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Re: st: Regressions with dependent continuous variable with bounded range


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Regressions with dependent continuous variable with bounded range
Date   Sun, 18 Dec 2011 15:58:28 +0000

I would rescale from [-3,3] to [0,1] and use logit with a continuous
proportion.

Logit plus a quadratic in the predictors is equivalent to fitting a
bell-like (approximately Gaussian) curve.

Nick

On Sun, Dec 18, 2011 at 2:55 PM, Brendan Halpin <brendan.halpin@ul.ie> wrote:
> I had missed the point about the bounded dependent variable.
>
> I would be inclined to say in that case that you certainly can't depend
> on interpreting the negative quadratic term as a weakening effect of the
> explanatory variable, as distinct from a ceiling effect. One way of
> looking at it is that there is a conceptual distinction between the
> effect of X being lower at high values of X, and its being lower at
> higher values of y-hat (this is a distinction that may not be possible
> to make empirically, however).
>
> A lot depends on what you want to say at a substantive level, and on how
> much impact the boundedness has on your data. If not too many y-hats
> approach the limits, then the linear model is probably good, but
> otherwise you might consider alternatives that take the boundedness into
> account (I made exactly this point to a colleague at a conference on
> Friday, suggesting ordered logit as an alternative to a linear model of
> a 5-point scale, as a robustness check on an interaction that was
> important to his story).
>
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