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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