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I am modelling whether a bird nest is build or not based on the date it was built, the geographical coordinates where the nest was built, and using the year when the nest was built as random effect - I am using generalised additive mixed models in R to do this.

My model: gam(Nest_building ~ s(Date) + te(Lon, Lat) + s(Year, bs="re")

My question concerns the spatial distribution of my nests: nests are distributed in patches of forests (i.e. there are gaps between the patches), rather than all in one big continuous forest patch. Should I account for this in my model? if so, how can I do this using GAMMs?

Thanks!

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What you are describing is called spatial autocorrelation: Observations physically closer to each other are assumed to be more strongly correlated to each other.

A common approach is to either:

  1. Include latitude and longtitude as fixed effects in the model. This is discussed here.
  2. Estimate the correlation as part of the GAMM fitting procedure using corExp(1, form = ~ Latitude + Longitude) as shown here (and also discussed in the other linked question).
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  • $\begingroup$ Hi @Frans Rodenburg, thanks for your answer. I am already including the greographical coordinates as fixed effect in my model (specifically as a 2-dimensional full tensor product smoother), as I mentioned in my question - I have detailed my model in my question now :) . Is it enough to include geographical coordinates as fixed effects in the regression model enough to account for big gaps (couple of km) between forest patches? $\endgroup$
    – Teresa
    Commented Jul 15 at 13:12
  • $\begingroup$ I am asking again because I remember that in a stats course the teacher explained that such big gaps with no information affect the outcome of the regression model, but I cannot find any information on how to deal with this. $\endgroup$
    – Teresa
    Commented Jul 15 at 13:22
  • $\begingroup$ @Teresa I do not think that these gaps you explain are an issue. I would suggest you try both methods and see what works well. Try plotting the (deviance) residuals against the latitude/longitude to see if there is still correlation remaining. $\endgroup$
    – Frans Rodenburg
    Commented Jul 15 at 13:59

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