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Re: st: sigma_u = 0 in xtreg, re
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
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 <[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:
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* http://www.stata.com/support/statalist/faq
* http://www.ats.ucla.edu/stat/stata/