Good questions.
For binary data, the correlation between two observations is going to be constrained by their means. This relationship is not accounted for in the moment based estimator GEE models typically use for the working correlation matrix. As a result you, could end up with predicted means from the response model and a working correlation matrix estimate that violate the range restrictions.
Often these potential range restriction violations are ignored since for most applications of GEE models the association between the observations is treated as a nuisance parameter and the primary scientific interest is in the response model.
In situations where the the association between observations might be of interest, or you are especially concerned about possible range violations for some reason, one alternative would be to use alternating logistic regression. This approach models the association between pairs of binary observations by using a model for the logarithm of the odds ratio instead of correlations. Both PROC GEE and PROC GENMOD support the use of alternating logistic regression for binary response data. PROC GEE also supports an extension of alternating logistic regression for ordinal response data. To request the use of alternating logistic regression in either procedure, you would use the LOGOR= option instead of the TYPE= option in the REPEATED statement.
For examples of using alternating logistic regression for binary response data, you can see Example 48.6 in the PROC GENMOD documentation or Example 47.4 in the PROC GEE documentation. Example 47.5 in the PROC GEE documentation provides an example of alternating logistic regression for ordinal response data.
For more information about alternating logistic regression, you can also refer to the "Alternating Logistic Regression" section in the documentation for either PROC GEE or PROC GENMOD.
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