GEE Analysis of Clustered Binary Data with Diverging Number of Parameters

• Activity Number: 291
• Type: Topic Contributed
• Date/Time: Tuesday, August 2, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Survey Research Methods
• Author(s): Lan Wang*+ and Jianhui Zhou and Annie Qu
• Companies: University of Minnesota and University of Virginia and University of Illinois at Urbana-Champaign
• Keywords: GEE ; clustered binary data ; high-dimensional data ; correlated data

Abstract

Clustered binary data with a large number of covariates have become increasingly common in many scientific disciplines. We consider a generalized estimating equations (GEE) approach to analyzing such data when the number of covariates grows to infinity with the number of clusters. This approach only requires the specification of the first two marginal moment conditions. The likelihood function does not need to be specified or approximated. In the first part of the talk, we consider an extension of the classical theory of GEE to the large n, diverging p framework. We provide appropriate regularity conditions and establish the asymptotic properties of the GEE estimator. In particular, we show that the GEE estimator remains consistent and asymptotically normal, and that the large sample Wald test remains valid even when the working correlation matrix is misspecified. In the second part of the talk, we propose penalized GEE for simultaneous variable selection and estimation. The properties of the penalized GEE are investigated in the ``large n, diverging p" setting which allows the possibility of p>n. . Furthermore, we propose an effective iterative algorithm to solve the penalized GEE