JSM 2011 Online Program

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Abstract Details

Activity Number: 83
Type: Contributed
Date/Time: Sunday, July 31, 2011 : 4:00 PM to 5:50 PM
Sponsor: IMS
Abstract - #303032
Title: Model Selection for Correlation Structure for Diverging Clustered Data
Author(s): Peng Wang*+ and Jianhui Zhou and Annie Qu
Companies: University of Illinois at Urbana-Champaign and University of Virginia and University of Illinois at Urbana-Champaign
Address: 101 Illini Hall, 725 South Wright Street, Champaign, IL, 61820, United States
Keywords: Generalized estimating equations ; Generalized information criterion ; Longitudinal data ; Oracle property ; Penalized estimating functions ; SCAD penalty

Identifying the correct correlation structure is essential in longitudinal and spatial data analysis. However, model selection for correlation structure remains a challenging problem due to lack of the likelihood function for non-normal data, and when the cluster size diverges as the sample size increases. We propose an alternative approach which approximates the inverse of the empirical correlation matrix using a linear combination of candidate basis matrices, and select the correlation structure by identifying groups of basis matrices with non-zero coefficients. This is carried out by minimizing the penalized estimating functions, which balances the complexity and informativeness of the correlation matrix. The new approach does not require estimating each entry of the correlation matrix, nor the specification of the likelihood function, and can effectively handle non-normal correlated data. Asymptotic theory on model selection consistency and oracle properties are established in the framework of diverging cluster size of correlated data. Our numerical studies indicate that even when the cluster size is quite large, the correlation structure can be identified effectively.

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