Moran's I Spatial Autocorrelation. Interpreting results.

I have carried out a Moran's I test on the residuals of a GLM model in the "ape" package in R which has returned the output below:

Observed: -0.158 Expected: -0.0303 SD: 0.058844 Probability: 0.030002

On this basis is it correct to state that there is negative spatial autocorrelation significant at the 95% confidence?

Am I correct in that an observed value close to -1 would indicate perfect negative autocorrelation and as such the negative autocorrelation seen here is relatively low?


TS Contributor
Yes, I would say that spatial autocorr is not so high in your case.
In the past, I also found it useful to plot the Moran's I at different lag intervals. I used the free SAM program ( I understand that, for each residual, you have the corresponding coordinates. So, feeding those data into SAM should be quite easy. Maybe that the significance could just be the result of a huge sample size. I do not know if that is your case, but it is worth keeping in mind that. I happen to have a very low (almost negligible) spatial autocorrelation among the residuals of a model that I have fit, but its statistical significance was due to the huge sample size (6000 observations).

Should spatial autocorr pose a problem to your modelling strategy, you could also try to randomly sample from the universe of your locations, in order to increase the distance between your sampling points relative to the whole dataset. This is something I happen to find in literature as one of the remedies to alleviate spatial correctional. Autoregressive models could also be put to work.

Hope this helps