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

account

-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

applicable.

C. In my study spatial autocorrelation of the residuals wasn't present

anymore after fitting of the logistic regression model. So I was lucky!!!!

Best regards,

Kris

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

standardized

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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