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I am mapping and modelling a disease of sheep. I have approx 4200 point locations in my dataset, each of which represents the centroid of a given sheep farm.

I have created a K-function difference plot (below) to assess whether my disease-positive farm density layer shows evidence of spatial dependence above and beyond that shown by my disease-negative farm density layer. From this plot I identified spatial dependence in my dataset out to a distance of 500m from a given disease-positive farm.

I have built a Poisson point process model and been through a model selection process. My model residuals appear to be relatively well behaved. See lurking variable plots below, raw and pearson residuals.

To assess the need (or not) for a spatial dependence/interaction term in my Poisson point process model, I created an inhomogeneous K-function plot from a density surface estimated from my final model. See inhomogeneous K-function plot below.

My questions:

1) Based on these plots, should I be including a spatial dependence/interaction term in my model? If so why?

2) Should the repulsion between points shown by the inhomogeneous K-function be accounted for in my Poisson point process model if it is not due to the disease itself? The inhomogeneous K-function plot shows no evidence that disease-positive farms cluster, but does show evidence consistent with repulsion. I believe this repulsion is an artifact of my data and not associated with the disease itself -I am using points to represent the area of a farm, so points can never be closer to each other than their farm borders.

Thanks in advance for any answers, I am very very appreciative!

K-function difference plot

Raw residuals from ppm

Pearson residuals from ppm

Inhomogeneous K-function

Patrick Taggart
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    Decidedly the wrong sort of question for SO. Not really sure whether it's appropriate for CrossValidated.com since I've never heard of a "ppm model", but maybe you will find some methodologist over there who understands your acronyms. If this were an R specific question then the correct venue might instead be either R-SIG-mixed-models or the R-SIG-spatial mailing lists. – IRTFM Mar 04 '19 at 02:27
  • I'm voting to close this question as off-topic because it almost entirely a methods question. – IRTFM Mar 04 '19 at 02:27
  • Thank you, I will post on CrossValidated.com – Patrick Taggart Mar 04 '19 at 03:32

1 Answers1

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It's not appropriate to use point process models for this problem. The farm locations are fixed, while the farm status (diseased or non-diseased) is the response variable.

A Poisson point process model would state that the farm locations are independent, and that's clearly not realistic. The results are consistent with farms being spaced apart which is realistic, but not informative for your real question.

In the spatstat package you could use the function relrisk to estimate the spatially-varying disease risk. But to evaluate evidence for contagion, conditional on the farm locations, you'd best use a package like spdep.

Adrian Baddeley
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