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

[Suryadipta Roy <sroy2138@gmail.com>]

Cam,
This is very interesting indeed! I had thought of SEM, but not this.

Sincerely,
Suryadipta.

On Mon, Dec 19, 2011 at 9:46 AM, Cameron McIntosh <cnm100@hotmail.com> wrote:
> An explorative approach to non-linearity might also be worth considering:
> Buckler, F., & Hennig-Thurau, T. (2008). Identifying Hidden Structures in Marketing’s Structural Models Through Universal Structure Modeling: An Explorative Bayesian Neural Network Complement to LISREL and PLS. Marketing -- Journal of Research and Management, 4(2), 47-66.http://www.neusrel.com/index.html
>
> Cam
>> Date: Mon, 19 Dec 2011 08:52:42 -0500
>> Subject: Re: st: Regressions with dependent continuous variable with bounded range
>> From: sroy2138@gmail.com
>> To: statalist@hsphsun2.harvard.edu
>>
>> 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
>> suggests non-linearity. I, of course, start with the linear form. We
>> 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,
>> Suryadipta.
>>
>> 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,
>> >> Suryadipta.
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