[R-sig-Geo] How to test spatial dependence in errorsarlm

[Roger Bivand]

On Mon, 14 Aug 2017, Javier García wrote:

> So testing for spatial dependence on the residuals by means of the
> lm.LMtests (option LMerr, the only that works with residuals) is wrong,
> isn't it? I had read in some forum that this was a posible way to test it...

There was some speculation that these tests might be used on an lm fit of 
the (I - \lambda W) y ~ (I - \lambda W) X model. These speculations have 
never been checked rigorously, so nobody knows whether they are of any 
value, probably not, and certainly we know nothing of their inferential 
basis.

>
> In my case the Moran test and the LM tests (both LMerr and LMlag, and 
> also their robust versions) are strongly rejected (p-values between 
> 4.307e-06 and 2.2e-16). As the rejection is stronger for the spatial 
> error model, my suspicion was that this could be the best model to 
> capture the spatial dependence (in fact the log-likelihood is bigger for 
> the spatial error model, and the AIC lower). However, how can I know 
> whether the spatial error model is a good option if I cannot test the 
> absence of spatial dependence in the residuals?

You by definition fix X and W as known, exogeneous, quantities. If X (and 
functional forms) and/or W do not meet these requirements, there is little 
good guidance. It depends on what you want: predict house prices where 
they are not observed; estimate \beta values; estimate the impact of a 
unit change in an X variable on house prices (y); whatever. A best-fit 
model suggests that you want to predict, but isn't necessary for impacts 
or betas if you trust X (and its functional forms) and W.

> And how can I know, as you suspect, whether I have a
> misspecification problem?

See a good deal of work by Daniel McMillen on these issues.

> Moreover, I also estimated the Durbin model, and in this case the LM 
> test on the residuals suggests no spatial dependence (for the spatial 
> lag model I get the opposite conclusion), but due to the nature of my 
> regression I don't think that this model is suitable (the regressors are 
> characteristics of houses such as size, number of rooms, etc).

This suggests that SLX or SDEM (see LeSage 2014 and SLX articles for a 
discussion) may address many of the issues of spatial autocorrelation by 
including (selected) WX. The Durbin versions of spdep functions do not 
(yet) let you choose which WX to include, always including all X - this is 
on my medium-term to-do list.

Roger

>
> Thanks a lot for your time.
> Best
> Javi
>
> -----Mensaje original-----
> De: Roger Bivand [mailto:Roger.Bivand at nhh.no]
> Enviado el: domingo, 13 de agosto de 2017 12:45
> Para: Javier García
> CC: r-sig-geo at r-project.org
> Asunto: Re: [R-sig-Geo] How to test spatial dependence in errorsarlm
>
> On Sun, 13 Aug 2017, Javier García wrote:
>
>> Hello everybody:
>>
>>
>>
>> I have estimated a spatial error model and now I would like to test
>> whether that model has really ?deleted? the spatial dependence. For
>> the spatial lag model and for the Durbin model the function lagsarlm
>> gives the LM test for residual autocorrelation test value, but the
> function errorsarlm does not.
>> Does anyone know how to do it in R?
>>
>
> As you should be aware from the literature, the only LM test that has been
> written (the maths) is a test for residual error autocorrelation for spatial
> lag models. Doing it in R will not help until someone (you?) does the maths.
> Computing a value is easy, but knowing what to infer from it is hard. By
> definition, if your model is well-specified, the residual autocorrelation is
> fully captured by its coefficient. I suspect that your model suffers from
> mis-specification problems.
>
> Roger
>
>>
>>
>> Thanks a lot in advance.
>>
>>
>>
>> Javi
>>
>>
>>
>>
>>
>>
>> JAVIER GARCÍA
>>
>>
>>
>> Departamento de Economía Aplicada III (Econometría y Estadística)
>>
>> Facultad de Economía y Empresa (Sección Sarriko)
>> Avda. Lehendakari Aguirre 83
>>
>> 48015 BILBAO
>> T.: +34 601 7126 F.: +34 601 3754
>> <http://www.ehu.es/> www.ehu.es
>>
>>
> http://www.unibertsitate-hedakuntza.ehu.es/p268-content/es/contenidos/inform
>>
> acion/manual_id_corp/es_manual/images/firma_email_upv_euskampus_bilingue.gif
>>
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>>
>>
>
>

-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
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Editor-in-Chief of The R Journal, https://journal.r-project.org/index.html
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