# [R] MA / RMA / Type II regression?

Prof Brian D Ripley ripley at stats.ox.ac.uk
Fri Feb 4 19:31:06 CET 2000

```On Fri, 4 Feb 2000, Pete St. Onge wrote:

> > (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.

Well, it assumes equal accuracies of x and y.  The sum of squares
of horizontal and vertical distances i just Euclidean distance^2 to the
projection on to the line, so this is just PCA. Use  princomp and
take the first principal component.

> 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).

More accurately the covariance ellipse.

There are lots of related things under names like functional relationships
and structural relationships, so this is almost certainly in Fuller's
of Seber's or Sprent's books.

--
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272860 (secr)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595

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