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Goodness-of-fit in two models for clustered binary data
Generalized Estimating Equations (GEE) and Mixed Effects Logistic Models have become popular methods for analyzing clustered binary data when regression is the primary focus. However, methods to assess the goodness of fit of the fitted models are not well developed. Recent work concerning the independence case of ordinary logistic regression provides the basis for a newly computed mean and variance for the Pearson chi-square statistic and the unweighted sums of squares statistic for the clustered binary data case. A simulation study was conducted to evaluate the performance of the Pearson chi-square statistic. the unweighted sums of squares statistic. as well as the Hosmer-Lemeshow statistic for the GEE model. Another simulation study was conducted to evaluate the performance of the several versions of the Pearson chi-square statistic. an unweighted sums of squares statistic, a Deviance statistic, as well as the Hosmer-Lemeshow statistic far the mixed effects logistic model. The factors that were varied were the number of clusters, the number of observations within a cluster, the magnitude of the correlation or random effect, and the number and type of covariates included in the model. The proposed methods were then applied to real data sets. Overall, several of the statistics that were examined had a satisfactory performance of a Type I error rate and are potentially effective in evaluating goodness of fit under certain conditions. Limitations are discussed.
Evans, Scott Richard, "Goodness-of-fit in two models for clustered binary data" (1998). Doctoral Dissertations Available from Proquest. AAI9841867.