[Openspace] Interpretation of the diagnostics test for spatial dependence

[Julia Koschinsky]

Alejandro,

The LM tests can reject the null of spatial randomness in favor of a spatial lag or error model based on the OLS residuals alone (they compare the slope of the likelihood functions for OLS and the spatial models, in which case the slope is zero) while the likelihood ratio test requires the estimation of either the lag or error model first. 

Basically, if the LM tests/Likelihood Ratio tests are not significant, as seems to be the case in your project, the regular non-spatial OLS estimation is adequate.

The details you ask about are explained, among other texts, in:

Anselin, L. and Bera, A. (1998). Spatial dependence in linear regression models with an introduction to spatial econometrics. In Ullah, A. and Giles, D. E., editors, Handbook of Applied Economic Statistics, pages 237-289. Marcel Dekker, New York.

Let me know if you have trouble accessing this chapter.
Julia

---- Original message ----
>Date: Tue, 30 Oct 2007 23:09:26 -0400
>From: ALEJANDRO CANADAS <canadas.1 at osu.edu>  
>Subject: [Openspace] Interpretation of the diagnostics test for spatial dependence  
>To: openspace at sal.uiuc.edu
>
>My name is Alejandro and I have started using GeoDa. I have some questions regarding the interpretation of the diagnostics for spatial dependence.
>
>Following the examples given in the GeoDa Manual 9.5-I in page 52 after doing a OLS regression the diagnostics for spatial dependence show evidence of spatial autocorrelation. They have very low p-values. Specifically the Lagrange Multiplier (lag) and Lagrange Multiplier (error) both probabilities are very low. I believe that the null hypothesis here is no spatial autocorrelation. Is that correct?
>
>Which is the difference between the Lagrange Multiplier and the robust LM?
>
>Then, after running a Spatial Lag Model with the same variables we obtain the Likelihood Ratio Test in the diagnostics test for spatial dependence. 
>
>Which is the null hypothesis in this stage? Which is the difference between the Likelihood Ratio Test and the Lagrange Multiplier?.
>
>If the meaning it is also no spatial autocorrelation, here we also reject the null so it seems that there is still spatial autocorrelation in the lag model.
>
>Finally, the same situation happens after running the spatial error model. Also here it seems to be spatial autocorrelation. So, I believe that I am wrong in the interpretation of the likelihood ratio test.
>
>Could you help me understand the interpretation of these diagnostics test for spatial dependence?
>
>How are the standard errors calculated in the lag and error models? Are they corrected for the presence of spatial autocorrelation? 
>
>
>
>Thank you for your help,
>
>
>Alejandro Cañadas
>Rural Finance Program
>Room 249-B
>Dept. of Agricultural, Environmental, and Development Economics
>The Ohio State University
>2120 Fyffe Road
>Columbus, OH, 43210
>Phone: (614)292-8019 
>Fax: (614)292-7362
>
>
>
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