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Can a random effects intercept variable be highly andbut coincidentally correlated to a response variable?

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Can a random effects variable be highly and coincidentally correlated to a response variable?

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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 and slopes for each random effects grouping. This means for plots inside an allotment that is entirely within an active lek, the intercept and slope(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

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 and slopes for each random effects grouping. This means for plots inside an allotment that is entirely within an active lek, the intercept and slope 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

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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