# Spatial Poisson model correlation structure

I'll preface this by saying I'm VERY new to this spatial epidemiology world. I'm running a spatial poisson model and have set its correlation structure as exponential. However once I arrived at my final model I tried running it with a spherical correlation structure. Is there a straight forward way to knowing which model/correlation structure is better? I've run some QQ plots as well as some predicted vs observed plots but I can't seem to arrive at anything definitive through that. The spherical correlation structure did increase the range of spatial dependence and it decreased the p-value of my explanatory variable from 0.02 to 0.00....

• You will probably get more responses if you describe your data set in more detail. I think what you are referring to has to do with spatial autocorrelation and, more specifically, the assumed model of spatial dependency (over geographic distance). You need to build an empirical semivariogram and then choose the theoretical semivariogram that best fits your data.This is often done in the context of interpolation, but, in your case you just need to characterize the spatial dependency to parameterize your model. – coreydevinanderson Dec 6 '18 at 17:04
• Thank you @coreydevinanderson after doing some more searching around I did find what you were describing! My model was using west nile virus case data in both humans and birds to describe the risk of Dengue fever across public health units. Unfortunately I had submitted my results before i found that information. What I ended up doing was using a plot of the observed and expected and compared this plot for a model with my spherical correlation structure and one with an exponential structure. I figured the plot that ended up having a more diagonal plot of points meant it was better. – Jamie Dec 6 '18 at 17:56
• As a follow up, this is probably a super silly question but do vector borne diseases ever have a more common spatial autocorrelation?? spherical vs gaussian vs exponential – Jamie Dec 6 '18 at 17:58
• I am not enough of an expert on the subject to posit a response. Usually when you are dealing with regression models, you look at the spatial structure of the residuals and you have to consider the source of the observed autocorrelation (i.e., Is it an inherent aspect of the response variable? Is it due to a potentially unmeasured predictor variable? etc.). I think it would be hard to generalize such a thing. – coreydevinanderson Dec 6 '18 at 19:29