On Tue, 2 Dec 2008, Jarle Brinchmann wrote:
Yes I think so if the errors were normally distributed. Unfortunately
I'm far from that but the combination of sem & its bootstrap is a good
way to deal with it in the normal case.
I must admit as a non-statistician I'm a not 100% sure what the
difference (if there is one) between a linear functional relationship
and a linear structural equation model is as they both deal with
hidden variables as far as I can see.
U and V are not 'variables' (not random variables) in a linear functional
relationship (they are in the closely related linear structural
relationship).
J.
On Tue, Dec 2, 2008 at 9:33 PM, Spencer Graves <[EMAIL PROTECTED]> wrote:
Isn't this a special case of structural equation modeling, handled by
the 'sem' package?
Spencer
Jarle Brinchmann wrote:
Thanks for the reply!
On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley <[EMAIL PROTECTED]>
wrote:
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.
This is indeed what I mean, poor phrasing of me. What I have is the
effectively the PDF for e & f for each instance, and I wish to get a &
b. For Gaussian errors there are certainly various ways to approach it
and the maximum-likelihood estimator is fine and is what I normally
use when my errors are sort-of-normal.
However in this instance my uncertainty estimates are strongly
non-Gaussian and even defining the mode of the distribution becomes
rather iffy so I really prefer to sample the likelihoods properly.
Using the maximum-likelihood estimator naively in this case is not
terribly useful and I have no idea what the derived confidence limits
"means".
Ah well, I guess what I have to do at the moment is to use brute force
and try to calculate P(a,b|X,Y) properly using a marginalisation over
U (I hadn't done that before, I expect that was part of my problem).
Hopefully that will give reasonable uncertainty estimates, lots of
pain for a figure nobody will look at for much time :)
Thanks,
Jarle.
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--
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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