[R-sig-ME] Is my model correct (1 random effect + spatially structured outcome) ?

[t***@uni-bremen.de]

Dear list,

i have already posted once about this dataset, however now with a
different approach.

My dataset consists of six sampling dates (several months apart) with
60 sampling stations each (within 100 square meters).
Initially, i wondered if i can calculate Tukey contrasts by sampling
dates if they are possibly both fixed and random.
This time, my approach is fairly basic. I would like to model the
influence of some environmental predictors (e.g. pH) on my outcome.
I dont think my stations (specified with x,y coordinates) have random
intercepts (as they are close to each other), but they likely feature
spatial autocorrelation.
This time, i treat time as random, and since the sampling dates are
months apart, and the sampling grid was always different, i assume
there is no temporal autocorrelation or effects
of repeated measures.
So, i would then fit a model like this:

model1 <- lmer(Outcome ~ Var1+Var2+...+(1|sampling date),
correlation=corXXXX(1,form=~x+y), data=data, REML=false)
(alternatively also as interaction between the fixed effect).

Assuming that i have normally distributed outcomes (which i dont), is
this a proper approach?

Alternatively, i could fit a model for each of the six sampling dates
independently, and not use random effects at all.

Thank you!

[Thierry Onkelinx]

Dear Tim,

lmer() from lme4 cannot handle correlation functions. lme() form nlme
can. But there the correlation is only within the most detailed level
of the random effects. Observations from different levels (here
sampling dates) are assumed to be independent. However they will share
the same parameters for the correlation function.

Another option would be to fit the model without spatial correlation
structure and then make a variogram of the residuals. It might be
harder to get a stable variogram with only 60 locations. If the
variogram indicates spatial correlation, then you will have to model
it.

Also provide sensible starting values for the correlation function.
The default value for the range is very small, often resulting in a
very small fitted range.

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
***@inbo.be
Havenlaan 88 bus 73, 1000 Brussel
www.inbo.be

///////////////////////////////////////////////////////////////////////////////////////////
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more than asking him to perform a post-mortem examination: he may be
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The plural of anecdote is not data. ~ Roger Brinner
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not ensure that a reasonable answer can be extracted from a given body
of data. ~ John Tukey
///////////////////////////////////////////////////////////////////////////////////////////

Post by t***@uni-bremen.de
Dear list,
i have already posted once about this dataset, however now with a different
approach.
My dataset consists of six sampling dates (several months apart) with 60
sampling stations each (within 100 square meters).
Initially, i wondered if i can calculate Tukey contrasts by sampling dates
if they are possibly both fixed and random.
This time, my approach is fairly basic. I would like to model the influence
of some environmental predictors (e.g. pH) on my outcome.
I dont think my stations (specified with x,y coordinates) have random
intercepts (as they are close to each other), but they likely feature
spatial autocorrelation.
This time, i treat time as random, and since the sampling dates are months
apart, and the sampling grid was always different, i assume there is no
temporal autocorrelation or effects
of repeated measures.
model1 <- lmer(Outcome ~ Var1+Var2+...+(1|sampling date),
correlation=corXXXX(1,form=~x+y), data=data, REML=false)
(alternatively also as interaction between the fixed effect).
Assuming that i have normally distributed outcomes (which i dont), is this a
proper approach?
Alternatively, i could fit a model for each of the six sampling dates
independently, and not use random effects at all.
Thank you!
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