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

[Thomas Merkling]

Dear Thierry,

Thanks for your answer.
Below is the piece of code I ran:
mod <- lmer(Laydate ~ Treatment + Year + (1|PairID), REML= FALSE, data = 
CRlF)
CRlF$resmod <- residuals(mod, type = "pearson")
plot(gstat::variogram(resmod ~ 1, loc = x+y, data = CRlF))

It seems like the variance is quite stable for distances up to 25 and 
then drops a bit. I did the same analysis with another response variable 
(egg weight) and got a similar pattern. (links to plot for laydate 
<https://drive.google.com/open?id=1T2n41DeSh0BlkZVX5t-E1IKdMuudujBy> and 
for eggweight 
<https://drive.google.com/open?id=10_ou4yQQkF-kVVnf7zbgHyMmUEABvnPU>)
So does it mean that there is no spatial auto-correlation then?

This would match the fact that our results don't change much if we add 
the Matern correlation random effects or not.
A reviewer suggested that spatial-autocorrelation isn't sufficient to 
account for the pseudo-replication in our data, and that we still have 
an issue of inflation of the degrees of freedom and suggested 
permutation tests to account for that, but is that really necessary?

Kind regards,
Thomas

On 22/04/2020 16:44, Thierry Onkelinx wrote:
> 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 <mailto:thierry.onkelinx using inbo.be>
> Havenlaan 88 bus 73, 1000 Brussel
> www.inbo.be <http://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 14:58 schreef Thomas Merkling 
> <thomasmerkling00 using gmail.com <mailto: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 <mailto:thierry.onkelinx using inbo.be>
>>     Havenlaan 88 bus 73, 1000 Brussel
>>     www.inbo.be <http://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 <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
>>
>>
>>                 [[alternative HTML version deleted]]
>>
>>         _______________________________________________
>>         R-sig-mixed-models using r-project.org
>>         <mailto:R-sig-mixed-models using r-project.org> mailing list
>>         https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>

	[[alternative HTML version deleted]]