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From |
John Antonakis <[email protected]> |

To |
[email protected] |

Subject |
Re: st: sigma_u = 0 in xtreg, re |

Date |
Mon, 29 Aug 2011 22:31:32 +0200 |

HTH, 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 22:29, Lloyd Dumont wrote:

>

> > (See output below.) Thanks again, John. Lloyd Dumont > > > . loneway Y ID > > One-way Analysis of Variance for Y: (mean) Y > > Number of obs = 3133 > R-squared = 0.0767 > > Source SS df MS F Prob > F > ------------------------------------------------------------------------- > Between ID 2.5284181 30 .0842806 8.59 0.0000 > Within ID 30.434161 3102 .00981114 > ------------------------------------------------------------------------- > Total 32.962579 3132 .01052445 > > Intraclass Asy. > correlation S.E. [95% Conf. Interval] > ------------------------------------------------ > 0.07005 0.01978 0.03128 0.10881 > > Estimated SD of ID effect .0271849 > Estimated SD within ID .0990512 > Est. reliability of a ID mean 0.88359 > (evaluated at n=100.77) > > > > > --- On Mon, 8/29/11, John Antonakis <[email protected]> wrote: > >> From: John Antonakis <[email protected]> >> Subject: Re: st: sigma_u = 0 in xtreg, re >> To: [email protected] >> Date: Monday, August 29, 2011, 3:31 PM >> Hi: >> >> You should visit what rho or ICC--intraclass correlation >> coefficient (in ANOVA speak) means. From the ANOVA >> perspective, here's one way to calculate it--check the Stata >> manual to see how it is precisely done in loneway): >> >> ICC1 = (MSb - MSw)/(MSb + ([k-1]*MSw) >> >> Where >> MSb = mean-square between >> MSw=means-square within >> k=average group size >> >> Here's an example (from the help file): >> >> . webuse auto7 >> . loneway mpg manufacturer_grp >> >> This gives: >> >> One-way >> Analysis of Variance for mpg: Mileage (mpg) >> >> >> >> Number of >> obs = 74 >> >> >> >> R-squared = 0.5507 >> >> Source >> SS >> df MS >> F Prob >>> F

>> Between manufactur~p 1345.588 >> 22 61.163092 >> 2.84 0.0011 >> Within manufactur~p 1097.8714 >> 51 21.526891

>> Total >> 2443.4595 73 >> 33.472047 >> >> Intraclass >> Asy. >> correlation >> S.E. [95% Conf. >> Interval] >> >> ------------------------------------------------ >> 0.36827 >> 0.13679 >> 0.10017 0.63636 >> >> Estimated SD of >> manufactur~p effect 3.542478 >> Estimated SD within >> manufactur~p 4.639708 >> Est. reliability of >> a manufactur~p mean 0.64804 >> (evaluated >> at n=3.16) >> >> Calculating ICC manually: >> >> . dis ( 61.1630923 - 21.5268908)/( 61.1630923 + >> ((3.16-1)*21.5268908)) >> >> Gives: >> .36815687 >> >> As for your data, it seems that you have a lot of >> within-cluster variability (that is much higher than >> between-group variability). This suggests that observations >> are pretty much "independent" (and once you see the formula >> for ICC, it is obvious that it will approach zero as the >> denominator becomes larger, ceteris paribus). >> >> Try running the following and see what you get: >> >> loneway y ID >> >> You should get an ICC (intraclass correlation) that is >> zero. >> >> If so, I would just estimate the following (and just to be >> sure that the SEs are consistent): >> >> reg y x, cluster(ID) >> >> HTH, >> John. >> >> __________________________________________ >> >> 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 20:45, Lloyd Dumont 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/ >> __________________________________________ >> >> 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 20:45, Lloyd Dumont 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/ >> > * > * 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/

**References**:**Re: st: sigma_u = 0 in xtreg, re***From:*Lloyd Dumont <[email protected]>

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