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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

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 -------------------------- Maarten L. Buis Institut fuer Soziologie Universitaet Tuebingen Wilhelmstrasse 36 72074 Tuebingen Germany http://www.maartenbuis.nl -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: Constructing a variable from standard deviations***From:*Stas Kolenikov <skolenik@gmail.com>

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