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Re: st: Constructing a variable from standard deviations

From   Maarten buis <>
Subject   Re: st: Constructing a variable from standard deviations
Date   Mon, 22 Nov 2010 15:41:06 +0000 (GMT)

-- Stas wrote:
> I disagree. Mathijs can run any regression he likes, can't he? It is
> just a matter of doing the inference right, if he needs to. If he
> needed to do inference with this regression, then of course without
> -robust- or -cluster(occupation)- option the results may be
> meaningless. Maarten is right: the basic assumption of OLS is that
> error variances are constant (and Mathijs cannot argue with that; he
> can report the finding that in his actual data this assumption does
> not hold, but this does not change the underlying assumption of the
> model). But if all Mathijs needs out of this regression is a
> reasonable line to take deviations from, then OLS is  pretty much as
> good as a line by any other sophisticated method.
> Maarten's solution will give asymptotically efficient estimates in
> presence of heteroskedasticity, i.e., will be slightly more accurate
> in large samples when heteroskedasticity is indeed present. I
> personally don't believe you can gain much from modeling
> heteroskedasticity unless the differences in variances are huge, like
> a factor of 20 or so, although I cannot ground my belief in anything
> outside the common statistical sense. In small samples, however,
> excessive modeling of difficult-to-identify phenomena (like
> heteroskedasticity here) usually leads to notable small sample biases,
> so in the end the estimates from the solution that Maarten suggested
> may not be of much greater accuracy unless the sample sizes are well
> into thousands (Mathijs did not give his original sample size for us
> to make a judgement).

I think of statistical modeling as building an argument: I have observed
stuff and the model summarizes that observed stuff such that I can 
answer my question. The method of summarizing (i.e. the model) should 
provide a clear link between the data and the things I want to know: In
Mathijs' case he wanted to know the residual variances for different 
groups (occupations), so to use a model that assumes constant residual 
variance at leasts blurs the argument he wants to make. 

Now having said all that, I just ran a simulation and that showed pretty
much what Stas said. So you could use Stas's solution, but then you would
have spent place in your paper explaining why a model that assumes 
constant residual variance was used to estimate differences in residual
variance between groups, with all the potential for misunderstandings that
comes with that... 

Mathijs: Don't read too much in these disagreements: I would say that the 
difference between Stas and I is more a matter of prefered style: as long
you supported your choice with a clear argument I would be more than happy 
with either solution if I were given that paper as a reviewer.

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen


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