[R] isotonic/ordered heterogeneity tests

From: Ben Bolker <bolker_at_zoology.ufl.edu>
Date: Fri, 02 May 2008 09:12:44 -0400

   dear R-help:

   one of my students is struggling to test an ordered alternative hypothesis on a set of groups (e.g., mu_a <= mu_b <= mu_c). There has been some literature on this topic -- a lot of this goes back to Bartholomew (1961); Gaines and Rice
(see refs below) are the ones who've popularized it in the
ecology community. The topic is closely related to isotonic regression, but all of the isotonic-regression stuff we've been able to discover in R so far (isoreg, the Iso and cir packages, etc.) are geared towards estimating smooth (or non-smooth) monotone relationships rather than towards testing ordered hypotheses. Computing p-values based on the Gaines and Rice (1990) algorithm is actually fairly hairy, because one has to calculate probabilities of amalgamating k groups into m ... the later Rice and Gaines "ordered hypothesis" algorithms look easier to code, but still not completely trivial.

   Does anyone have any hints toward implementations of these or similar methods, or do we have to do it ourselves ... ?
(We're not proud -- pointers to straightforward ways to this
on other platforms [cough]SAS[cough] would be great too.)

   thanks,
     Ben Bolker

Gaines, Steven D., and William R. Rice. 1990. Analysis of Biological Data When there are Ordered Expectations. The American Naturalist 135, no. 2:310-317.

Rice, William R., and Steven D. Gaines. 1994a. Extending Nondirectional Heterogeneity Tests to Evaluate Simply Ordered Alternative Hypotheses. Proceedings of the National Academy of Sciences of the United States of America 91, no. 1:225-226.

Rice, William R., and Steven D. Gaines. 1994b. The Ordered-Heterogeneity Family of Tests. Biometrics 50, no. 3:746-752.



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