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

[Cameron McIntosh <cnm100@hotmail.com>]

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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