Journal
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume 107, Issue 497, Pages 205-213Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/01621459.2011.645785
Keywords
Correlation structure selection; Estimating functions; Generalized estimating equations; Homoscedasticity; Information unbiasedness; Perturbation
Categories
Funding
- U.S. National Science Foundation [DMS 0904177]
- Natural Science and Engineering Research Council of Canada
- Direct For Mathematical & Physical Scien [1208939, 0904177] Funding Source: National Science Foundation
- Division Of Mathematical Sciences [1208939, 0904177] Funding Source: National Science Foundation
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In this article, we focus on the circumstances in quasi-likelihood inference 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 model misspecification of the variance/covariance structure through a comparison between two forms of information matrix: the negative sensitivity matrix and the variability matrix. We establish asymptotic distributions of the proposed IR test statistics. We also suggest an approximation to the asymptotic distribution of the IR statistic via a perturbation resampling method. Moreover, we propose a selection criterion based on the IR test to select the best fitting variance/covariance structure from a class of candidates. Through simulation studies, it is shown that the IR statistic provides a powerful statistical tool to detect different scenarios of misspecification of the variance/covariance structures. In addition, the IR test as well as the proposed model selection procedure shows substantial improvement over some of the existing statistical methods. The IR-based model selection procedure is illustrated by analyzing the Madras Longitudinal Schizophrenia data. Appendices are included in the supplemental materials, which are available online.
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