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Re: st: A question about modelling heterogenous variances

Subject   Re: st: A question about modelling heterogenous variances
Date   Fri, 21 Oct 2005 17:34:14 +0200

Maybe you could use Harvey's (1976) multiplicative heteroscedastic regression.
It's documented in Stata Technical Bulletin 42. Type

net describe sg77

for details. Best, Peter


> Hi,
> Consider the following problem: I want to regress age on sex, but my
> dataset was collected from four sites, so I'd like to control for site. I
> could do:
> xi: reg age
> But graphical examination suggests that different sites had different
> variances. What's the solution?
> I've done some research already, and it seems that if I use either -vwls-
> with the sd option, or -reg- with the aweight option, I'll be able to get
> round this to a certain extent. The problem is I'll first need to estimate
> the variance in another way, most likely by obtaining the residuals from
> an OLS regression first.
> Besides the rather long-winded way of this approach, theoretically the
> estimates won't be optimal because the variances estimates are not based
> on the weighted regression. But still, if this is the best way to go about
> the problem, I'll probably use it. One question is: Can the use of aweight
> be readily extended to more complicated models such as -glm- or -xtgee- to
> account for heterogeneity in variances? If so, how?
> One of the great features of Stata is its robust option in many estimation
> commands. Theoretically in normal linear regression, it replaces the
> variance matrix of our error (e) with an empirical one based on the
> residuals. I foresee that one solution to my problem would be to create a
> variance matrix that is half way between the OLS and this empirical one,
> that is one that has its residuals averaged within each group (site). One
> problem with the robust option is that often if my subgroup size is too
> small, it gives rubbish estimates of Standard error. I wonder if this
> could be a solution to this too. Has anyone done methodological
> investigation into this technique?
> Yours,
> Tim Mak
> PS this query has been posted in allstat
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