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


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Dependent var is a proportion, with large spike in .95+
Date   Thu, 4 Sep 2008 18:07:56 +0100

Austin Nichols has kindly pointed out that what I wrote below is not
correct as a summary of what was in the article. See the article itself
for the story. Thanks to Austin for the quick fix. 

-----Original Message-----
From: Nick Cox 
Sent: 04 September 2008 17:50
To: 'statalist@hsphsun2.harvard.edu'
Subject: FW: st: RE: Dependent var is a proportion, with large spike in
.95+

A formal statement can be found within 

http://www.stata-journal.com/sjpdf.html?articlenum=gr0010

together with explicit code for exploring the question graphically.
Whatever the parameters, the result of a logit transform of a beta
distribution is a logistic distribution, which is bell-shaped. 

Of course, real datasets might not be so well behaved, as I presume all
agree. 

Nick Cox 

Jverkuilen 

#A good approximation is if that you take #logits of a beta-distributed
#variable, the distribution looks bell-
#shaped. That's true even for
#highly skewed betas with modes near 0 #or near 1. 

Yes, so long as the distribution is not J- or L-shaped, which can happen
with the beta. It can handle those shapes and endpoint bimodality too.


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