[R-sig-Geo] Spatial Regression

[Roger Bivand]

On Tue, 23 Jun 2009, Adrian Toti wrote:

> Hi Roger,
>
> You wrote: "If both spatial coefficients are significant in a general model,
> you know with little chance of mistake that your model is badly
> misspecified".
> I am assuming that you mean the Rho coefficient (lagged dependent) and the
> lagged coefficients (for the independent variables) in the spatial Durbin
> model.

No, the original questioner was thinking of a model like:

y = \rho W y + X \beta + u

u = \lambda W u + e

with both a lag coefficient \rho and an error coefficient \lambda. You end 
up with a messy interaction between the \rho and \lambda terms, something 
like:

(I - \rho W) (I - \lambda W) y = (I - \lambda W) X \beta + e

or

y = (I - \rho W)^{-1} X \beta + (I - \rho W)^{-1} (I - \lambda W)^{-1} e

> What about a situation where using lm.LMtests function one can make a
> decision for a lag or error model but using spatial Durbin model in any
> situation (meaning when error or lag is a better fit) the lagged dependent
> and some of the lagged independent are significant?  So does that still mean
> that the model is misspecified?
>
> Another information if it can be helpful: when I compare the spatial Durbin
> fit with with the error or lag and use LR.sarlm to compare the
> models, Durbin model shows always a better fit.
>

Yes, they often do, but comparing the AIC values may prefer the lag or 
error models because adding extra variables is penalised.

Roger

> Thanks,
>
> Adrian
>
>
> On Fri, Jun 19, 2009 at 12:29 PM, Roger Bivand <Roger.Bivand at nhh.no> wrote:
>
>> On Fri, 19 Jun 2009, youngbin wrote:
>>
>> Hi,
>>>
>>> 1. While conducting spatial regression models, R does not directly provide
>>> the Rsquared values. Does anybody have an idea how to get the Pseudo
>>> Rsquared values in spatial regression models?
>>>
>>
>> The models are fitted with maximum likelihood, so R squared is not a very
>> suitable measure, although I'm sure you can find various ways of computing
>> them. On the other hand, you can also get the AIC and log-likelihood for OLS
>> and some other models, and they also provide a way of comparing models.
>>
>>
>>> 2. Regarding spatial regression models, how to conduct the general spatial
>>> model which both the lag and error are included?
>>>
>>>
>> This is not provided, and is not even well understood in spatial statistics
>> (there are very complicated interactions between the lag and error
>> components). Spatial Durbin models do provide a general structure within
>> which both lag and error models nest. If both spatial coefficients are
>> significant in a general model, you know with little chance of mistake that
>> your model is badly misspecified, I'm afraid. The only possible alternative
>> is that you have well-motivated behavioural models for both processes and
>> their interactions.
>>
>> Hope this helps,
>>
>> Roger
>>
>> Thanks
>>>
>>> youngbin
>>>
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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
>>
>>
>> _______________________________________________
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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