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

• Published in: Communications in Statistics - Theory and Methods Vol. 40; no. 21; pp. 3839 - 3856
• Main Authors: Gosho, Masahiko, Hamada, Chikuma, Yoshimura, Isao
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Taylor & Francis Group 01.11.2011; Informa UK Limited; Taylor & Francis
• Subjects: Balancing; Correlation; Covariance matrix; Criteria; Criterion; Distribution theory; Estimating; Exact sciences and technology; General topics; Generalized estimating equation; Longitudinal data; Mathematical analysis; Mathematics; Multivariate analysis; Parametric inference; Primary 62J12; Probability and statistics; Relative efficiency; Sciences and techniques of general use; Secondary 62H12; Simulation; Statistics; Working correlation structure; Rank statistic; Primary 62J 12; Statistical distribution; Generalized estimating equation; Non parametric estimation; Longitudinal data; Working correlation structure; Multivariate analysis; Statistical simulation; Relative efficiency; Parametric method; Hypothesis test; Statistical test; Criterion; Generalized equation; Selection criterion; Approximation theory; Test statistic; Secondary 62H 12; Correlation matrix; Structure equation; Time correlation; Statistical association; Statistical estimation; Covariance matrix; Statistical method; Selection problem; Correlation analysis; Estimating equation
• ISSN: 0361-0926; 1532-415X
• DOI: 10.1080/03610926.2010.501938

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.