Dear R-sig-Geo members,

I'm currently stuck on a problem that no one at my institution seems able
to answer. I have two empirical surfaces and I would like to test if one is
more curved than the other. One of the surfaces is complex, so I don't
think that parametric methods are an option.

My two surfaces (low and high-density) are composed of a binomial response
variable measured along continuous variables 1 and 2. I have fit thin-plate
splines to these data using the Tps function in Fields. My statistic of
interest is the effective degrees of freedom, eff.df, optimized for each
density level using GCV, because I think this is the best estimate of the
overall curvature of each surface. Is this correct?

To account for unequal sampling between the two surfaces, I used a
permutation test to compare the observed difference in eff.df to a null
distribution of random differences in eff.df. To generate this null
distribution, I randomized assignment of the binomial response variable
within each dataset (using sample) and refit the splines, leaving
everything else constant.

Here is the problem: the null distribution of eff.df has an incredibly
large range - about 10x larger than the observed difference in eff.df. Is
this due to the sparse binomial response data? This large range seems
robust to any method or dataset that I use (mgcv, Tps, REML, bootstrapping,
2 continous variables or 5). For example, in one case the observed eff.df
for the two surfaces was 40 and 20, but the null range of eff.df ranged
from 20 to 120 (with modes at 20 and 120!).

Should I be worried about this? If so, could you suggest an alternative
approach?


Thank you for your response,

Christopher Martin
http://fishlab.ucdavis.edu/?page_id=5
Ph.D. candidate
Population Biology Graduate Group
University of California, Davis

	[[alternative HTML version deleted]]

