Hi - Can someone please point me to practical guidance for fitting a
theoretical model to an empirical variogram, particularly in choosing
maximum range and bin widths?  I have US state lung cancer rates, with state
centroid locations projected from lat/long using an equal distance
projection method.  On this scale, my inter-state distances range from about
100-4500km.  The empirical variogram suggests that an exponential model
would fit reasonably well.  I first used geoR's variofit function that
resulted in a range parameter of 2512.  Thus a sample estimate of spatial
autocorrelation between Maryland and Vermont (700km) is exp(-700/2512)=0.76.
This is so high that we were suspicious, so we tried gstat's fit.variogram
function to confirm.  Using the defaults for maximum distance (cutoff) and
lag width, this function gave a range parameter estimate of 348, which then
gives an autocorrelation estimate of exp(-700/348)=0.13.  Further
investigation showed that the notation and estimation methods of the 2
functions are comparable, but the difference is in the defaults used to
create the empirical variograms.  The resulting autocorrelation estimate can
be very different for lag (bin) widths of 100km vs 200km, as illustrated in
the MD-VT example.  The 200km width gives a minimum # of pairs of 9 in the
first bin, so it would seem that the 100km width is too small (too few
points), but the 100km width gives more believable results.  The ASDA book
has a discussion of the trade-offs of larger widths for stability vs smaller
widths for better detail of the semivariance curve.  Is there any rule of
thumb for a minimum # of pairs per bin or bin widths, or is this just a
variation of the statistical question "how small is too small"?

Any advice would be welcome.  Thank you in advance.

 

Linda Williams Pickle, Ph.D.

Principal and Chief Statistician

StatNet Consulting, LLC

 

 


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