Effects and Detection of Link Misspecification in Generalized Linear Mixed Models

• Activity Number: 186
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Shun Yu*+ and Xianzheng Huang
• Companies: and University of South Carolina
• Keywords: cluster data ; grouped data ; skew normal ; probit link

Abstract

We study properties of maximum likelihood estimators of parameters in a generalized linear mixed model (GLMM) for a binary response in the presence of link misspecification. In particular, we investigate asymptotic bias of the estimators based on the observed individual binary responses and the counterpart estimators resulting from the induced grouped binary responses. Utilizing properties of these two sets of estimators, we develop an informative diagnostic test that can reveal the direction of link misspecification. Further insights on the effects of link misspecification on maximum likelihood estimation are gained by studying analytically the estimators under an assumed GLMM with the probit or the logistic link. Large-sample numerical study and finite-sample simulation experiments are carried out to illustrate and empirically justify the theoretical findings.