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Re: st: sigma u listed as zero despite unit variance


From   "Mark Schaffer" <M.E.Schaffer@hw.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: sigma u listed as zero despite unit variance
Date   Tue, 24 Feb 2004 17:13:11 -0000

Amber,

The most likely explanation is that the estimates of the two sigmas 
are such that the esitmate of one of them (sigma_u) is <0.  This can 
happen in finite samples.

If you use the -sa- option, you'll get a different set of estimates 
of the sigmas, and the estimated sigma_u might well be >0.

I am pretty sure there was a nice explanation of this by someone on 
Statalist about a year ago, but I can't remember the data or who it 
was.  A trawl through the Statalist archives might turn up something.

--Mark

Date sent:      	Tue, 24 Feb 2004 11:14:03 -0500 (EST)
To:             	statalist@hsphsun2.harvard.edu
Subject:        	Re: st: sigma u listed as zero despite unit variance
From:           	"Amber E. Boydstun" <aboydstun@psu.edu>
Send reply to:  	statalist@hsphsun2.harvard.edu

> Hi Mark,
> 
> Thanks for your help!  You're right that when I run normal OLS I get
> the same results (posted below).  Can you tell me, is the reason that
> the random effects estimator has degenerated into the OLS estimator
> that I have such a small range of variance of mean dependent variable
> values across my units (from .6603999 to .6897267)?  I guess I just
> thought that this small range would still count as SOME amount of
> random error that would register as a very small sigma_u, but
> something slightly greater than zero.  Thanks again.
> 
> - Amber
> 
> 
> 
> regress dppct educpct repubpct fundpct whitepct;
> 
>       Source |       SS       df       MS              Number of obs =
>           220
> -------------+------------------------------           F(  4,   215) =
>    3.57
>        Model |  .134161295     4  .033540324           Prob > F      =
>         0.0077
>     Residual |  2.02150052   215  .009402328           R-squared     =
>      0.0622
> -------------+------------------------------           Adj R-squared =
>  0.0448
>        Total |  2.15566182   219  .009843205           Root MSE      =
>         .09697
> 
> ----------------------------------------------------------------------
> --------
>        dppct |      Coef.   Std. Err.      t    P>|t|     [95% Conf.
>        Interval]
> -------------+--------------------------------------------------------
> --------
>      educpct |   .0596706   .0526787     1.13   0.259    -.0441622   
>      .1635033
>     repubpct |   .2223392   .1046384     2.12   0.035     .0160906   
>     .4285877
>      fundpct |   .2698267   .1397987     1.93   0.055    -.0057248   
>      .5453781
>     whitepct |   .2623254   .1236531     2.12   0.035     .0185978    
>     .506053
>        _cons |   .2656249   .1358642     1.96   0.052    -.0021714   
>        .5334213
> ----------------------------------------------------------------------
> --------
> 
> On Tue, 24 Feb 2004 15:34:25 +0000, "Mark Schaffer" wrote:
> 
> > Amber,
> > 
> > I think this means the random effects estimator has degenerated, so
> > to speak, into the OLS estimator.  Try running the regression using
> > simple pooled OLS, i.e., using -regress-, and see if the results are
> > the same.
> > 
> > --Mark
> > 
> > Date sent:      	Tue, 24 Feb 2004 10:29:44 -0500 (EST)
> > To:             	statalist@hsphsun2.harvard.edu
> > Subject:        	st: sigma u listed as zero despite unit variance
> > From:           	"Amber E. Boydstun" <aboydstun@psu.edu> Send reply
> > to:  	statalist@hsphsun2.harvard.edu
> > 
> > > I'm very confused about why the sigma_u listed in the output from
> > > a random effects model reports a value of zero, despite the fact
> > > that I have unit variance in my dataset (I promise).  I'm
> > > attaching the output below.  Could someone please tell me what
> > > this means?  Thanks!
> > > 
> > > 
> > > 
> > > 
> > > xtreg dppct educpct repubpct fundpct whitepct, re;
> > > 
> > > Random-effects GLS regression                   Number of obs     
> > > =  
> > >     220 Group variable (i) : cohort                     Number of
> > > groups   =        10
> > > 
> > > R-sq:  within  = 0.0577                         Obs per group: min
> > > =  
> > >      22
> > >        between = 0.6344                                   avg =   
> > >         22.0 overall = 0.0622                                  
> > >        max =  
> > >             22
> > > 
> > > Random effects u_i ~ Gaussian                   Wald chi2(4)      
> > > =  
> > >   14.27 corr(u_i, X)       = 0 (assumed)                Prob >
> > >   chi2   
> > >     =    0.0065
> > > 
> > > ------------------------------------------------------------------
> > > ---- --------
> > >        dppct |      Coef.   Std. Err.      z    P>|z|     [95%
> > >        Conf. Interval]
> > > -------------+----------------------------------------------------
> > > ---- --------
> > >      educpct |   .0596706   .0526787     1.13   0.257    -.0435777
> > >        .1629189
> > >     repubpct |   .2223392   .1046384     2.12   0.034     .0172516
> > >       .4274267
> > >      fundpct |   .2698267   .1397987     1.93   0.054    -.0041737
> > >         .543827
> > >     whitepct |   .2623254   .1236531     2.12   0.034     .0199697
> > >       .5046811
> > >        _cons |   .2656249   .1358642     1.96   0.051     -.000664
> > >          .5319138
> > > -------------+----------------------------------------------------
> > > ---- --------
> > >      sigma_u |          0
> > >      sigma_e |  .09882399
> > >          rho |          0   (fraction of variance due to u_i)
> > > ------------------------------------------------------------------
> > > ---- -------- Amber E. Boydstun Graduate Student Department of
> > > Political Science Penn State University University Park, PA
> > > 16802-6200 aboydstun@psu.edu * *   For searches and help try: * 
> > > http://www.stata.com/support/faqs/res/findit.html * 
> > > http://www.stata.com/support/statalist/faq * 
> > > http://www.ats.ucla.edu/stat/stata/
> > 
> > 
> > Prof. Mark E. Schaffer
> > Director
> > Centre for Economic Reform and Transformation
> > Department of Economics
> > School of Management & Languages
> > Heriot-Watt University, Edinburgh EH14 4AS  UK
> > 44-131-451-3494 direct
> > 44-131-451-3008 fax
> > 44-131-451-3485 CERT administrator
> > http://www.som.hw.ac.uk/cert
> > *
> > *   For searches and help try:
> > *   http://www.stata.com/support/faqs/res/findit.html
> > *   http://www.stata.com/support/statalist/faq
> > *   http://www.ats.ucla.edu/stat/stata/
> > 
> > 
> 
> Amber E. Boydstun
> Graduate Student
> Department of Political Science
> Penn State University
> University Park, PA 16802-6200
> aboydstun@psu.edu
> *
> *   For searches and help try:
> *   http://www.stata.com/support/faqs/res/findit.html
> *   http://www.stata.com/support/statalist/faq
> *   http://www.ats.ucla.edu/stat/stata/


Prof. Mark E. Schaffer
Director
Centre for Economic Reform and Transformation
Department of Economics
School of Management & Languages
Heriot-Watt University, Edinburgh EH14 4AS  UK
44-131-451-3494 direct
44-131-451-3008 fax
44-131-451-3485 CERT administrator
http://www.som.hw.ac.uk/cert
*
*   For searches and help try:
*   http://www.stata.com/support/faqs/res/findit.html
*   http://www.stata.com/support/statalist/faq
*   http://www.ats.ucla.edu/stat/stata/



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