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Re: st: discrete dep var in OLS and implications for goodness-of-fit


From   n j cox <n.j.cox@durham.ac.uk>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: discrete dep var in OLS and implications for goodness-of-fit
Date   Sun, 21 Oct 2007 23:22:33 +0100

I am not clear what kind of comments you
really want here, but I think you are
conflating some distinct issues.

OLS is an estimation method. What seems more
pertinent here is that you are fitting a linear
structure. It is easy to imagine set-ups
in which a discrete response nevertheless
follows some approximately linear structure
and even easier to imagine set-ups in which
it doesn't. On the whole, in my experience,
ordinal responses tend to participate in some
non-linear relationships,
but that doesn't mean that yours does.

In any case, the justification for what you
doing should flow from the underlying
science and the general behaviour of your data,
and I can't see that anybody on the list can
comment on either.

I am aware that this won't help much at
all but I think you'll have to give more information
to get a much better answer.

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

Lloyd Dumont

I am running an OLS model on a discrete
dependent variable that takes on whole number values
between 0 and 5, inclusive.  It is actually an ordered
categorical, so an ordered logit would be more
approrpriate than OLS.  But, OLS coefficients are
easier to explain.  So, I figured I would make sure
the results are qualitatively identical, and then
present and interpret the OLS estimates.

Questions:
- The R2 is not very high.  I think it is biased
downward by the fact that the dep var is not really
continuous.  Is this true, and is there a good
reference I can look at to understand this?

-Are their any other big pitfalls to my decision to
run OLS on a variable that wasn't really made for OLS?

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