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