Logistic Regression of Binary Independent Variables in a Bahadur Framework

• Activity Number: 31
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Wenyaw Chan*+ and Chih-Hsien Wu and Lin-An Chen and Elaine Symanski
• Companies: The University of Texas at Houston and The University of Texas at Houston and National Chiao-Tung University and The University of Texas at Houston
• Keywords: Bahadur distribution ; Logistic Regression

Abstract

Logistic regression is commonly assumed to have a linear relationship between the logit of the conditional odds of the outcome and the predictors. When these predictors are binary, this model may be oversimplified and often leads to an overdispersion problem. Thus, when several binary variables are observed on the same individual, it is more natural to view these variables as having a Bahadur distribution. In this research, we examine a logistic regression model when the outcome and two predictors follow a Bahadur distribution. This work accounts for the two-way or three-way correlations, which are used for defining this joint distribution, constrained by the marginal means. This approach offers advantages because it avoids the overdispersion problem and provides insight regarding the inclusion of the interaction term. The estimated regression coefficients or their corresponding odds ratios from the proposed and traditional models will be compared along with their standard errors. Particularly when overdispersion occurs, the comparison will be extended to examine results from common methods, such as the random-effects model, which handle this problem.