Spatial Regression
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