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

[Thierry Onkelinx]

Dear Thomas,

Extract the residuals from the model. Then use gstat::variogram() to
calculate the empirical variogram of the residuals.  If there is spatial
autocorrelation, you'll see an increase in the variance as the distance
between observations increases.

I would expect that the birds have a stronger effect than the nests. Hence
I'd use Pair ID. If the dataset would span more than 2 years you could try
both a Pair and Nest random effect.

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
thierry.onkelinx using inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

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Op wo 22 apr. 2020 om 14:58 schreef Thomas Merkling <
thomasmerkling00 using gmail.com>:

> 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
> thierry.onkelinx using inbo.be
> Havenlaan 88 bus 73, 1000 Brussel
> www.inbo.be
>
>
> ///////////////////////////////////////////////////////////////////////////////////////////
> To call in the statistician after the experiment is done may be no more
> than asking him to perform a post-mortem examination: he may be able to say
> what the experiment died of. ~ Sir Ronald Aylmer Fisher
> The plural of anecdote is not data. ~ Roger Brinner
> The combination of some data and an aching desire for an answer does not
> ensure that a reasonable answer can be extracted from a given body of data.
> ~ John Tukey
>
> ///////////////////////////////////////////////////////////////////////////////////////////
>
> <https://www.inbo.be>
>
>
> Op wo 22 apr. 2020 om 11:44 schreef Thomas Merkling <
> 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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>>
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