Identifying the Mean-Variance Relationship in Logistic Regression Models

• Activity Number: 37
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Katherine Cai*
• Companies: Arizona State University
• Keywords: mean-variance relationship ; generalized linear models ; correlated data ; generalized method of moments ; simulation ; logistic regression

Abstract

In generalized linear models, the random component has a specified probability distribution which assumes a particular relationship between the mean and variance. While it is common for the variance to be proportional to the mean of a random variable, the data may not exhibit the relationship prescribed by the selected distribution. We expand on a parametric robust method of determining the mean-variance relationship for generalized linear models presented by Tsou. The binary case is evaluated for logistic regression models, and generalized method of moments is investigated as an alternative method of estimation. A comparison of both methods is provided through simulations and a numerical example.