I asked a related question before here on the difference between GEE method with exchangeable varcov structure v. Robust standard errors known as Huber White method in group randomized trials. As Macro pointed out Freedman in his 2006 paper The American Statistician called On The So-Called “Huber Sandwich Estimator” and “Robust Standard Errors explains that with a little modification of the huber white method, we can get valid inference by both solving the issue with Heteroscedasticity and Correlation among clusters.
I have a study with 34 schools randomly assigned to treament/control. The ICC in the study is 0.04 (although is small but is statistically significant, more info here) with the design effect of 17.7. The ICC indicates some degree of similarities among students within schools (i.e. clusters). Schools have different number of students varying from 150 to 800.
My question is if you wanted to analyze the data, which method you would choose to get valid inference? Huber-White or GEE with exchangeable varcov matrix? I'm in favor of GEE because of two reasons:
1) we have unbalanced clusters 2) Our estimates with GEE are more efficient.
If you choose GEE, could you explain why and what GEE can do that HuberWhite cannot do and the other way around?
I appreciate your help.