RE: st: how to replicate Stata's random effects estimation results?

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

An alternative is look directly at the code Stata uses for random effects.  This can be found in the ado file xtreg_re.ado, which is sitting in your ..ado\base\x folder.  Reading Stata code isn't easy, but I think in this case it's a practical suggestion.

Looking at the code, I can see that the first 200 lines or so are mainly taken up with data preparation and obtaining the estimate of theta used for quasi-demeaning.  Once this is obtained, the code is very simple and there is in fact an internal call to -regress- to get the RE results (just after the comment in the file that says "obtain random-effects estimates").

Replicating the RE results thus amounts to replicating the derivation of theta, which is either a constant (in the case of balanced data) or a column vector.  There is an option to report theta, so you can start by replicating the RE estimator for balanced data by quasi-demeaning by hand using the reported theta.

The code for deriving theta looks pretty messy, though, I must confess.

--Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of 
> Stas Kolenikov
> Sent: 02 September 2010 23:21
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: how to replicate Stata's random effects 
> estimation results?
> 
> You can probably replicate -xtreg-, re- using Mata, but to 
> get as far down as -regress-, you would need to perform a 
> special transformation of the data by the inverse square root 
> of the covariance matrix of all observations (the Kronecker 
> product of the identity matrix and the covariance matrix of 
> residuals if the data are homoskedastic and balanced). This 
> will give you some insight into numerics such as Cholesky 
> decomposition of a matrix, but I doubt one can benefit 
> greatly from trying to get this by hand.
> 
> On Thu, Sep 2, 2010 at 9:02 AM, Ada Ma <heu034@googlemail.com> wrote:
> > Statalisters,
> >
> > I want to replicate Stata's Random Effects estimates using only the
> > -regress- command, to gain better understanding as well as to do 
> > something that the current -xtreg- command wouldn't allow me to do.
> >
> > Do you know of any demonstration where people have been able to 
> > replicate Stata's RE estimates by hand?  Or journal articles that 
> > describe exactly how the RE estimates are calculated?  I 
> have looked 
> > through several econometrics textbooks and it is not entirely clear.
> >
> > Many thanks in advance.
> >
> > Regards,
> > Ada
> >
> >
> > --
> > Ada Ma
> > Research Fellow
> > Health Economics Research Unit
> > University of Aberdeen, UK.
> > http://www.abdn.ac.uk/heru/
> > Tel: +44 (0) 1224 555189
> > Fax: +44 (0) 1224 550926
> > *
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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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> 


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