When the moran's I test on residuals show no significant spatial autocorrelation, the spatial linear regression model reports poor fit (higher AIC) compared to a non-spatial regression model.

So, when moran's I indicate no significant spatial autocorrelation, we can directly settle with non-spatial "linear" regression model.

I hope that helps.

Thanks.

Mounisai Siddartha Middela Thank you.

Dear Sowjanya,

the answer is "yes".

You need to go for a spatial regression model when there is spatial autocorrelation (SAC) in response variable but not in regression model residuals, because it is proved that, if you have SAC on residuals and you omit to model it, you just have wrong standard errors (so, wrong inference, but the estimated coefficients of the X's are correct), if you have SAC on the response variable and you omit to model it, you will even have wrong estimates.

Best,

Rodolfo

Dear Rodolfo Metulini ,

Would you mind giving an example or share the research that proved it?

When Moran's I on the residuals indicated the absence of spatial autocorrelation, well-established packages like "spdep" and "spatialreg" show poorer fits for spatial models considering either spatial lag or spatial error. And I did not find any significant differences in the estimates between non-spatial and spatial models.

In the case I am talking about, the moran's I in the residuals is 0.006, while the moran's I in the dependent variable is 0.05. The AIC of the spatial lag model, in this case, is 1835 (while the non-spatial model AIC is 1834).

Please let me know if I am getting something wrong here.

And I had a reviewer commenting "there is no need to consider spatial autocorrelation when there is no spatial dependence in residuals."

Thanks for your reply.

Regards,

Siddartha.

Dear Mouni, thanks for your comment: it makes me realize that I reversed SAC in the residuals and SAC in the response.

Let start from the basic assumption of the OLS.

A basic assumption of OLS is that E(e_i|X) = 0, for all i.

When residuals are spatially autocorrelated this assumption is not satified.

So, SAC in residuals makes the OLS biased and unconsistent.

When the response is spatially autocorrelated, no basic assumption are violated, but a desirable one is: that of uncollinearity among explanatories, since X and WY are likely correlated.

So, when you have SAC in the response, OLS is not biased, but you may have wrong standard errors.

All in all, reviewer is partially right: ignoring SAC in the residuals (when you have it) is a big mistake, ignoring SAC in the response (when you have it) is a moderate mistake.

About the Moran I, you might look to their p-values, the Moran Index is not informative, per se.

I hope this helps,

Best, Rodolfo

Dear Rodolfo Metulini ,

Thanks for your very helpful comment. I second your comment on looking at the Moran Index p-values as you said for better information.

Best, Siddartha.

Dear Rodolfo Metulini thank you for explaining clearly.

Mounisai Siddartha Middela thank you for your comment asking to elaborate Rodolfo's comment.