Dear all,

I want to distribute a vector of known values onto a lattice, while still making sure that the Moran autocorrelation is higher than a specific threshold.

I know of several ways of getting a lattice with some pre-determined levels of approximate spatial autocorrelation, but all involve some random number generation of one sort or another, whereas I want cell values to have some pre-determined values.

I assume that I could:
1) generate a lattice
2) randomly distribute my pre-determined values
3) compute Moran's I, then randomly permutate two cell values
5) recompute Moran's I and, and if higher that the one calculated in 3) keep the new lattice
6) back to 3) for permutation, or stop when Moran's I higher than my threshold, or kill the simulation when i've reached a specific number of iterations.

The above is obviously so inefficient that it is likely to be of no use for a lattice of even a moderate size or for a high autocorrelation threshold to be reached. I intend to work on approx. 100*100 lattice, with values equally distributed between 0-100, and autocorrelation threshold of approx. 0.3.
 
Any suggestions (hum..., even 'don't even think of doing something like this'), would be appreciated.
Thanks,
simon


      
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