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Biometrika 2008 95(4):891-905; doi:10.1093/biomet/asn051
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© 2008 Biometrika Trust

Articles

Model diagnostic tests for selecting informative correlation structure in correlated data

Annie Qu

Department of Statistics, University of Illinois at Urban-Champaign, Champaign, Illinois 61820, U.S.A. anniequ{at}illinois.edu

J. Jack Lee

Department of Biostatistics, University of Texas, M.D. Anderson Cancer Center, Houston, Texas 77030, U.S.A. jjlee{at}mdanderson.org

Bruce G. Lindsay

Department of Statistics, The Pennsylvania State University, Pennsylvania 16802, U.S.A. bgl{at}psu.edu

Received for publication 1 August 2006. Revision received 1 March 2008.
  Abstract

In the generalized method of moments approach to longitudinal data analysis, unbiased estimating functions can be constructed to incorporate both the marginal mean and the correlation structure of the data. Increasing the number of parameters in the correlation structure corresponds to increasing the number of estimating functions. Thus, building a correlation model is equivalent to selecting estimating functions. This paper proposes a chi-squared test to choose informative unbiased estimating functions. We show that this methodology is useful for identifying which source of correlation it is important to incorporate when there are multiple possible sources of correlation. This method can also be applied to determine the optimal working correlation for the generalized estimating equation approach.

Key Words: Cancer prevention • Chi-squared test • Generalized estimating equation • Generalized method of moments • Goodness-of-fit test • Information matrix test • Model selection • Quadratic inference function • Working correlation


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