Goodness of Fit Tests for Logistic GEE Models: Simulation Results

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Abstract
Generalized Estimating Equations (GEE) have become a popular regression method for analyzing clustered binary data. Methods to assess the goodness of fit of the fitted models have recently been developed. However, published evaluations of these methods under various scenarios are limited. Research conducted for the ordinary logistic regression model provided the basis for a newly computed mean and variance for the Pearson statistic and the unweighted sums of squares statistic for the GEE case. A simulation study was conducted to evaluate the performance of these statistics under various scenarios. The factors that were varied were the number of clusters, the number of observations within a cluster, the magnitude of the correlation, and the number and type of covariates included in the model. Overall, the Pearson and unweighted sums of squares statistics had a satisfactory performance of a type I error rate and are potentially effective in evaluating goodness of fit under certain conditions.