Cokriging with a categorical covariable?

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05-20-2015 03:25 AM
BethBrockett
New Contributor

Hello, sorry for any cross postings - I posted this question yesterday but don't think I posted it in the right space.

I am using cokriging to model a continuous variable across my study unit (soil carbon). I have one continuous covariable (soil moisture) but also a categorical covariable (vegetation community). I am using the Geostatistical Analyst Wizard to do this. (I ran linear models in R to establish the significant covariables and any transformations required).

Am I right in thinking that I can't include the categorical covariable directly into the model? If so, can anyone please suggest a way that I can include this information within a cokriging model?

I am using cokriging as it is enabling me to compare the cross validation statistics with and without the covariables. But open to suggestions of other methods which allow inclusion of covariables and provide some idea of model fit, that I can apply in ArcMap.

Many thanks

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larryzhang
Regular Contributor

Beth,

As you are open to new way, the advice is as follows, which use ordinary Kriging with regression:

  • In the last decade, a number of ‘hybrid’ interpolation techniques, which combine kriging and use of auxiliary information, has been developed and tested. Here, two main paths can be recognised: co-kriging and kriging combined with regression (McBratney et al., 2000). The latter path was shown to be more attractive for combination of kriging and CLORPT techniques, among others because fewer model parameters need to be estimated (Knotters et al., 1995).
  • In many cases, kriging combined with regression has proven to be superior to the plain geostatistical techniques yielding more detailed results and higher accuracy of prediction. Hudson and Wackernagel (1994) showed that kriging with use of elevation data improves mapping of temperature. Knotters et al. (1995) compared ordinary kriging with co-kriging and regression-kriging for soil mapping purposes, favouring the latter. Bourennane et al., 1996 and Bourennane et al., 2000 showed that prediction of horizon thickness is more accurate with the use of a slope map as external drift. In several other studies Odeh et al., 1994, Odeh et al., 1995, Goovaerts, 1999b and Bishop and McBratney, 2001, combination of kriging and correlation with auxiliary data outperformed ordinary kriging, co-kriging and plain regression. Although the hybrid interpolation techniques are becoming increasingly popular, there is still a need for a generic methodology that combines theory of generalized linear models (GLM) with universal kriging. Gotway and Stroup (1997) and Opsomer et al. (1999) give good starting points.
  • In mining and reservoir modeling studies,  very common to apply ...

pls keep posting your findings and share your experience

BethBrockett
New Contributor

Dear Larry,

This is very helpful, thank you.

I assume that regression-kriging will need to be carried out outside of the ArcMap Geostatistical Analyst? In a programme such as R?

I will certainly post my experiencesof trialing this - in case they help others.

Best wishes, Beth

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larryzhang
Regular Contributor

With R, pls refer to 'Regression on categorical variables' at http://www.r-bloggers.com/regression-on-categorical-variables/  and open the attachment, which might be meaningful to your practice...

larryzhang
Regular Contributor

On your question 'cokriging continuous variable - soil carbon with categorical variable - vegetation', you can try GoCAD (if available to you).

+++++++++++++

Generally speaking, geostatistical analysis of categorical variables is by many referred to as the indicator geostatistics. One of those is Regression-kriging of indicators.

With Regression-kriging of indicators, one approach to interpolate vegetation categorical variables is to first assign memberships to point observations and then to interpolate each membership separately. This approach was first elaborated by de Gruijter et al. (1997) and then applied by Bragato (2004) and Triantafilis et al. (2001). An alternative is to first map cheap, yet descriptive, diagnostic distances and then classify these per pixel in a GIS (Carr´e and Girard, 2002).

BethBrockett
New Contributor

Dear Larry,

Thank you. I have not come across GoCAD - but will investigate. Is this software I'd need to carry out the rest of your suggestion?

Thanks for clarifying indicator kriging - I assumed it was just used for categorical dependent variables.  I will read through your suggested references and see if I can apply this in ArcMap Geostatistical Analyst. I am not very expert at this - so I'm afraid I'll need to do a bit of reading around before I totally understand your second paragraph.

Thanks again, your help is much appreciated. Beth

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