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st: RE: proportion as a dependent variable


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: proportion as a dependent variable
Date   Mon, 14 Jul 2003 13:35:24 +0100

Ronnie Babigumira
 
> I was attending a workshop in which one of the presenters 
> had a regression
> in which a dependent variable was a proportion. One of the 
> participants
> noted that it was wrong but didnt follow it up with a clear 
> explanation.

Presumably the argument was that, given predictor x,
a linear form a + bx must predict response values outside [0,1] for 
some x, so that at least in principle the functional 
form cannot be appropriate. In practice, if response were (say) 
proportion female and x were time, then the time at which the 
proportion passed outside the interval might be far outside the 
range of the data, but there are plenty of exceptions. 

This is most commonly mentioned, at least in my reading, 
as a simple argument why a + bx is likely to be a poor form 
for predicting responses which are either 0 or 1, an 
argument which usually leads to a case for logit or 
probit models. But the argument seems almost as strong 
for proportions. And -- historically -- logit as a 
transformation for continuous responses preceded logit 
as (in modern terms) a link function for binary responses. 
(The terminology of logit is more recent than its use.) 

Generalised linear models offer a nice approach to this 
question using e.g. logit link and some sensible family. 

There is a FAQ with further comments at 

How does one estimate a model when the dependent variable 
is a proportion?
http://www.stata.com/support/faqs/stat/logit.html

Nick 
n.j.cox@durham.ac.uk 

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