I'm trying to model count data with both a Poisson regression model and a Negative binomial model. These counts are referred to the spread of a disease in each spatial unit area (I have 110 obs). I work with R or SAS and I would like to do something like a SAR model but referred to counts (I need non-negative fitted values, of course). How can I account for spatial dependence? The only thing I can reasonably do is to use a SLX model (SAS allows you to do that) and comment the regression coefficients of the neighborhood. But is this a "real" spatial dependence? Which software can handle such (rare?) models?

  • $\begingroup$ Have you looked at Poisson / Negative binomial Markov Random Fields (MRF)? Multivariate Negative Binomial distributions can be constructed by using a multivariate gamma distribution as the mean for conditionally independent Poisson variables. Do you have publically available data and do they show clear signs of over-dispersion? And is there positive correlation between neighbouring areas? $\endgroup$ – Ege Rubak Sep 16 at 21:24
  • $\begingroup$ I have run a classical Poisson model and the data did show overdispersion. Things got better with the negative binomial model (I got an alpha of about 0.6) and the deviance residuals were okay. All these models were spatial lag-of-x models, so I got a set of coefficients related with the effect of the neighbours on the i-th spatial unit: this is the only way I used to model the space dependence, but I don't know if it is a good method. Can the models you mentioned be run in R or SAS? $\endgroup$ – maestus Sep 19 at 19:53
  • $\begingroup$ I'm not sure what is available in R/SAS these days. I looked at multivariate negative binomial distributions 10 years ago and at that point there wasn't much around, but it may be better now. I also probably have some old experimental R code that I could try out if you have example data publicly available? $\endgroup$ – Ege Rubak Sep 22 at 8:02

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