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# Re: st: gllamm

 From Sophia Rabe-Hesketh <[email protected]> To [email protected] Subject Re: st: gllamm Date Thu, 22 May 2003 13:10:08 +0100

```Dear Wiji,

In linear random effects models, the residual mean
times the shrinkage factor gives you the 'posterior
mean' of the random effect, i.e. E[u|y,x]. This is also
known as the empirical Bayes predictor and, in the
linear case, as the BLUP (best linear unbiased predictor).

However, in a RE probit model, there is no closed-form
expression for the posterior mean. Gllamm therefore
uses numerical integration (adaptive quadrature
if you used the recommended 'adapt' option for
estimation), both for the posterior mean and standard
deviation. For more details, you may want to have a
look at my talk at the UK Stata Users' Group Meeting
which will soon be available from:

http://ideas.repec.org/s/boc/usug03.html

Best regards,

Sophia

At 10:08 AM 5/20/2003 +0100, you wrote:
>Dear Colleagues,
>I am using gllamm to estimate a RE probit and saving the estimated
residuals for further analysis. I understand this gives an estimate of the
individual specific unobservable. Reading through the manual and also
Harvey Goldstein's book, I worked out that the residual mean that is used
in the calculation of the individual heterogeneity term is calculated as
y(i,j)-(xb)ij. This is the value that gets multiplied by the shrinkage factor.
>Could someone please tell me how this term is calculated when the
dependent variable is discrete taking values of 0 or 1. I have just tried
to check this manually with the towerl.dta data supplied with gllamm but it
does not give me the same answer. So I guess they must be calculating using
a different formula in the discrete case.
>Many thanks for your help.
>best
>wiji
>
>
>
>=================================
>Professor Wiji Arulampalam,
>Department of Economics,
>University of Warwick,
>Coventry,
>CV4 7AL,
>UK.
>Tel: +44 (24) 7652 3471
>Sec. Tel: +44 (24) 7652 3202
>Fax: +44 (24) 7652 3032
>email:  [email protected]
>http://www.warwick.ac.uk/fac/soc/economics/staff/faculty/arulampalam/
>RES2003: http://www.warwick.ac.uk/res2003/
>
>
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```

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