Information Matrices in Estimating Function Approach: Test for Model Misspecification and Model Selection

• Activity Number: 580
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Qian Zhou*+ and Peter Song and Mary Thompson
• Companies: Harvard School of Public Health and University of Michigan and University of Michigan
• Keywords: Estimating functions ; Generalized estimating equations ; Information unbiasedness ; Model misspecification

Abstract

In this paper, we focus on the situations that the estimation accuracy of mean structure parameters is guaranteed by correct specification of the first moment, but the estimation efficiency could be diminished due to misspecification of the second moment. We propose an information ratio (IR) statistic to test for misspecification of the variance/covariance structure through comparing two forms of information matrix: the negative sensitivity matrix and variability matrix. We also propose an information discrepancy criterion (IDC) to select the best fitting variance/covariance structure from a class of candidates. Simulation studies have shown that the IR statistic provides a powerful test to detect different scenarios of misspecification. In addition, the IR test and IDC show substantial improvement over existing methods, including the information matrix test of White (1982) and others.