I am looking at the relationship between life expectancy and smoking rate within the London boroughs.
I thus created a bayesx spatial regression model including a term which assigns spatial covariates to deal with the spatial autocorrelation. From what I have read about the bs='spatial' argument, this specifies that the spatial covariates are created using a Markov random field prior.
boro<-poly2nb(london) boro2<-nb2gra(boro) i<-0:(length(london$GSS_CODE)-1) star2<-bayesx(london$LE~london$smrate+ sx(i,bs='spatial', map=boro2))
So from this I can look at the spatial weights which are generated by using the function
predict(star2, type = "terms")
Which gives me information on the spatial weights that were created for my spatial covariates in the column of Mean:
So these are the 32 weights that are assigned to my 32 polygons. What I am not sure about is how these weights are thus applied in order to account for the existing spatial autocorrelation?
If a polygon x is a neighbour of two adjacent polygons (y and z), then do the observed values for my independent variable (smoking rate) from y and z get multiplied by their respective wieghts and then added to contribute to the estimated fitted value of my dependent variable (life expectancy) for the polygon x?