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# Re: st: sigma_u = 0 in xtreg, re

 From Lloyd Dumont To statalist@hsphsun2.harvard.edu Subject Re: st: sigma_u = 0 in xtreg, re Date Mon, 29 Aug 2011 13:29:18 -0700 (PDT)

Hello, John.  That was super helpful, particularly your suggestion that I review the formula and meaning of ICC.

I did what you suggested.  Interestingly, the ICC for Y is small, but not infinitesimally so.  I mean, if ICC is about .07 when run as –loneway- (apparently on the same sample that the –xtreg- is run on), then why wouldn’t sigma_u in the -xtreg- be about .07 ?

(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 <John.Antonakis@unil.ch> wrote:

> From: John Antonakis <John.Antonakis@unil.ch>
> Subject: Re: st: sigma_u = 0 in xtreg, re
> To: statalist@hsphsun2.harvard.edu
> 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
> __________________________________________
>
>
> 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
> __________________________________________
>
>
> 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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