Re: st: How to model heterogeneity in level 1 residual variance (sigma^2)?

 From rgutierrez@stata.com (Roberto G. Gutierrez, StataCorp) To statalist@hsphsun2.harvard.edu Subject Re: st: How to model heterogeneity in level 1 residual variance (sigma^2)? Date Thu, 20 Mar 2008 10:52:57 -0500

```HsienYuan Hsu <hsuhy0914@gmail.com> writes:

> I am tring to model heterogeneity in level 1 residual variance (sigma^2).

> In my model, I have
> DV: mathach
> IV: Female

> If I use the syntax:
> xtmixed  mathach female || id:female , cov(unstruct) nocons , ml

> It gives me "one sigma^2.  However, I want to model the sigma^2 for male and
> female, respectively.  Does any expert know the syntax?

Modeling observation-level heterogeneity requires first creating a variable
identifying the observations and then explicitly adding this level to the
model

. gen obs = _n
. xtmixed mathach female || id:female, cov(unstruct) nocons ///
|| obs:female, nocons ml variance

When you fit this model, the variance component for the "obs" level represents
the added variability due to being female at the residual level.
Mathematically, sigma^2 for males is var(Residual) as labeled in the output;
sigma^2 for females is var(Residual) + var(female), for var(female) as given
in the "obs:" level of the model.

If this model does not converge, it is most likely because there is no added
variability due to being female -- sigma^2 for females is actually less than
that for males.  No problem -- simply reverse the coding

. gen male = 1 - female
. xtmixed mathach female || id:female, cov(unstruct) nocons ///
|| obs:male, nocons ml variance

and now sigma^2 for females is var(Residual) and that for males is
var(Residual) + var(male).

--Bobby
rgutierrez@stata.com
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```