Hello everyone,
I am pretty new to INLA and not a statistician, so I apologize if the question is too naive or not properly formulated!
I am predicting the probability of presence of forest. My data are in a 10x10 m raster resampled to 1x1 km units. The response (number of forest pixels to number of open land pixels in a 1km2 unit) is following a binomial distribution, and the predictors are various environmental variables (temperature, precipitation, terrain indices) - median value for 1km2 unit.
What I would like to know is how to geometrically interpret the hyperparametres of Matérn model - the precision (shape/scale) and range. If I got it right, the range refers to the range of spatial autocorrelation. Beguin et al. however use a logarithm of the range of spatial autocorrelation. Why should be a log(distance) used rather than just distance? And how can the precision (shape/scale) be interpreted?
Simplified example of the formula:
formula_matern <- n_success ~ temperature + precipitation + terrain +
f(node,
model='matern2d',
nrow=nrows,
ncol=ncols,
nu=1,
hyper=list(range=list(initial=log(range.sp.aut), fixed=TRUE), # ???
prec=list(initial=precision, # ???
param=c(shape,scale)))) # ???
Thanks a lot for help!
Zofie