The models are used in the same way as standard generalised linear models, and the coefficients have the same interpretation. They measure differences in the response for a unit change in the predictor, averaged over the whole sample. GEE models are thus particularly suitable when the correlation is of no substantive interest and is merely a nuisance parameter.
The data used for the example in section 3 illustrate a common, but very simple situation. The number of hospital visits for 72 children were recorded, together with the sex of the child and the age and smoking status of the mother. We are interested in whether maternal smoking is related to the number of hospital visits and the obvious analysis is a Poisson regression. The complication is that the number of hospital visits was recorded over four separate time periods. Using these as separate observations violates the independence assumption for Poisson regression; adding them together to get a single outcome is likely to result in overdispersion and loses any information about variation over time.
With a working covariance model of independence the parameter estimates will be the same as from a Poisson regression, but the standard errors will be valid. This is often sufficient, especially when the correlations are not too high and the number of observations on each individual is the same.
Another popular model is the exchangeable correlation model, in which all pairwise correlations between different times are the same. This is analogous to the popular but unreliable method of analysing repeated Normal measurements using split-plot ANOVA. An exchangeable correlation GEE fits the same working modelbut gets asymptotically valid standard error estimates even when the correlations are not truly exchangeable.
It is probably the case that observations close together in time are more similar than those far apart in time. A working covariance model that incorporated this structure might give better estimates. One possible correlation structure for these data would be stationary 3-dependence. This working model estimates three correlation parameters: the correlations at lag 1, lag 2 and lag 3. If there were sufficient data it would even be possible to estimate all 6 correlation parameters. This is known as the ``saturated'' working model. In addition to possibly greater efficiency these alternative working models provide estimates of the correlations between different time points. It should be noted, however, that these estimates have low efficiency and may be biased if the working model is not close to the truth.
Little is known about good ways of choosing correlation structures. The options provided in this implementation allow reasonable flexibility to approximate a wide range of structures. In the next section these data are analysed in Lisp-Stat using multiple correlation structures and diagnostic methods.