## AI-GEOSTATS: SUMMARY: semivariogram for binary data

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• Hi again and thanks for your answers, you have really helped me out. Here are the answers I have received so far: ______________________ Pierre Goovaerts
Message 1 of 1 , Jan 16 6:37 AM
you have really helped me out.

______________________

Hi Malin,

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.

Pierre

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YES I used that option and that seems to explain the situation!

___________________________

Dear Malin:
The semivariogram of an indicator variable is always less than 1.

Proof:
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.

Regards
Marco Alfaro

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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

___________________________________

Malin Fahller
Geographical Information Technology
Luleå University of Technology
SE- 971 87 LULEÅ
SWEDEN

phone: (+46) (0)920 914 66
fax: (+46) (0)920 728 30

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