spatial auto-correlation or more complicated pseudo-replication?

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 at inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be


///////////////////////////////////////////////////////////////////////////////////////////
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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

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Op wo 22 apr. 2020 om 14:58 schreef Thomas Merkling <
thomasmerkling00 at 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 at 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 at 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 Mat?rn 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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