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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)?

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    $\begingroup$ If you have different sites and more measurements for each site, I would use a multilevel model. en.wikipedia.org/wiki/Generalized_linear_mixed_model $\endgroup$
    – boscovich
    Oct 1, 2012 at 21:00
  • $\begingroup$ Thanks @andrea - I'm planning on running a random intercepts model w/ proc glimmix in SAS. I just got hung up on the weighting issue. $\endgroup$
    – RobertF
    Oct 2, 2012 at 2:53
  • $\begingroup$ no need to use any kind of weight, then. $\endgroup$
    – boscovich
    Oct 2, 2012 at 4:51

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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.

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  • $\begingroup$ Thank you @Placidia, this is helpful. I was considering a random effect for the site variable since in effect there are an indeterminate number of similar archaeological sites throughout Europe given the number of urban areas during this period (Roman Empire), of which only a handful have been excavated. Here I'm presuming those sites which have been excavated are a random sample from this larger population of sites. $\endgroup$
    – RobertF
    Oct 2, 2012 at 15:46
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    $\begingroup$ @Placidia is right: site needs not to be random, but I see why you (@RobertF) want to model it as such. But also consider the number of sites you sampled from. If they're too few, maybe using a random effect for site might not be a good idea. $\endgroup$
    – boscovich
    Oct 3, 2012 at 9:25
  • $\begingroup$ PS (@RobertF): to be clear, when I say "site needs not to be random", I am thinking of conditional (fixed-effects) logistic regression $\endgroup$
    – boscovich
    Oct 3, 2012 at 9:38
  • $\begingroup$ I'm sorry, I should have specified - there are 17 sites in my friend's sample, with # records per site ranging from 4 to 373 for 16 of those sites, plus a single site with 1,386 records. It's not a big sample, but perhaps large enough to warrant using a random effect? $\endgroup$
    – RobertF
    Oct 3, 2012 at 18:31
  • $\begingroup$ Based on what you describe, I agree that "site" should be random. $\endgroup$
    – Placidia
    Oct 3, 2012 at 21:30
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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.

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