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I have a large set of point count data from 15 different sites that I wish to compare using R studio. Each site was surveyed multiple times each month from 2006-2015, except for some sites which were only surveyed for a year or two. Is it possible to compare counts across all sites using a mixed-effects model even though the sampling effort at each site has such a wide range?

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Yes.

  • mixed-effects models are particularly well suited to unbalanced designs, as groups with less data will automatically get "shrunk" toward the overall (population) mean values
  • there is some discussion about "how many groups are enough" for mixed modeling, e.g. here, but 15 would at least be considered "medium" (as opposed to <5, which would almost definitely be too few, or >50, which would almost definitely considered plenty)
  • we might need to know a little bit more about what you want to know: what does "compare counts across all sites"? If you want to test whether particular sites have statistically significantly different occupancy probabilities from other sites, and you're following a standard frequentist approach, then you need to treat site as a fixed effect rather than a random effect ...
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