Goodness-of-fit for GEE: an example with mental health service utilization

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Abstract
Suppose we use generalized estimating equations to estimate a marginal regression model for repeated binary observations. There are no established summary statistics available for assessing the adequacy of the fitted model. In this paper we propose a goodness‐of‐fit test statistic which has an approximate chi‐squared distribution when we have specified the model correctly. The proposed statistic can be viewed as an extension of the Hosmer and Lemeshow goodness‐of‐fit statistic for ordinary logistic regression to marginal regression models for repeated binary responses. We illustrate the methods using data from a study of mental health service utilization by children. The repeated responses are a set of binary measures of service use. We fit a marginal logistic regression model to the data using generalized estimating equations, and we apply the proposed goodness‐of‐fit statistic to assess the adequacy of the fitted model. Copyright © 1999 John Wiley & Sons, Ltd.