AI-GEOSTATS: SUMMARY: semivariogram for binary data
- Hi again and thanks for your answers,
you have really helped me out.
Here are the answers I have received so far:
Pierre Goovaerts answered:
In theory and under stationary of order 2,
indicator semivariogram values should not exceed
0.25 which is the maximum variance that you could obtain
for indicator variables, for a proportion of 50%.
I am wondering whether you have used the option
"standardize sill" in gamv, which could explain
these values larger than 1.
YES I used that option and that seems to explain the situation!
Marco Alfaro answered:
The semivariogram of an indicator variable is always less than 1.
The experimental semivariogram is (1/2) of the mean of the squared differences Z(xi+h)-Z(xi) but the values of Z are 0 or 1, then the semivariogram is (1/2) of the mean of the absolutes values of Z(xi+h)-Z(xi). Now you use the triangular inequality and you get that the semivariogram is less than 1.
Brian Gray wrote:
believe that geostatisticians resolve this by setting "out of bounds" values to the extremes (eg 0 or 1). However, statisticians resolve this issue for nonspatial data by using an inverse link to a cdf--which, of course, is on [0,1]. Examples include logistic and probit regression. See Gotway, CA and WW Stroup. 1997. A generalized linear model approach to spatial data analysis and prediction. JABES 2: 157-178. Gumpertz, ML, C Wu and JM Pye. 2000. Logistic regression for Southern Pine Beetle outbreaks with spatial and temporal correlation. Forest Science 46: 95-107. Brian
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