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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.

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

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