GEE empirical se's vs model based se's

[emaguin]

With modelse specificied gee reports both empirical and model-based se's. I'll stipulate that somwhere the documentation discusses the differences but i didn't see it obviously. Could someone please educate me on the how and why they differ. Since the empirical se's are provide by default, i kind of assume that they are the preferred version but is there a brief background on that?

Thanks, Gene Maguin

[MichaelL_SAS · Accepted solution]

The "Parameter Estimate Covariances" section of the PROC GENMOD documentation describes the formulas for the model and empirical covariance matrix estimates. 

The model based estimate is the inverse of the generalized Hessian used in the GEE fitting algorithm. The empirical, or robust, covariance is a "sandwich" estimator that uses the inverse of the generalized Hessian as the "bread" and the outer product of the score functions as the "meat". 

The empirical estimate is the default because it is robust to misspecification of the working correlation structure, in particular it provides a consistent estimate for the covariance matrix even when the working correlation structure is misspecified. In general, the model based covariance matrix only provides a consistent estimate when the working correlation structure is correctly specified. 

One point to keep in mind when using the empirical covariance estimate is that when there are a small number of clusters or subjects in the data, it can tend to underestimate standard errors leading to more liberal tests and confidence intervals.