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Goodness‐of‐fit Tests for GEE with Correlated Binary Data
Author(s) -
PAN WEI
Publication year - 2002
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00091
Subject(s) - mathematics , goodness of fit , statistics , covariate , logistic regression , binary data , statistic , pearson's chi squared test , test statistic , chi square test , residual , logistic distribution , press statistic , regression analysis , binary number , econometrics , statistical hypothesis testing , ancillary statistic , algorithm , arithmetic
The marginal logistic regression, in combination with GEE, is an increasingly important method in dealing with correlated binary data. As for independent binary data, when the number of possible combinations of the covariate values in a logistic regression model is much larger than the sample size, such as when the logistic model contains at least one continuous covariate, many existing chi‐square goodness‐of‐fit tests either are not applicable or have some serious drawbacks. In this paper two residual based normal goodness‐of‐fit test statistics are proposed: the Pearson chi‐square and an unweighted sum of residual squares. Easy‐to‐calculate approximations to the mean and variance of either statistic are also given. Their performance, in terms of both size and power, was satisfactory in our simulation studies. For illustration we apply them to a real data set.