Which model is better for investigating outcome – exposure relationship spatially?
· Data are counties
· Dependent variable is incidence per county
· Independent variable is median of XXX per county
· Spearman’s correlation, significant and negative
· Spatial autorelation of incidence values close to zero
· Local clusters, detected but majorities are single counties
· Geographically weighted regression, local coefficients mix of positive and negative but global regression coefficient negative
With this background, we should go for geographically weighted regression or bayesian convolution model with structured and unstructured random effects.
I am not convinced that countries are in general an appropriate level for measuring exposure due to large within country variations. I would need to know the context in which you are doing this work.
If your counties(local areas) are in clusters, perhabs you are interested in mapping Spatial Relative Risk or exposure to unknown spatial risk factors which are defined via the cluster analysis -Identifiying the exposed and unexposed populations. Your questions are a bit difficult to understand, but I think you need to check your model specification, since single counties are identified as clusters.
Though am not that very familiar with Bayesian Spatial Mapping and Analysis, but I am more certain that it is better in this situation. The Spearman’s correlation, significant and negative [high ranks of one variable frequently occur with low ranks of the other variable, ordinal?] implies that classical OLS (including [spatial] weighted regression, which will often give negative intercept coefficient) may not be appropriate and particular when the error term is autocorrelated or when an Instrumental variable exists unaccounted for in your Model!
You mentioned that "Spatial autorelation of incidence values [were] close to zero", howbeit consider reading Osei F.B. (2019) who adopted bivariate conditional autoregressive (BiCAR) priors, for broader space to decide on which gives sufficient answer to your research question. see[ Osei, F.B., Stein, A. Bayesian Random Effect Modeling for analyzing spatial clustering of differential time trends of diarrhea incidences. Sci Rep 9, 13217 (2019). https://doi.org/10.1038/s41598-019-49549-4]
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