Hi Alexandre
I came across this interesting paper (may be of use)
Spatial autocorrelation, model selection and hypothesis testing in geographical
ecology: Implications for testing metabolic theory in New World amphibians
Fernanda A.S. Cassemiro, José Alexandre Felizola Diniz-Filho, Thiago Fernando
L.V.B. Rangel, Luís Maurício Bini
Neotropical Biologyand Conservation 2, 3 (2007).
I like the work of de Smith, Goodchild and Longley (2015). See Geospatial
Analysis - spatial and GIS analysis techniques and GIS software
Also look up differing model selection techniques - you don't have to use AIC -
there are plenty of others to use and try.
Best
Ling
Ling HuangSacramento City College
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On Saturday, September 12, 2015 8:29 PM, Alexandre Fadigas de Souza
<[email protected]> wrote:
Hello,
A few days ago I posted the following question on how to incorporate spatial
autocorrelation in a multivariate GLM. I got some kind answers, which I thank
and reproduce below.
Regards,
Alexandre
************
Dear friends,
I would like to ask for some advice.
I am embarking in the analysis of 3,000 plant species occurrence data across
biogeographic scales in South America. I am willing to try to jump from more
traditional distance-based multivariate analysis (e.g., RDA on
hellinger-transformed abundance data) to multivariate GLM as proposed by you
(mvabund package) and also by Yee (VGAM package).
However, distance-based methods have grown to incorporate spatial dependency
through the development of MEM and AEM techniques, which model symmetric and
asymmetric spatial relationships and can be included in the explanatory side of
the analysis.
Reading the multivariate GLM papers, however, I have not find exactly how to
control or include spatial autocorrelation. I am thinking of including MEM and
perhaps AEM variables simply as co-variables added to the explanatory
environmental variables in the multivariate GLM.
Is this a step I will regret later on? Is this ok?
A second quick wondering: common GLM analyzes are carried out as a series of
nested models in which we exclude variables from an initial full model based
on anovas/AIC. I suppose this is also true for multivariate GLM. Is it? Can I
compare successive models using the same approach used in common GLM?
Thanks in advance for any thoughts,
All the best,
Alexandre
Replies **************************
Hi Alex,
Thanks for the e-mail, sounds like interesting stuff!
Yes you could as you say use the MEM and AEM techniques with manyglm, while
this is not the best of approaches for handling spatial data, it is the
simplest and currently the best one given the current lack of code for an
alternative.
And yes you could use an AIC approach for model selection.
***
Hi,
the only thing i am aware of is the spatial autocorrection function available
in the nlme package:
for example:
null.model <- lme(fixed = A~B, data = data, random = ~ 1 | dummy, method="ML")
cor.model <- update(null.model, correlation = corExp(form = ~ x + y), method =
"ML")
argument "correlation" accepts several forms of spatial models based on
variogram (here exponential based on xy coordinates). One can extract model
goodness with extract.aic() or just summary().
However, this is univariate glm (but can be extended to interaction) and as far
as i was told these procedures only exist for gaussian distributions, not for
poisson/NB, which are better for species data most of the time.
I was looking for the same, but in the end i went back to RDA with dbMEMs and
used the aforementioned procedure
only for highly correlated univariate pairs in the dataset.
Please let me know, if you are more successful.
***
Hi Alexandre,
Not sure what the best solution is, but a few hacker ideas come to mind.
First, you could create a spatially lagged variable from scratch. This would
be created by deciding on a neighborhood size, say first order neighbors, and
then creating a variable that was the average response (Y) value for the first
order neighbors. Neighborhood size could be guestimated by looking at residual
maps. This is similar to what happens in simultaneous autoregressive (SAR)
lagged models. Then this lagged variable could be a fixed covariate in your
model. You could test residuals from the lagged model to see if this removed
your spatial autocorrelation.
Since you mentioned a GAM approach, you could also do a spatial GAM, where Lat
and Long variables are specified as smooth covariates with lots of knots to
account for short range spatial structure. Again, you could test your residuals
to see if this removed your spatial autocorrelation.
If you are comfortable with Bayesian modeling, Banerjee et al. (2015,
‘Hierarchical modeling and analysis for spatial data’) have a chapter on
multivariate spatial modeling, with a brief mention of generalized linear
models.
Some food for thought.
***
Alexander,
Any chance you might include spatial dependency (however you may choose to do
it) as a random effect in a mixed-model structure? This way you can either run
the model with the spatial dependency to test this explicitly or remove this
effect from the model structure.
And yes, you can use AIC to rank multivariate models.
Just a quick note.
***
Furthermore I received the suggestion to read the following papers:
Spatial factor analysis: a new tool for estimating joint species distributions
and correlations in species range
James T. Thorson1*, Mark D. Scheuerell2, Andrew O. Shelton3, Kevin E. See4,
Hans J. Skaug5
and Kasper Kristensen. Methods in Ecology and Evolution 2015
Geostatistical delta-generalized linear mixed models improve precision for
estimated abundance indices for West Coast groundfishes. James T. Thorson1*,
Andrew O. Shelton2, Eric J. Ward2, and Hans J. Skaug. ICES Journal of Marine
Science; doi:10.1093/icesjms/fsu243
The importance of spatial models for estimating the strength of density
dependence.JAMES T. THORSON,1,6 HANS J. SKAUG,2 KASPER KRISTENSEN,3 ANDREW O.,
HELTON,4 ERIC J.WARD,4 JOHN H. HARMS,1 AND JAMES A. BENANTE. Ecology, 96(5),
2015, pp. 12021212.
