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

 From Suryadipta Roy To statalist@hsphsun2.harvard.edu Subject Re: st: Regressions with dependent continuous variable with bounded range Date Sun, 18 Dec 2011 11:56:13 -0500

Dear Brendan and Nick,

Thank you so much for the detailed suggestions! I will try to
implement these. Infact, I was just reading the paper by Papke and
Wooldridge (Journal of Econometrics, 2008) "Panel data methods for
fractional response variables with an application to test pass rates"
in order to understand the application better.

Best regards,

On Sun, Dec 18, 2011 at 10:58 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> 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 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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