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I'm working on an ecological study, where I've got 10 years of data for all 3000+ counties in the US. I'm interested in different perspectives on whether in a study like this one should weight the counties based on their population (of interest). More specifically, I'm modeling the relationship between drug prevalence and other characteristics among the general population, so I could weight the counties by their total population. Clearly, weighting will give dominance to urban areas and diminish the influence of rural areas on the estimates.

From my perspective, whether or not to include the weights depends on the research question of interest. If one is trying to get a national estimate, then weighting by population would be appropriate. If one is trying to describe the "average" county, then I'd suggest not using weights, so that each county is treated equally.

I know ecological analysis is done in a variety of fields, and I'm interested both in what people think in general, and then what is common practice in different fields. I'm working with public health experts, who generally have an epidemiological frame, but the work also crosses over into other social science fields.

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The exact answer to your question is: it depends.

If the ecological results were collected by a stratified sample, you might consider using weights for a number of reasons: to correct for the precision of the ecological-level estimates, to account for finite population sampling (in very small clusters), and/or to standardize results to a different population.

If you supply inverse probability weighting, where each participant takes as their weight the inverse of the probability of their sampling, you actually upweight participants from rural areas if the design is simple random sampling, and likely downweight participants from rural areas if the design is stratified sampling.

If you are using a heirarchical model, typically weights are obtained which roughly correspond to the precision of the county level results you obtain. But this fundamentally differs from other inference because the target of inference here is county level and not individual level.

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