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


From   "Millimet, Daniel" <millimet@mail.smu.edu>
To   "<statalist@hsphsun2.harvard.edu>" <statalist@hsphsun2.harvard.edu>
Subject   Re: st: Test for significance of the difference between knee locations?
Date   Thu, 18 Oct 2012 21:29:36 +0000

One should also note that testing equality of the max/min presumably uses the delta method to obtain std errors.  Other methods exist that may be superior.  Joe Hirschberg at Melbourne has lots of work comparing different methods for inference concerning turning points.

Dann

Sent from my iPad

On Oct 18, 2012, at 4:13 PM, "Austin Nichols" <austinnichols@gmail.com> wrote:

> Jordan Silberman <silberman.stata@gmail.com>:
> Do not test all coefs' equality if you want to test whether maxima or
> minima are in the same position on the x axis. Rather solve for maxima
> or minima by setting the first derivative to zero to find that the
> extremum is where x equals the negative of the linear term's coef
> divided by twice the quadratic term's coef (-b/2a in the usual
> parlance, for y=ax^2+bx+c).
> 
> sysuse nlsw88, clear
> *compare extremum positions for quadratics, e.g. for
> *tw qfit wage age if union==0||qfit wage age if union==1
> reg wage c.age##c.age##i.union, nohe
> loc 1 (k1:-_b[age]/_b[c.age#c.age]/2)
> loc 2 (k2:-(_b[age]+_b[1.union#c.age])/
> loc 2 `2'(_b[c.age#c.age]+_b[1.union#c.age#c.age])/2)
> nlcom `1' `2', post
> test k1==k2
> * or keep your command shorter
> g a2=age^2
> g ua=union*age
> g ua2=union*a2
> g na=(union==0)*age
> g na2=(union==0)*a2
> g nu=(union==0)
> reg wage union ua ua2 nu na na2, hascons
> test ua=na
> nlcom (k1:-_b[na]/_b[na2]/2) (k2:-_b[ua]/_b[ua2]/2), post
> test k1==k2
> 
> *do not test all 3 param like so:
> reg wage union ua ua2 nu na na2, hascons
> test ua=na
> test ua2=na2, accum
> test union=nu, accum
> 
> 
> On Thu, Oct 18, 2012 at 4:25 PM, Jordan Silberman
> <silberman.stata@gmail.com> 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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