# [R-sig-phylo] phylogenetically-informed Reduced Major Axis regression in R?

Simon Blomberg s.blomberg1 at uq.edu.au
Thu Apr 21 03:51:20 CEST 2011

```I think it is important to point out, that while RMA may superficially
be an attractive method, it relies on  the ratio of error variances
being unity. This is almost always incorrect. It usually results in a
massive over-correction of the slope bias with respect to the OLS
estimator. That is, the slope is made much too steep. I would not
encourage anyone to use RMA for anything other than in the case where
there is sufficient within-species replication to estimate the error
variances with some precision, and then use an appropriate
generalization of RMA that allows for the variance ratio to be other
than unity. Fiddling around with "phylogenetically-informed" RMA is like
rearranging the deck chairs on the Titanic. The problem is discussed in
depth in:

R. J. Carroll and D. Ruppert 1996, The Use and Misuse of Orthogonal
Regression in Linear Errors-in-Variables Models. The American
Statistician, Vol. 50, No. 1, pp. 1-6

Carroll et al. 2006, Measurement Errors in Nonlinear Models. A Modern
Perspective. 2nd Edition, Chapman & Hall. Chapter 3.

Simon.

This is On 21/04/11 01:13, Joe Felsenstein wrote:
> Liam said:
>
>> Just calculating the slope is straightforward.  For tree and column
>> vectors x&  y (in order tree\$tip.label):
> The relevant point to keep in mind is that once you
> have made maximum likelihood estimates of the means,
> variances and covariances of the variables, the
> Reduced Major Axis is simply a function of these,
> and its ML estimate is that function of the ML estimates
> of the covariances.  You don't need to do any
> separate ML estimation for the RMA.
>
> If you want to test hypotheses about the RMA,
> if you can recast them as hypotheses about the
> slopes and correlations (say that the slope is
> zero) then the test can be done there, and no
> separate test of the RMA is needed.
>
> In the next release of my program Contrast in
> PHYLIP, I will have an option to print out the
> RMA and its other axes, which did not involve
> anything more complicated than computing them
> from the covariances that it was already estimating.
>
> Joe
> ----
> Joe Felsenstein, joe at gs.washington.edu
>    Dept. of Genome Sciences, Univ. of Washington
>    Box 355065, Seattle, WA 98195-5065 USA
>
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--
Simon Blomberg, BSc (Hons), PhD, MAppStat.
Lecturer and Consultant Statistician
School of Biological Sciences
The University of Queensland
St. Lucia Queensland 4072
Australia
T: +61 7 3365 2506
email: S.Blomberg1_at_uq.edu.au
http://www.uq.edu.au/~uqsblomb/

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