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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 22:31:32 +0200

The calculations for rho and ICC are not the same....best you review what rho does, exactly.

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:
> 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
>> 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:
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>>> *   http://www.stata.com/support/statalist/faq
>>> *   http://www.ats.ucla.edu/stat/stata/
>> *
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>>
> *
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