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


From   brendan.halpin@ul.ie (Brendan Halpin)
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Regressions with dependent continuous variable with bounded range
Date   Sun, 18 Dec 2011 14:55:47 +0000

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).

Regards,

Brendan
-- 
Brendan Halpin,   Department of Sociology,   University of Limerick,   Ireland
Tel: w +353-61-213147  f +353-61-202569  h +353-61-338562;  Room F1-009 x 3147
mailto:brendan.halpin@ul.ie    ULSociology on Facebook: http://on.fb.me/fjIK9t
http://teaching.sociology.ul.ie/bhalpin/wordpress         twitter:@ULSociology
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