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

Jarle Brinchmann jbrinchmann at gmail.com
Tue Dec 2 22:03:56 CET 2008

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.


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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