There are two intrinsic impediments. First, -rho- is treated as an
ancillary parameter in -xtreg-: it does not estimate its standard
errors or anything. You can get around this with -mle- option that
will estimate the sigma's, and then you would have to form -rho- and
its standard error from there. Second, I am not aware of any
statistically justified methodology of comparing two coefficient
estimates in two models the way you want. In any nested model testing,
you are imposing some restrictions, like setting the coefficient of
gender equal to zero (effectively omitting it). This is not a
restriction on -rho-, however. I don't think you can compare
unrestricted estimates in two estimated models -- at least if they are
estimated on the same data set. If they were estimated on independent
data sets, then you could test them assuming covariance is equal to
zero, so the test would be effectively a two-sample t-test.
A better way for you to go is to use some sort of structural equation
modeling with multiple group comparisons where you would be allowing
-sigma_u- and -sigma_e- to vary between males and females. If you are
brave enough, you can dig into -xtreg- code (saving it under a
different name, of course) to allow the variance parameters to be
dependent on some covariates, like gender, and then test if those
heteroskedastic models are significantly different from the regular
-xtreg-. If not, you may want to (ask your students to) locate
appropriate structural equation modeling software (AMOS, LISREL,
M-plus, EQS) on your campus to run a model like that. This might also
be doable in -gllamm-.
Note that you are assuming quite restrictive things here like known
linear part of the model, known distribution, and known form of
heteroskedasticity. While you can interpret the panel regression
models as fitting linear regression models with some variations for
the panel structure, with a nice feature of being the MLEs if the data
just happened to be normal, you need to put more thought into the
MLEs.
On 3/7/06, Visintainer, Paul <PAUL_VISINTAINER@nymc.edu> wrote:
> Thanks, Joseph. I have the text to which you refer, but I couldn't find a way to formally test it in -xtreg-, just -bootcor-. I'll give your approach a try.
>
> -p
>
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu on behalf of Joseph Coveney
> Sent: Tue 3/7/2006 2:07 AM
> To: Statalist
> Subject: Re: st: rho in xtreg
>
> Paul Visintainer wrote:
>
> -xtreg- produces "rho" which can be interpreted as a reliability
> coefficient (e.g., the intraclass correlation). If one adds another
> covariate (e.g., gender), rho is "adjusted" for gender. Is there a way
> in -xtreg- to test whether rho differs by level of the covariate? That
> is, whether the rho for males differs from the rho for females?
>
> --------------------------------------------------------------------------------
>
> If I understand correctly, you can model separate residual variances and
> then use a likelihood ratio test to see whether this adds anything to a
> model that doesn't allow for residual variance to differ between sexes.
>
> This can be done using -gllamm- (see S. Rabe-Hesketh and A. Skrondal,
> _Multilevel and Longitudinal Modeling Using Stata_ (College Station, Texas:
> Stata Press, 2005), pp. 92-94), but as far as I know not yet with -xtmixed-.
>
> Joseph Coveney
>
> sysuse bplong
> tabulate sex, generate(sex_)
> eq het: sex_1 sex_2
> xi: gllamm bp i.when sex, i(patient) s(het) adapt
> estimates store Het
> xi: gllamm bp i.when sex, i(patient) adapt
> lrtest Het .
> exit
>
> *
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>
>
>
--
Stas Kolenikov
http://stas.kolenikov.name
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