I used gstat to fit a Matern variogram model to my crop yield by setting the kappa = 0.5. To my surprise, its parameter estimates are exactly the same with that of exponential. Does it mean that there is no point in fitting a matern model? When I set the kappa = 0.7, the parameter estimates are now different from that exponential. Could anyone tell me the appropriate value for kappa? Having known that matern is a generalized form of theoretical variogram, is it worth fitting a matern model when I have already fitted the common theoretical variogram (spherical Gaussian, and exponential)?
exponential model
model psill range
1 Nug 0.04281109 0.00000
2 Exp 0.76810071 5.45954
Matern Model
model psill range kappa
1 Nug 0.04281109 0.00000 0.0
2 Mat 0.76810071 5.45954 0.5
R Script## Exponential variogram model
exp.var
Indeed, a Matern variogram model with kappa=0.5 represents a exponential model, and when kappa -> infinity then it represents a gaussian model. (see Minasny, B., & McBratney, A. B. (2005). The Matérn function as a general model for soil variograms. Geoderma, 128(3), 192-207.)
Regards
For crop yields, the loi de terroir says that a de Wijs process plus a white noise adequately describes fertility variations (See McCullagh and Clifford, 2006) and there is little advantage in pursuing a model based on Matérn covariances. Note that, the de Wijs process lies on the boundary of Matérn covariance class where kappa = 0 and range is infinite.
But fitting the de Wijs process plus white noise possess daunting computational challenge. To reduce computation burden, recently, Dutta and Mondal (2012) exploited the explicit connection between the de Wijs process and the first order intrinsic autoregression and developed novel matrix-free methods that are not only fast for small data sets but also provide answer for large arrays (500x1000) in a very reasonable amount of time.
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