Criterion for the Selection of a Working Correlation Structure in the Generalized Estimating Equation Approach for Longitudinal Balanced Data

Abstract The generalized estimating equation is a popular method for analyzing correlated response data. It is important to determine a proper working correlation matrix at the time of applying the generalized estimating equation since an improper selection sometimes results in inefficient parameter estimates. We propose a criterion for the selection of an appropriate working correlation structure. The proposed criterion is based on a statistic to test the hypothesis that the covariance matrix equals a given matrix, and also measures the discrepancy between the covariance matrix estimator and the specified working covariance matrix. We evaluated the performance of the proposed criterion through simulation studies assuming that for each subject, the number of observations remains the same. The results revealed that when the proposed criterion was adopted, the proportion of selecting a true correlation structure was generally higher than that when other competing approaches were adopted. The proposed criterion was applied to longitudinal wheeze data, and it was suggested that the resultant correlation structure was the most accurate. Keywords: CriterionGeneralized estimating equationLongitudinal dataRelative efficiencyWorking correlation structure2000 Mathematics Subject Classification: Primary 62J12Secondary 62H12 Acknowledgments The authors would like to thank Mr. Masakazu Andoh of Rho, Inc., for his valuable comments. They are also grateful to the two reviewers for their constructive comments and suggestions. Notes IN: independent; EX: exchangeable; AR: AR(1); TS: time-stationary; TV: time-varying. IN: independent; EX: exchangeable; AR: AR(1); TS: time-stationary; TV: time-varying. EX: exchangeable; AR: AR(1); TS: time-stationary; TV: time-varying. EX: exchangeable; AR: AR(1); TS: time-stationary; TV: time-varying. EX: exchangeable; AR: AR(1); Specified corr: specified working correlation structure.