### Tuesday, March 07, 2006

## Re: st: rho in xtreg

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 > > * > * For searches and help try: > * http://www.stata.com/support/faqs/res/findit.html > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > > >

-- Stas Kolenikov http://stas.kolenikov.name

* * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

Tag: statalist