[R] nls and geometric mean regression

[Michael Bedward]

Hello folks,

I'm seeking opinions about the validity of the following use of the
nls function...

A colleague and myself are working with tree allometric data
consisting of measurements of individual trees in semi-arid Australian
woodland species. We need to make predictions of trunk diameter (DBH:
diameter at breast height) given tree height and vice versa. I _think_
this falls into the category of model II regression in that both
variables are measured with error in our data, and we desire agreement
between forward and reverse predictions.

Our chosen function to relate DBH to tree height is:

dbh = exp( b0 + b1 / (b2 + height) )

the reverse function is:

height = b1 / (log(dbh) - b0) - b2

To arrive at parameter estimates that give agreement between the
forward and reverse functions we have fitted each function separately
to the same dataset using nls, and then calculated the geometric means
of the separate parameter values inspired by this discussion...
http://tolstoy.newcastle.edu.au/R/help/05/06/5992.html

This has all be successful in so far as the resulting model II-ish
parameter values yield symmetric predictions and a plot of the
function together with the separately fitted functions appears
'sensible'. But I'd be keen to hear from anyone about whether this
procedure is invalid or ill-advised for any reason, and if there are
better approaches that we should investigate.

Michael