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Re: st: Question on Logit/Probit

From   Maarten buis <>
Subject   Re: st: Question on Logit/Probit
Date   Mon, 26 Mar 2007 08:07:08 +0100 (BST)

--- David Cobey <> wrote:
> > > I'm trying to estimate the percentage of an area under high yield
> > > variety crops as time changes. I hoping to estimate a basic S
> > > shaped technology diffusion model.  Can I use logit and probit
> > > for a continuous dependant variable ranging from 0-1 or does
> > > logit/probit only work for discrete variables?

--- At 11:45 PM 3/25/2007, Jeremy Miles wrote:
> > I think you want to use a beta regression.  I don't know if it
> > exists (I've never tried to find it in Stata).

--- Richard Williams <> wrote: 
> Come to think of it, I believe Maarten Buis said something about this
> not too long ago.  I assume he must sleep some time, so I'll post the
> link to his page:

I am awake now. David is referring to what is sometimes called a
fractional logit model. Which can be estimated using -glm-. Richard is
referring to -betafit-, which was written by Nick Cox, Stephen Jenkins,
and me.

The the mean fraction is modeled in the same way in both the beta
regression model and the fractional logit (both a logistic curve). The
difference is in how the variance is modeled. With beta regression you
specify also an explicit model for the variance, while with fractional
logit you treat the variance as a nuisance parameter. 

Another thing that some people care about is that fractional logit can
handle proportions of exactly zero or one, beta regression can't. In
many cases (but not always) I would argue that those proportions should
be modeled as a separate process. See for instance: .

Hope this helps,

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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