Re: [Gretl-users] restricted logit
On Thu, 17 Jun 2010, Sven Schreiber wrote:
Hi,
I'm trying to get the estimates from a restricted logit model.
Here's roughly what I mean to do (except it's not working the way I want):
<script>
open greene12_1
logit selfemp age income const
matrix unrestricted = $coeff
restrict
b[age]=1
end restrict
matrix restricted = $coeff
unrestricted
restricted
</script>
I also tried the "--full" option for the restrict block, but that just
gives me errors.
Is there a way in gretl to get restricted logit estimates? (without
manually coding it, I mean)
There isn't. With a bit of work, the --full option could be extended to
logit/probit models. However, why should we? Let me explain: in the case
of logit/probit models, the situation is very different if your constraint
is homogeneous or not. (Just to establish notation: you would like to
estimate a vector \beta under the constraint R\beta = d. If d zero?)
If it is, estimating the restricted model is trivial, because it
just implies re-defining the regressors, so that poses no problem and the
--full option is not really needed. (Example: x1*b1 + x2*b2, under the
constraint b1=b2 becomes (x1+x2)*b1; easy)
If d is NOT zero (like in your example), then it isn't clear to me why you
would want to test such a constraint, since the \beta vector in
logit/probit models is identified up to a scale factor, which is why
everyone uses the arbitrary convention of setting \sigma^2 to 1.
In other terms, in this context it makes sense to compare the relative
magnitude of coefficients, but (if I'm not mistaken) a hypothesis on their
absolute value does not.
Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche
r.lucchetti(a)univpm.it
http://www.econ.univpm.it/lucchetti