Question about weighted logistic regression I'm helping a friend perform a logistic regression on field data pulled from several archeological sites. By chance the overwhelming majority of records in the analysis dataset were collected from a single site. 
In order to prevent the characteristics of this one site "overwhelming" the other sites, is it appropriate to apply weights (by site) to the records, say weight=1/(stnd error)? 
 A: I would not apply weights. Include a term for "site" in your logistic regression. It would not need to be a random effect, as Andrea suggests above. A fixed effect could be appropriate, depending on the number of sites and how they were chosen.
I think the algorithm "understands" that different numbers are involved and adjusts accordingly. Weighting takes place where the raw data are not involved but only a mean (or proportion) from each group is recorded. You then need to weight the means by group size. 
However if the sites are fairly heterogeneous, and the bulk of your data comes from only one, it might be wiser to limit the analysis to that one site. 
A: I have been thinking about this some more and I am concerned that the parameter estimates of the model might be swamped by the larger site. I suggest that after fitting the model, you pay close attention to how the residuals look by site. If your model is basically fitting the big site and letting everything else slide, you should see patterns of residuals if you plot residuals against site.
If there is a problem, I was thinking that you could select random samples of items from the big site - sample size to be similar to the other sites - and fit a bunch of models that way. You could average parameter values over the sampled estimates.
