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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   st: RE: Dependent var is a proportion, with large spike in .95+
Date   Thu, 4 Sep 2008 13:12:53 +0100

My take differs from anybody else! From what you say, this is not a
spike. It is just strong skewness. 

A spike in my book is a big group of identical values, in this context
usually lots of exact zeros or exact ones (or 100%s, naturally). 

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. Here, as in many other
places, the logit works wonders. So, your proportion data are fit for a
beta model to the extent that their logits look bell-shaped. Of course,
you might end up fitting a mediocre model if you can't think of or fit a
better one. 

However, if you have any exact zeros or ones, you can't take logits, and
equivalently you can't really fit a beta. You need either a fudge that
denies that the zeros or ones really are that or a mixture model such as
others are referring to. 

Nick [not Nic] 
n.j.cox@durham.ac.uk 

Dan Weitzenfeld

I am trying to determine which testing factors drive a proportion
dependent variable, PercentNoise.
In searching the archives, I came across -betafit-, and a link to the
FAQ: "How do you fit a model when the dependent variable is a
proportion?"  In that response, Allen McDowell and Nic Cox write, "In
practice, it is often helpful to look at the frequency distribution: a
marked spike at zero or one may well raise doubt about a single model
fitted to all data."
That describes my situation exactly:  I have a marked spike in my
histogram at the top bin, roughly .95 - 1.  I am wondering how to
account for this.
Does -betafit- take such a possibility into account?
Can someone briefly describe how I could use multiple models to fit
all the data, as implied in the FAQ response?
My fallback is setting a pass/fail bar and converting my proportions
to a binary, then using probit/logit.  But the obvious drawback is
that I am throwing away information by collapsing the continuous
(albeit bounded) proportion variable to a binary.


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