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Re: st: nonlinear N effect


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: nonlinear N effect
Date   Wed, 6 Mar 2013 13:20:16 +0100

On Wed, Mar 6, 2013 at 12:14 PM, Boris Peko wrote:
> Hi! I have a non-linear effect but not U-shape or reverse U-shape.
> Effect is N-shaped, dependent variable rises, then fell, then rises.
> How can I test that in Stata?
> More important, what method should I use if I do not want to use
> predetermined inflection point?

The test depends on the _exact_ null hypothesis and the method you
used to estimate your model.

One possibility would be to add a third degree polynomial (cubic
curve), which could be an N-shaped curve. The extrema of this curve
have a closed form solution, so you can quickly look if the turning
point happen within the range of the data. -orthpoly- could be useful
for reducing multicolinearity and improving the stability of the
estimates. However, a cubic curve is often too restrictive and too
sensitive to outliers for my taste, just as a second degree polynomial
(quadratic curve) is often too restrictive and too sensitive to
outliers for hypothesised U-shaped and reverse U-shaped curves.

A better alternative would probably be -fracpoly-, but this also
depends on all kinds of details of your data, the substantive
background of your study, tribal habits within your
(sub-(sub-))discipline, etc..

Hope this helps,
Maarten


---------------------------------
Maarten L. Buis
WZB
Reichpietschufer 50
10785 Berlin
Germany

http://www.maartenbuis.nl
---------------------------------
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