Hello,
I have little experience estimating spatial regression models, but I am performing an analysis with cities and towns as the units of observation and it seems that it may be important to do so. I used “spatreg” for my analysis. The Morans I indicates spatial autocorrelation in the OLS residuals and the LM and RML statistics indicate estimation of a spatial error model over a spatial lag model. I found no obvious way to test the residuals of the estimated spatial error model for spatial autocorrelation. I used the following syntax to create a variable “residmat1” containing the residuals : matrix residmat= e(resid) , svmat residmat. I then used the command “spatgsa residmat1 , weights(W2) moran” to test for the presence of spatial autocorrelation. The results indicate there is still spatial autocorrelation. Since I was not sure that I used the spatreg program properly, I downloaded “sppack” to re-estimate my model. Use of spreg also led me to choose a spatial error model. The coefficient estimates for all of the covariates were quite similar. However, the estimated coefficient for the coefficient on the spatial error term was different. Both were significantly different from 0, but the coefficient estimate on the error exceeded 1 if spatial weights (specified as a row normalized function of distance between centroids based on latitude and longitudes). The coefficient on the error did not exceed 1 if the weights were not row normalized, and it was smaller than the one obtained from spatreg and significantly different from 0.
I have two concerns. First, the estimated coefficients on the covariates were very similar in models estimated by spatreg and spreg, the error coefficients were very different. It is also not clear to my why the error coefficient was so different using spreg depending on row normalization. Second, if the spatreg results are credible, then it does not appear that I have reduced the spatial autocorrelation enough to be confident about the results. In fact, since OLS results are qualitatively very similar to those in the spatial error model, it leads me to think that I am doing something wrong. Most of the material on spatial regression models that I have read cover the initial test of spatial autocorrelation in the OLS model, and how to evaluate LM tests to choose a spatial error versus spatial lag model. They don’t discuss much about further testing for spatial autocorrelated errors in a spatial error or spatial lag model, and what to consider if spatial autocorrelation is still present.
Are there materials beyond the help menu for these programs that illustrate how they are used? Does the approach I used to compute Morans I for a spatial error model make sense? How common is it for spatial autocorrelation to remain after estimation of an indicated spatial error or spatial lag model. How can one tell whether it was actually reduced or not? Morans I for the OLS and spatial error model are similar in magnitude with p-values < .001. Thank you in advance for advice.
Frank Porell
I have little experience estimating spatial regression models, but I am performing an analysis with cities and towns as the units of observation and it seems that it may be important to do so. I used “spatreg” for my analysis. The Morans I indicates spatial autocorrelation in the OLS residuals and the LM and RML statistics indicate estimation of a spatial error model over a spatial lag model. I found no obvious way to test the residuals of the estimated spatial error model for spatial autocorrelation. I used the following syntax to create a variable “residmat1” containing the residuals : matrix residmat= e(resid) , svmat residmat. I then used the command “spatgsa residmat1 , weights(W2) moran” to test for the presence of spatial autocorrelation. The results indicate there is still spatial autocorrelation. Since I was not sure that I used the spatreg program properly, I downloaded “sppack” to re-estimate my model. Use of spreg also led me to choose a spatial error model. The coefficient estimates for all of the covariates were quite similar. However, the estimated coefficient for the coefficient on the spatial error term was different. Both were significantly different from 0, but the coefficient estimate on the error exceeded 1 if spatial weights (specified as a row normalized function of distance between centroids based on latitude and longitudes). The coefficient on the error did not exceed 1 if the weights were not row normalized, and it was smaller than the one obtained from spatreg and significantly different from 0.
I have two concerns. First, the estimated coefficients on the covariates were very similar in models estimated by spatreg and spreg, the error coefficients were very different. It is also not clear to my why the error coefficient was so different using spreg depending on row normalization. Second, if the spatreg results are credible, then it does not appear that I have reduced the spatial autocorrelation enough to be confident about the results. In fact, since OLS results are qualitatively very similar to those in the spatial error model, it leads me to think that I am doing something wrong. Most of the material on spatial regression models that I have read cover the initial test of spatial autocorrelation in the OLS model, and how to evaluate LM tests to choose a spatial error versus spatial lag model. They don’t discuss much about further testing for spatial autocorrelated errors in a spatial error or spatial lag model, and what to consider if spatial autocorrelation is still present.
Are there materials beyond the help menu for these programs that illustrate how they are used? Does the approach I used to compute Morans I for a spatial error model make sense? How common is it for spatial autocorrelation to remain after estimation of an indicated spatial error or spatial lag model. How can one tell whether it was actually reduced or not? Morans I for the OLS and spatial error model are similar in magnitude with p-values < .001. Thank you in advance for advice.
Frank Porell
