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Re: st: sigma_u = 0 in xtreg, re


From   John Antonakis <John.Antonakis@unil.ch>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: sigma_u = 0 in xtreg, re
Date   Mon, 29 Aug 2011 21:31:14 +0200

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/


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