Does ArcGis 10.3 has a special algorithm to handle categorical variable in simple co-kriging?

[clementbataille]

Hi,

I am working in building some geochemical map of soils using point data and geological maps as covariates. The geological covariate is a simplified geological map that groups geological units into 5 clusters. I have first used regression kriging by fitting a model between the geological variable and my target variable and further kriging the residuals. I obtained some decent rme but I was not too pleased with the visualization. I initially assumed that cokriging was not appropriate in my case because of the non gaussian distribution of the geological covariate. However, I tried to apply simple cokriging just to see the results. When using my geological map as a covariate and my target variable observations, i  got really good results in term of map visualization and model performance. I did not apply any transformation and only tuned the variogram. The simple cokriging model gave a much better rmse than the regression kriging. That was counter intuitivr to me as i had read that regressiin krigging does better at handling categorical covariates. Surprisingly, when applying an ordinary cokriging and tuning the variogram using exactly the same input data I could not obtain anything close in term of performance or visualization as the simple cokriging. The ordinary cokriging using exactly the same input data gave completely different results and did not handle the categorical geological covariate well. 

So here is my question: Does the simple cokriging algorithm in arcgis has a built in function to recognize categorical covariates? It seems to me that when I applied the simple cokriging, it worked as if I applied a kriging with barriers and fitted variograms independently for each geological clusters. Can a esri specialist on kriging check on the simple cokriging algorithm? I would like to be able to justify this map and why simple cokriging does so well. 

Thank you for your help.

Clement

[DanPatterson_Retired]

vangelo-esristaff‌ perhaps you can comment.  I didn't know that kriging of any kind had been extended to categorical data (aka, nominal scale).

[VinceAngelo]

At the risk of further tarnishing my reputation as an expert of all things GIS, "I got nuthin'."

 -V

[JenoraD_Acosta]

slynch-esristaff‌ or EKrause-esristaff‌ Any insight?

[EricKrause]

Hi Clement,

Geostatistical Analyst does not treat categorical data any differently than continuous data.  It doesn't know that your categorical field is a categorical field, and it is just operating on the numbers in the field the same way it does with any other field.  This is true for all types of kriging, simple and otherwise.

As for why you are seeing better maps with simple cokriging than with regression kriging and ordinary cokriging, I honestly do not know.  As you said, you should expect regression kriging to outperform cokriging for categorical covariates.  We often see simple kriging outperform ordinary kriging, but that is mostly due to the very flexible transformation, which you said you didn't use.  The counter-intuitive results may have something to do with how the categories are coded (how are they coded?) in your database. 

Before I write this off as just "some datasets are weird", I want to talk to a couple of colleagues.  However, they are on vacation right now.  I will see them next week at the User Conference, but we may not have time to discuss this.  If I don't get a chance to discuss it at the User Conference, I will talk to them the week after and get back to you.

Sorry I couldn't be more help right now, but this is a bit of a mystery, and there might not be any rational explanation other than just quirks in this particular dataset.

-Eric Krause

[clementbataille]

Hi Eric,

Ok. Thank you all for your replies and your time. As you said it must be something weird about this particular dataset. The category (or geological clusters) are coded as integers (1 to 5). The codes were assigned randomly (i.e. there is no linear correlation between my target variable and the cluster codes). I could try to change the geological covariate coding and see if it changes the results. It might have something to do with that. Thanks for the idea on the coding. Even though that would be the coding of the category,  I still cannot explain why the cokriging using OK is so different from the cokiriging using SK. This is just very strange.

Best,

Clement

[EricKrause]

Did you use the same semivariogram parameters for simple and ordinary cokriging?  If any of the parameters are very different, the two surfaces could end up looking very different.

Remember that in cokriging, you must estimate three different covariance models: the semivariogram for the primary dataset, the semivariogram for the secondary dataset, and the cross-covariance between them.  You can change which model you are viewing by using the control at the top of the Wizard.  "Var1 - Var1" shows the primary semivariogram.  "Var1 - Var2" shows the cross-covariance.  "Var2 - Var2" shows the semivariogram for the secondary dataset.  Unless all three of these models are set to the same (or similiar) values, simple and ordinary cokriging may produce very different maps.