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

[Jordan Silberman <silberman.stata@gmail.com>]

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."

On Thu, Oct 18, 2012 at 4:36 PM, Roger B. Newson
<r.newson@imperial.ac.uk> wrote:
> What is the "knee" of a quadratic model? I never knew that they had knees
> (although I might expect a 3-parameter linear spline to have a knee).
>
> Best wishes
>
> Roger
>
> Roger B Newson BSc MSc DPhil
> Lecturer in Medical Statistics
> Respiratory Epidemiology and Public Health Group
> National Heart and Lung Institute
> Imperial College London
> Royal Brompton Campus
> Room 33, Emmanuel Kaye Building
> 1B Manresa Road
> London SW3 6LR
> UNITED KINGDOM
> Tel: +44 (0)20 7352 8121 ext 3381
> Fax: +44 (0)20 7351 8322
> Email: r.newson@imperial.ac.uk
> Web page: http://www.imperial.ac.uk/nhli/r.newson/
> Departmental Web page:
> http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/
>
> Opinions expressed are those of the author, not of the institution.
>
>
> On 18/10/2012 21:25, Jordan Silberman wrote:
>>
>> Hi Stata folks,
>>
>> I'm searching for a method I can run in Stata that will allow me to
>> test whether the location of the knee for one quadratic model
>> significantly differs from that of another quadratic model.
>>
>> I have 2 quadratic models, each modeling a different category of
>> healthcare costs as a function of age. Let's say, for illustrative
>> purposes, that the knee of the first quadratic model occurs at age 45,
>> and the knee for the second model occurs at age 55.
>>
>> Can anybody suggest a method for testing whether the former "knee age"
>> differs significantly from the latter "knee age?" The idea is to test
>> the hypothesis that there is a difference across the 2 models in the
>> age at which the costs growth rate begins to increase.
>>
>> Any suggestions would be greatly appreciated.
>>
>> Thanks,
>> Jordan
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