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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 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: RE: proportion as a dependent variable***From:*Richard Herrell <rherre2@uic.edu>

**st: RE: RE: proportion as a dependent variable***From:*"Joao Pedro W. de Azevedo" <jazevedo@provide.com.br>

**References**:**st: proportion as a dependent variable***From:*"Ronnie Babigumira" <ronnie.babigumira@ios.nlh.no>

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