[R-sig-ME] spatial auto-correlation or more complicated pseudo-replication?

[Thomas Merkling]

Dear Thierry,

Thanks for reply. We used a sample of the population for our experiment, 
but for this sample we have information (treatment and Prop variable at 
each scale for all the nests.
How would you suggest to test/check is there is spatial autocorrelation?
I tried with the DHARMa package (which makes a Moran's I test adapted to 
mixed models), but it doesn't show if autocorrelation changes with 
distance, it just gives a p-value. I tried with a model with PairID as 
random effect (p = 0.33), but if I include nest as a random effect (some 
pairs changed in between the 2 years of the experiment, so there are 
less Nest IDs than Pair IDs) the p-value becomes 0.054 ...

Kind regards,
Thomas

On 22/04/2020 13:57, Thierry Onkelinx wrote:
> Dear Thomas,
>
> Do you have information on all the nests or only on a sample of the 
> nests? In case you have data on every nest, then I would look at a 
> simple model with only treatment and an iid nest effect. Then see if 
> there is spatial autocorrelation. Variation at small ranges would 
> indicate an effect of the treatment of the neighbouring nests.
>
> Best regards,
>
> ir. Thierry Onkelinx
> Statisticus / Statistician
>
> Vlaamse Overheid / Government of Flanders
> INSTITUUT VOOR NATUUR- EN BOSONDERZOEK / RESEARCH INSTITUTE FOR NATURE 
> AND FOREST
> Team Biometrie & Kwaliteitszorg / Team Biometrics & Quality Assurance
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>
> Op wo 22 apr. 2020 om 11:44 schreef Thomas Merkling 
> <thomasmerkling00 using gmail.com <mailto:thomasmerkling00 using gmail.com>>:
>
>     Hi all,
>
>     I'm wondering how to best model data from an experimental design
>     involving a spatial component. This is a study on seabirds nesting on
>     artificial cliffs: each nest has been attributed an experimental
>     treatment (supplemented or not), while making sure that there was a
>     variable proportion of surrounding nests of the opposite
>     treatment. Our
>     main goal was to investigate if laying date of a focal pair was
>     influenced by its treatment and/or by the proportion of surrounding
>     nests of the opposite treatment (hereafter, "Prop"), which we
>     calculated
>     at 3 different spatial scale (local, panel and global, see
>     https://drive.google.com/open?id=1OrJQCkNfBO6KOBHSlkOoQyAdTrqtIdY8
>     for a
>     visual representation).
>
>     Hence, the treatment information of a focal pair is used in the
>     "Treatment" predictor variable, but also in the calculation of "Prop"
>     for the surrounding pairs (the number of pairs affected depending
>     on the
>     spatial scale considered), thereby leading to some
>     pseudo-replication.
>     Since this is dependent on the distance (i.e. "Prop" of pairs
>     closer to
>     a focal one are more influenced than pairs further away), we thought
>     that accounting for spatial auto-correlation for be sufficient. We
>     used
>     the spaMM package to do so, and our models look something like:
>
>     Laying ~ Treatment * Prop + Year + (1|PairID) + Matern(Y2011|x + y) +
>     Matern(Y2012|x + y)
>
>     with two Matérn correlation random effects (one for each year of the
>     study) being included (x and y being the spatial coordinates of
>     the nests).
>
>     My question is: Is this random effect structure taking into
>     account the
>     fact that "Prop" of a focal pair depends on the "Treatment" of the
>     surrounding pairs or not ? If not, how can we account for that?
>
>     Thanks in advance for your help!
>     Thomas
>
>
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