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| From | Stas Kolenikov <skolenik@gmail.com> |
| To | statalist@hsphsun2.harvard.edu |
| Subject | Re: st: sigma_u = 0 in xtreg, re |
| Date | Mon, 29 Aug 2011 16:26:26 -0500 |
John, certainly so asymptotically when the true sigma_u = 0. Whether that is exactly true in finite samples, I don't know, although at the face of it, it looks reasonable: set seed 1234 set obs 100 gen id = _n gen ni = rpoisson(5) + 1 expand ni gen x = uniform() gen y = x + rnormal() xtreg y x, i(id) reg y x On Mon, Aug 29, 2011 at 4:14 PM, John Antonakis <John.Antonakis@unil.ch> wrote: > One clarification; when rho = 0 aren't these estimates simply OLS estimates? > > Best, > J. > > __________________________________________ > > Prof. John Antonakis > Faculty of Business and Economics > Department of Organizational Behavior > University of Lausanne > Internef #618 > CH-1015 Lausanne-Dorigny > Switzerland > Tel ++41 (0)21 692-3438 > Fax ++41 (0)21 692-3305 > http://www.hec.unil.ch/people/jantonakis > > Associate Editor > The Leadership Quarterly > __________________________________________ > > > On 29.08.2011 22:50, Stas Kolenikov wrote: >> >> Note that you have a very decent R^2, especially the between one. It >> looks, hence, that all of the bewteen-panel variability in Y is >> explained by the between-panel variability in X's (the ICC's were >> quite similar for each of the variables), so there indeed is little >> left that needs explaining. -xtsum- is somewhat misleading here, as >> this is a marginal measure, not a conditional one (which is what >> matters for the regression). >> >> Technically speaking, you are hitting a corner solution for sigma_u. >> In the simplest form of the estimator for sigma_u, it is formed as >> [mean total square] - [mean within square], so substraction of two >> non-negative quantities gave you a negative quantity (which was >> truncated upwards to zero). More elaborate estimators exist that >> guarantee both within and between sigmas to be positive, but for a >> vast majority of situations, the simple one should do just fine, so >> that's what -xtreg, re- does. >> >> On Mon, Aug 29, 2011 at 1:45 PM, Lloyd Dumont<lloyddumont@yahoo.com> >> wrote: >>> >>> Hello, Statalist. >>> >>> I am a little confused by the output from an -xtreg, re- estimate. >>> >>> Basically, I end up with sigma_u = 0, which of course yields rho = 0. >>> That seems very odd to me. I would guess that that should only happen if >>> there is no between-subject variation. But, (I think) I can tell from >>> examining the data that that is not the case. >>> >>> I have tried to create a mini example… First, I will show the xtreg >>> results. Then, I will show you what I think is the evidence that there >>> really IS some between-subject variation. >>> >>> Am I missing something obvious here? Thank you for your help and >>> suggestions. Lloyd Dumont >>> >>> >>> . xtreg Y X, re >>> >>> Random-effects GLS regression Number of obs = >>> 3133 >>> Group variable: ID Number of groups = >>> 31 >>> >>> R-sq: within = 0.4333 Obs per group: min = >>> 1 >>> between = 0.8278 avg = >>> 101.1 >>> overall = 0.4579 max = >>> 124 >>> >>> Wald chi2(1) = >>> 2644.38 >>> corr(u_i, X) = 0 (assumed) Prob> chi2 = >>> 0.0000 >>> >>> >>> ------------------------------------------------------------------------------ >>> Y | Coef. Std. Err. z P>|z| [95% Conf. >>> Interval] >>> >>> -------------+---------------------------------------------------------------- >>> X | -.0179105 .0003483 -51.42 0.000 -.0185932 >>> -.0172279 >>> _cons | 1.004496 .0017687 567.92 0.000 1.001029 >>> 1.007963 >>> >>> -------------+---------------------------------------------------------------- >>> sigma_u | 0 >>> sigma_e | .07457648 >>> rho | 0 (fraction of variance due to u_i) >>> >>> ------------------------------------------------------------------------------ >>> >>> >>> >>> >>> . xtsum X >>> >>> Variable | Mean Std. Dev. Min Max | >>> Observations >>> >>> -----------------+--------------------------------------------+---------------- >>> X overall | 3.277883 3.875116 0 42.5 | N = >>> 3137 >>> between | 1.286754 0 6.890338 | n = >>> 31 >>> within | 3.729614 -3.612455 42.24883 | T-bar = >>> 101.194 >>> >>> >>> >>> . xtsum Y >>> >>> Variable | Mean Std. Dev. Min Max | >>> Observations >>> >>> -----------------+--------------------------------------------+---------------- >>> Y overall | .9457124 .1025887 0 1 | N = >>> 3133 >>> between | .0315032 .8387879 1 | n = >>> 31 >>> within | .0985757 -.0235858 1.106925 | T-bar = >>> 101.065 >>> >>> . >>> >>> >>> * >>> * For searches and help try: >>> * http://www.stata.com/help.cgi?search >>> * http://www.stata.com/support/statalist/faq >>> * http://www.ats.ucla.edu/stat/stata/ >>> >> >> > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/statalist/faq > * http://www.ats.ucla.edu/stat/stata/ > -- Stas Kolenikov, also found at http://stas.kolenikov.name Small print: I use this email account for mailing lists only. * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/