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Re: st: sigma_u = 0 in xtreg, re
From
Stas Kolenikov <[email protected]>
To
[email protected]
Subject
Re: st: sigma_u = 0 in xtreg, re
Date
Mon, 29 Aug 2011 16:26:26 -0500
John,
certainly so asymptotically when the true sigma_u = 0. Whether that is
exactly true in finite samples, I don't know, although at the face of
it, it looks reasonable:
set seed 1234
set obs 100
gen id = _n
gen ni = rpoisson(5) + 1
expand ni
gen x = uniform()
gen y = x + rnormal()
xtreg y x, i(id)
reg y x
On Mon, Aug 29, 2011 at 4:14 PM, John Antonakis <[email protected]> wrote:
> One clarification; when rho = 0 aren't these estimates simply OLS estimates?
>
> Best,
> 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 22:50, Stas Kolenikov wrote:
>>
>> Note that you have a very decent R^2, especially the between one. It
>> looks, hence, that all of the bewteen-panel variability in Y is
>> explained by the between-panel variability in X's (the ICC's were
>> quite similar for each of the variables), so there indeed is little
>> left that needs explaining. -xtsum- is somewhat misleading here, as
>> this is a marginal measure, not a conditional one (which is what
>> matters for the regression).
>>
>> Technically speaking, you are hitting a corner solution for sigma_u.
>> In the simplest form of the estimator for sigma_u, it is formed as
>> [mean total square] - [mean within square], so substraction of two
>> non-negative quantities gave you a negative quantity (which was
>> truncated upwards to zero). More elaborate estimators exist that
>> guarantee both within and between sigmas to be positive, but for a
>> vast majority of situations, the simple one should do just fine, so
>> that's what -xtreg, re- does.
>>
>> On Mon, Aug 29, 2011 at 1:45 PM, Lloyd Dumont<[email protected]>
>> 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
>>>
>>> .
>>>
>>>
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>>
>>
> *
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--
Stas Kolenikov, also found at http://stas.kolenikov.name
Small print: I use this email account for mailing lists only.
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