Issue- I'm creating a logistic mixed model where the response variable (if a plot falls within an active bird lek area) is highly related to a term I may include as a random effects term (grazing allotment). This can be seen in the below map. The intention of the analysis is to examine vegetative differences on plots within (n=80) and outside (n=110) of active lek areas. The inventory was originally stratified by allotment and soil type. Most allotments are entirely within an active lek area (there are only 4 active lek areas) or outside of them. Therefore if I were to include allotment as a fixed effects term, it would be a great predictor of active lek area (although not informative). I want to account for the variability due to potentially different grazing intensities in the different allotments, but I don't want to have the model be predicting better merely because I included allotments in the model. Is it safe to include it as a random effects term?

How I think it works- Obviously, I don't completely get how these models work. From my understanding you would have different intercepts for each random effects grouping. This means for plots inside an allotment that is entirely within an active lek, the intercept (and slopes) could be anything for the plots to predict correctly, right? If that were correct, than I would not be able to relate vegetative differences as well to lekking areas. Do I have this right? Thank you in advance.

model<-glmer(ActLek~ CovLitter+HighMedGrassCov + NativeForbCover + HeiQ75 + ShrH75 + AllHeiCV + Elevation + SlopePerRise + (1|Allotment)+(1|soil), family=binomial(link="logit"), data=mtr, control=glmerControl(optimizer="bobyqa"))

Map of plots and allotment boundaries relative to active leks

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    $\begingroup$ Do you expect that two plots that are 1km apart and within an allotment will be more similar than if they were 1km apart but in distinct allotments? If the latter, then consider using a spatial random effect. But the main issue to me is that you have lots of spatial aggregation, and an effective sample size of 6 regions? $\endgroup$ – Andrew M May 25 '16 at 21:02
  • $\begingroup$ Thank you. I suspect they might be different but am not certain there are a different # of animals on different allotments and they sometimes graze in different seasons. But there is a lot of within-allotment variability in how livestock graze and which pasture they use. When I include allotment as random effects term, the model does a much better job in predicting (90%) withheld data and the fixed effects terms lose their significance. I am concerned that the model is performing better because certain allotments are totally within active lek areas (or outside them). $\endgroup$ – Mina May 26 '16 at 16:52
  • $\begingroup$ Plots were only located on federal lands within lek areas that had been used since 2003, which may explain why it looks aggregated. As far as sample size, I've only have plots within 6 active lek or habitat areas, but I would think the sample size would be the number of plots within those areas. $\endgroup$ – Mina May 26 '16 at 16:55
  • $\begingroup$ I would think the sample size would be the number of plots within those areas n=80, because those are all the active lek areas within the two public land tracts. So, the populations of active leks were sampled, although there were 6 spatial chunks. Had we used a smaller buffer around active leks there would actually be many more spatial chunks. $\endgroup$ – Mina May 26 '16 at 17:22
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    $\begingroup$ Hi Mina- trying to think of ways you can avoid this confounding. Instead of including allotment as a random effect to control for differences in grazing, do you have data on actual grazing intensity? If so, you could potentially drop the random effect and instead use grazing intensity as a continuous predictor. Otherwise, Your observations are not completely confounded, and so you may be just running inrto an issue of statistical power for the remainder of your fixed effects. $\endgroup$ – colin Jun 2 '16 at 14:27

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