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

[Prof Brian Ripley]

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 <spencer.graves at pdf.com> 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 <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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>>>
>>
>
> ______________________________________________
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>

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
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