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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 Mon, 19 Dec 2011 08:52:42 -0500

```Dear David,
Thank you very much for the useful suggestions! I completely
understand the points that have made, and will definitely explore
them. Actually, the incorporation of the quadratic x is driven by the
theoretical hypothesis, which has implications for the signs of x and
x-squared. A basic scatter diagram: twoway scatter y x, by(year) also
can also probably compare between the models on the basis of LR tests,
or AIC/BIC criteria. Interestingly, a logit regression of the form
that Nick suggested gives me the (statistically significant) expected
signs of the coefficients. However, I would have to check the
robustness etc.

Best regards,

On Sun, Dec 18, 2011 at 2:11 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> Dear All,
>
> Is it well-established that the effect is quadratic in x, as opposed
> to being nonlinear in x (the functional form might be quadratic or
> something else entirely)?  If the form is not necessarily quadratic, a
> good strategy would fit the linear term in x and then examine the
> pattern of nonlinearity by plotting the residuals against x.  A
> quadratic term can provide a reasonable approximation for some
> patterns of nonlinearity, but not for others.
>
> Also, centering x at a suitable value (often near the middle of its
> range) would be a good preliminary step.
>
> David Hoaglin
>
> On Sun, Dec 18, 2011 at 11:56 AM, Suryadipta Roy <sroy2138@gmail.com> wrote:
>> 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,
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