### Thursday, March 09, 2006

## RE: st: What distribution are the coefs of Random-effects GLS regression ?

We often make the assumption that these coeficient estimates are normally distributed with the given standard errors as SD, but this is only true aymptotically. For a finite number of clusters, almost any distribution is possible. If the number of clusters is small (say under 50), getting the empirical distribution of the coeffs via bootstrap is probably a better apporach than assuming normality.

Al Feiveson

-----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols Sent: Thursday, March 09, 2006 9:48 AM To: statalist@hsphsun2.harvard.edu Subject: Re: st: What distribution are the coefs of Random-effects GLS regression ?

The heading on each column of the table of estimates shown in your post gives the answer: z implies std normal in most settings. .di 2*(1-norm(abs(-1.45))) gives an approx. answer, subject to rounding error in z. . di 2*(1-norm(abs(-.2144353 /.1475938))) would do better, and . di 2*(1-norm(abs(_b[grant]/_se[grant]))) better still, I would guess.

On 3/9/06, ronggui <ronggui.huang@gmail.com> wrote: > . xtreg lscrap d88 d89 grant grant_1,re i(fcode) > ------------------------------------------------------------------------ ------ > lscrap | Coef. Std. Err. z P>|z| [95% Conf. Interval] > -------------+-------------------------------------------------------- > -------------+-------- > grant | -.2144353 .1475938 -1.45 0.146 -.5037139 .0748433

> I thought it was T-distribution, but I can't get the exact result with

> the output. > for example, the coef of grant. > . dis ttail(157,1.45)*2 > .14905327

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