Geometrical interpretation of hyperparametres of Matérn-model

[Žofie Cimburova]

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.

 

I am reproducing the approach of Beguin et al. (http://onlinelibrary.wiley.com/doi/10.1111/j.2041-210X.2012.00211.x/full) for hierarchical spatial modelling with spatially autocorrelated distributional data using a Matérn-model to account for spatial autocorrelation among units. (Their code is in the Supporting Information section.)

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

[Helpdesk]

Hi

I think you're better off moving to the more general SPDE models, for
which your case is a special case. go through the SPDE-tutorials,

http://www.r-inla.org/examples/tutorials

and you should be fine.

best
H

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[Nicola Criscuolo]

Hi Zofie,

I am following the guidelines of the same exact paper to work with my data, which however are distributed as a Poisson since they're counts per pixel. Have you found a way to interpret the hyperparameters of the Mátern model and to create a variogram?

Thank you in advance for your help.

Nico

[Finn Lindgren]

You can use inla.matern.cov() to compute the Matern covariance/correlation function for given parameter values. The parameter kappa = sqrt(8*nu)/range, where nu = alpha - dim/2 ( = 1 for default models in 2D).

Finn

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[Nicola Criscuolo]

Thank you for the answer Finn! Could you just specify where I can extract the distance argument (x =) for the inla.matern.cov() function? Is it something I can extract after fitting the model or that I have to calculate?

Thanks a lot!

[Finn Lindgren]

You’ll need to construct it yourself; it’s just the distances for which you want to evaluate the covariances. What those distances are depends on the aim of computing the covariances.

Finn

On 3 Dec 2021, at 01:21, Nicola Criscuolo <nico.cris...@gmail.com> wrote:



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[Nicola Criscuolo]

Thanks for the clarification Finn!