GEOSTATS: logistic regression with spatially autocorrelated data-Answers
Herewith a summary of the answers and comments on my question about logistic
regression (see below for the original message).
Overall, it seems that many people are working with logistic regression of
spatially autcorrelated data. However, the solutions for this problem are
scarce and often very complex..
A. To test for spatial autocorrelations of the regression residuals, A.
Lister and A. Getis suggest the use of the Moran coefficient. This can be
done with Spacestat for instance.
Gilles Bourgault remarked that while fitting semivariograms of the
standardized regression residuals - as I have done -, the nugget effect is
often overestimated since there is a lack of measurements for the short lag
distances (I' m working with a 20m x 20m grid). However, I don't think this
is a problem since the only thing we want to do is to test if the samples we
are working with are spatially autocorrelated. So, in my opinion, it doesn't
matter if spatial autocorrelation is present at shorter lag distances!
B. If the degree of spatial autocorrelation is much larger than can be
explained from the spatial covariates (which means that the residuals are
still spatially autocorrelated), then models should be build that properly
account for both the spatial autocorrelation and the dependence on covariates
(Huffer & Wu , 1998).
In the following papers spatial autocorrelation is explicetely taken into
-Huffer & Wu (1998) Biometrics 54, 509-524. 'Markov Chain Monter Carlo for
Autologistic Regression Models with application to the distribution of plant
species' Fred Huffer has written a Fortran/S-plus program for this which is
available on the website of Florida State University.
-Heagerty & Lele (1998) Journal of the American Statistical Association
93(443), 1099-1111. A composite likelihood approach to binary spatial data
-Albert & McShane (1995) Biometrics. A generalized estimating equations
approach for spatially correlated binary data
-Chung & Agterberg (1980) Mathematical Geology. Regression models for
estimating mineral resources from geological map data
However, most of these methods are not straithforward and not easily
C. In my study spatial autocorrelation of the residuals wasn't present
anymore after fitting of the logistic regression model. So I was lucky!!!!
Original message :
"In a +/- 25ha forest, I've mapped the forest ground flora on the basis of a
20m x 20m grid (a total of > 700 grid cells). Quite logically, the
distribution of the mapped plant species is not random, but exibits a high
degree of spatial autocorrelation.
In order to explain the spatial distributions of these plant species, I
performed a logistic regression with the species presence/absence data and pH,
soil type, illuminance, ... as indipendent variables.
To check for spatial autocorrelation I calculated semivariograms for the
residuals of the logistic regressions.
Is the applied method correct and are my conclusions justified?"
Laboratory for forest, nature and landscape research
Vital Decosterstraat 102, B-3000 Leuven
tel. : +32-16 329737 fax. : +32-16 329760
e-mail : kris.verheyen@...
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