[R] MA / RMA / Type II regression?

[Pete St. Onge]

> (What is MA/RMA regression? I don't know them, not by that name
> anyway.)
     Major Axis and Reduced Major Axis are the terms, and Geometric Mean
(GM) regression is also sometimes used, if I remember correctly. My
understanding in the latter is that it minimizes the squares of both the
horizontal and vertical distances from the regression line, and thus do not
impart any particular 'accuracy' to the predictor variable. If I'm not
completely wrong, the slope of the GM regression of Y on X should be the
inverse of the GM regression of X on Y.

This regression technique seems to be seldom used in the ecological
literature, even though there seems to be frequently error in the predictor
variable (eg. roundoff and measurement error in watershed size estimates
based on map data, etc). I've yet to see it in the mainstream stats
packages, and only know of the technique through two papers, both from the
same author. The primary paper is:

Ricker, W.E. 1973. Linear regressions in fishery research. Journal of the
Fisheries Research Board of Canada. 30:409-434.

MA is not so much a regression, according to this paper, but rather the
major axis of the corellation ellipse (assuming equal scales in the X and Y
axes).

> I hope you plotted FIT vs. residuals there and not really OBS
> vs. resid. The latter are well-known to generate apparent linear
> relations when none is in fact present, especially when the original
> relation is weak, as in.
> 
> x<-rnorm(20)
> y<-0.01*x + rnorm(20)
> plot(y ,residuals(lm(y~x)))

Actually, I did in fact plot the fitted data versus the residuals as well,
and see no pattern in the residuals. There is considerable scatter, so the
relationships are weak (but significant nonetheless). However, the same
trend in the OBS-RESID graphs is seen in three data series (nutrient export
as a function of catchment size, in three treatments), hence my concern
about type I vs type II regression.

Like I said, I've yet to see these technique in any statistics package, and
was wondering if this already existed within R. If it doesn't yet, then I
should be easily able to calculate it using these formulas and other R
functions, or at worse hacking the lm function to do the GM univariate
regression (I don't see any details / suggestions for the use of 
GM regression on multivariate data). One this would be done, I wonder if it
should be possible to use anova to compare two different GM lines.

To this end, any ideas or suggestions are appreciated.

Thanks,

Pete

-- 
Pete St. Onge - McGill U.  Limnology - Fun with Ropes & Buckets
pete at seul.org                  http://wwp.mirabilis.com/4322052
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