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Re: st: Tobit model using GLLAMM

From   Maarten Buis <[email protected]>
To   [email protected]
Subject   Re: st: Tobit model using GLLAMM
Date   Tue, 24 Jul 2012 11:37:46 +0200

On Tue, Jul 24, 2012 at 11:12 AM, Spriensma, A.S. wrote:
> I'm working on a Tobit model in GLLAMM.
> This model uses the Identity link for the Gaussian distribution and the sprobit (scaled Probit) for the Binomial distribution.
> Does anyone know the reason why a 'scaled Probit' is used instead of an ordinary Probit? And is it also possible to use a Logit link instead?

This follows from the logic behind a Tobit model:

It starts with a latent variable that follows a Gaussian/normal
distribution (conditional on some explanatory variables). If that
latent variable is larger than some cut-off values (often 0) than you
observe that latent variable otherwise you observe the cut-off value.

So the probability of being cut-off can be derived from the cumulative
density function of the Gaussian/normal distribution, hence the probit
link function. Moreover, we have some information about the variance
of that normal distribution from the non-cut-off observations: hence
the scaled probit rather than "regular" probit, which assumes the
variance equals 1.

You'd probably be able to derive a similar model starting with a
latent variable that follows a logistic rather than a Gaussian
distribution in order to be able to use the logit link function.
However, this will also change the other parts of the model. So you
cannot just change the scaled probit to a (scaled) logit link function
without changing the logic behind this model.

Hope this helps,

Maarten L. Buis
Institut fuer Soziologie
Universitaet Tuebingen
Wilhelmstrasse 36
72074 Tuebingen
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