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RE: Re: st: Dependent continuous variable with bounded range


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: Re: st: Dependent continuous variable with bounded range
Date   Thu, 17 Apr 2008 19:03:47 +0100

Good point. In fact a little thought shows that if a variable is bounded
on [0,1] then as the mean goes
to either 0 or 1 the variance must go to 0, because the mean can only
approach 0 or 1 
if all values approach 0 or 1. That is true regardless of whether the
variable is discrete or continuous. 
(Same is true for any finite bounds.) 

Verkuilen, Jay

Nick Cox wrote:

>However, it may well be that the discreteness of the binomial is not
all crucial here, 
rather the shape of its variance function. People with a closer
knowledge of the literature or a deeper theoretical understanding may
wish to comment. The binomial is recommended in
http://www.stata.com/support/faqs/stat/logit.html<<

In point of fact, the variance function of the beta distribution is the
same as the binomial, up to an additional free scale constant. Both are
proportional to E(X)(1-E(X)). You would definitely want to free up the
scale parameter for continuous data, though. 


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