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Re: st: RE: proportion as a dependent variable
How would one model, say, hematocrit as a DV (% of red blood cells in
whole blood) in a way that the predictor variables would have a clear
On Mon, 14 Jul 2003, Nick Cox wrote:
> 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?
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