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RE: st: RE: Dependent var is a proportion, with large spike in .95+


From   jverkuilen <jverkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Dependent var is a proportion, with large spike in .95+
Date   Thu, 4 Sep 2008 23:36:37 -0400

The inverse logit-beta distribution turns out to be kind of interesting. I have a Mathematica notebook of the transformation if anyone cares. It is only symmetric when the beta is symmetric and starts to resemble (graphically---I did no formal proof... yet) extreme value distributions when the beta is skewed. There may be an advantage for estimation for using the IL-Beta, however. 



-----Original Message-----
From: "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To: statalist@hsphsun2.harvard.edu
Sent: 9/4/2008 5:46 PM
Subject: RE: st: RE: Dependent var is a proportion, with large spike in .95+

Maarten buis wrote:

>Good point, a beta distribution can be skewed. To find out if your data
>is beta distributed you can use -hangroot-, -pbeta-, and/or -qbeta-,
>all downloadable from SSC. Type -findit hangroot-, -findit pbeta-,
>and/or -findit qbeta- to find them. 

These are useful but remember that the regression model assumes that the
response variable is *conditionally* beta. The marginal distribution
without regressors can be markedly different from a beta as Y|X ~ Beta
!=> Y ~ Beta. 

I am very interested in the point Nick raised about logit transforming
the response. This is implicit in the ML equations because the
sufficient statistics are log(y) and log(1-y) and it's easy to rewrite
things in terms of log(y/(1-y)). I need to look at the distribution of
the inverse logit-beta. I suspect it'll line up nicely with the
exponential-gamma distribution. 

JV

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