[R] linear functional relationships with heteroscedastic & non-Gaussian errors - any packages around?

Spencer Graves spencer.graves at pdf.com
Tue Dec 2 21:33:51 CET 2008

      Isn't this a special case of structural equation modeling, handled 
by the 'sem' package? 


Jarle Brinchmann wrote:
> Thanks for the reply!
> On Tue, Dec 2, 2008 at 6:34 PM, Prof Brian Ripley <ripley at stats.ox.ac.uk> 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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