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Re: st: Test for significance of the difference between knee locations?


From   Maarten Buis <maartenlbuis@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Test for significance of the difference between knee locations?
Date   Fri, 19 Oct 2012 10:05:34 +0200

On Thu, Oct 18, 2012 at 11:26 PM, Jordan Silberman wrote:
> According to one approach (from Dmitri Kaplan, described here:
> http://www.mathworks.com/matlabcentral/fileexchange/35094-knee-point/content/knee_pt.m),
> the knee is the x value that minimizes the sum of the squared errors
> of two linear regressions--one modeling all points left of the knee
> and one modeling all points right of the knee. It's an estimate of the
> point at which the slope "turns."

That is certainly not standard terminology, so you should have made
clear exactly what you wanted in your original question. Moreover,
your description is still not precise enough.

I guess you mean to find the optimum (maximum or minimum), the point
where the slope changes sign. As was already mentioned this is -b/2a
(if we use the parametrization: ax^2 + bx +c). However, a "slope
turning" could also be interpreted as referring to an inflection point
(especially if I look at the example graph provided in your link). The
inflection point is the point where the slope of the slope changes
sign. In that case the answer is also simple: A quadratic curve has by
definition no inflection point, as the second derivative of a
quadratic curve is a constant so it cannot change sign.

Hope this helps,
Maarten

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

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