I wonder if you are using this term in its correct technical sense.
A linear functional relationship is
V = a + bU
X = U + e
Y = V + f
e and f are random errors (often but not necessarily independent) with
distributions possibly depending on U and V respectively.
and pairs from (X,Y) are observed. As U and V are not random, there is
no PDF of X or Y: each X_i has a different distribution. If you know
the error distribution for each X_i and Y_i, you can easily write down a
log-likelihood and maximize it.
The first hit I got on Google,
http://www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/FREML.asp,
has a reference to a paper for the Gaussian case.
But finding R code for the non-Gaussian case seems a very long shot.
Jarle Brinchmann wrote:
[apologies if this appears twice]
It did ...
Hi,
I have a situation where I have a set of pairs of X & Y variables for
each of which I have a (fairly) well-defined PDF. The PDF(x_i) 's and
PDF(y_i)'s are unfortunately often rather non-Gaussian although most
of the time not multi-modal.
For these data (estimates of gas content in galaxies), I need to
quantify a linear functional relationship and I am trying to do this
as carefully as I can. At the moment I am carrying out a Monte Carlo
estimation, sampling from each PDF(x_i) and PDF(y_i) and using a
orthogonal linear fit for each realisation but that is not very
satisfactory as it leads to different linear relationships depending
on whether I do the orhtogonal fit on x or y (as the errors on X & Y
are quite different & non-Gaussian using the covariance matrix isn't
all that useful
either)
Does anybody know of code in R to do this kind of fitting in a
Bayesian framework? My concern isn't so much on getting _the_ best
slope estimate but rather to have a good estimate of the uncertainty
on the slope.
Cheers,
Jarle.
--
Brian D. Ripley, [EMAIL PROTECTED]
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 272866 (PA)
Oxford OX1 3TG, UK Fax: +44 1865 272595
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