[R-sig-Geo] testing prediction of estimated spatial models

[Roger Bivand]

On Tue, 17 Apr 2012, Roosbeh Nowrouzian wrote:

> Dear lest members:
>
> After spatial model specification, estimation, and testing specification,
> the predictive ability of estimated model should be tested. prediction is
> of interest of practitioners. At this point I have estimated a
> Spatial Auto-regressive model.

Yes and no. Most spatial regressions are not intended to be used for 
prediction. In both econometrics and ecology, the analyst is most 
interested in the significance or not of the model coefficients, and in 
making inferences about them. Prediction is not central here.

If the spatial process is expressed by a weights matrix rather than by a 
variogram, it is less obvious how to predict onto an extended graph, 
rather than a continuous surface. If the prediction locations have point 
support, and the weights are defined as function of distance, then you may 
get close to the geostatistical predictive setting, but with a rather 
primitive model of the spatial process. If the prediction locations have 
other support and/or the weights are not defined in terms of distance, the 
relationship is less obvious (see Melanie Wall, 2004).

> My question is after dividing the data to
> training set and testing set, how can I apply estimated
> model(Using training data set ) to the testing data set which I have the
> location and all explanatory variables. So by comparing predicted value to
> observed, the predictive ability of model can be estimated. Or is there any
> tool to define Cross Validation of estimated model (I believe writing a
> loop to exclude a point and estimate the model and then predict the value
> for that point and compare to the observed value takes so much time and is
> not possible).

I had a speculative paper in Journal of Geographical Systems (2002) about 
this, but work is continuing on establishing the options for adequate 
prediction in spatial regession, that paper used ad-hoc approaches that 
are not necessarily sound.

The predict() method for sarlm objects in spdep does provide what you may 
need, using the training+test data set as newdata, with spatial weights 
for both training and test locations.

Hope this helps,

Roger

> I like to know your opinion about this issue and appreciate your help
> regarding this issue.
>
> Thanks
> Roosbeh Nowrouzian
> PhD student
> Department of Civil and Coastal Engineering
> University of Florida
>
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>
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-- 
Roger Bivand
Department of Economics, NHH Norwegian School of Economics,
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