[R-sig-Geo] Moran test on residuals of a logistic regression

[Roger Bivand]

On Tue, 19 Sep 2006, guis at teledetection.fr wrote:

> Hi
> 
> I have a logistic regression model, and I would like to see if the
> residuals of this model are spatially autocorrelated. I saw that the
> lm.morantest function could be used to test for autocorrelation in
> residuals from a linear model (lm). Does a similar function exist for
> residuals of a logistic regression models? (one of the arguments of the
> lm.morantest is an lm object: x.lm)

No, it doesn't.

> I thought of extracting the residuals of my model (with the residuals
> function) and then applying a moran.test, but I read that this wasn't
> correct as there was no correction for the fact that these were residuals
> (I didn't understand why). 

The classic reference is Cliff and Ord (1981) p. 200, section 8.2.4, who 
point out that sample model residuals are correlated anyway, because they 
are estimated using the fitted regression coefficients. An alternative 
they also mention but discard is to test n-k independent BLUS residuals, 
chosen by dropping k spatial units. They also state that "random 
permutations are not the appropriate reference set for testing the 
residuals". So lm.morantest() or its Saddlepoint approximation equivalent 
are the only game in town for Moran's I of regression residuals. Of course 
I can be computed, but the basis for inference will most likely be 
unsound.

> Is there a way to specify that the moran.test is
> applied to residuals, making it possible to use this function in my case? 
> I have a last question : if I extract residuals of the logistic models,
> what type of residuals should I choose : deviance, pearson, working,
> response, partial...?

(All responsibility waived!!)

If you replace the test:

if(class(model) != "lm")

in lm.morantest()

with:

if(!inherits(model, "lm"))

lm.morantest() will "work" for some definition of work on glm objects 
using deviance residuals. Until somebody tests this properly, I would 
certainly not advise using the output for anything other than electron 
recycling.

Hope this helps,

Roger

> I would be grateful for any help
> Thanks
> 
> Helene Guis
> PhD student CIRAD - University of Franche-Comté, France.
> guis at teledetection.fr
> 
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no