# (Co)kriging / co-located kriging with heterogenous measurement errors

I have a large set of polygons on a map, some of which contain data on 2 count variables, say ($$z_{1}$$ and $$z_{2}$$) that are correlated. In fact, $$z_{2}$$ most likely causes $$z_{1}$$ without the possibility of reverse causation. I need to interpolate $$z_{1}$$ to polygons with missing values, possibly with the help of $$z_{2}$$ within a co-kriging/co-located kriging setting. There is a couple of important aspects to the data:

1. Both $$z_{1}$$ and $$z_{2}$$ oberved data measurements have standard errors that are independent of each other.
2. There are also 4 types of polygons in my set, such that some have data on both $$z_{1}$$ and $$z_{2}$$, some have one or the other, and some have neither.

Questions:

1. How can I incorporate the measurement error from the input data to interpolate $$z_{1}$$, preferably with the help of $$z_{2}$$?

2. Subsequently, is there a trade-off in terms of the accuracy of the resultant values to using co-kriging to interpolate $$z_{1}$$ to polygons that contain neither $$z_{1}$$ nor $$z_{2}$$?

Any advice, applied resources, code samples, or papers would be welcome.

I am aware of the issues surrounding Area-to-Area and Area-to-Point kriging, so let's assume these considerations are not part of this question. In full disclosure, I am piggybacking off this and this posts that provided some insight, but left me curious for more. Also, I am using R, so any advice on a package(s) that may be useful like DiceKriging is appreciated.

• The techniques of geoRglm are the appropriate ones, but I don't know whether the software has implemented cokriging.
– whuber
Jun 21 '20 at 13:44