-fit test for logistic regression models based on case-control data by adapting the Nikulin–Rao–Robson–Moore test. The statistic proposed by Zhang requires the partition of covariate space and the cutoff points for partition are assumed to be known and fixed by experience. Due of lack of a uniform rule for choosing appropriate cutoff points, we propose a data-driven strategy for grouping data and a new statistic for testing logistic regression models based on case-control data. The proposed statistic has an asymptotic chi-squared distribution. Our simulation results show that the proposed statistic is more powerful than the one proposed by Zhang. Application of the proposed statistic to two real datasets is also presented.

Keywords:

• Case-control data
• Density ratio model
• Empirical likelihood
• Goodness-of-fit
• Logistic regression

Mathematics Subject Classification:

• 62G30
• 62G10

Acknowledgment

We are grateful to the National Science Foundation of USA for support through grant DMS-0603873.