Re: st: Polynomial Fitting and RD Design

[Austin Nichols <austinnichols@gmail.com>]

Maarten--
Note that the standard for this design is local linear regression with
a triangle (AKA edge) kernel, as implemented in -rd- on SSC.  But the
poster asked about replication, not an optimal design.

On Thu, Sep 1, 2011 at 5:24 AM, Maarten Buis <maartenlbuis@gmail.com> wrote:
> On Thu, Sep 1, 2011 at 10:31 AM, Nick Cox wrote:
>> Sure, but that still leaves the non-numeric issues. I guess the main
>> issue is just reproducing behaviour with smooth curves, but what
>> arguments justify any kind of quartic here?
>
> No disagreement with you on that point. Actually I think that such
> high degree polynomial is rather dangerous for this purpose as these
> curves tend to move rather wildly away from the data at the extreme
> ends of the curve, and in these models the break is such an extreme
> end. As a consequence the break dummy may just capture this misfit to
> the data rather than a real break. Patrick may want to consider a
> fractional polynomial model instead. Below is an example on how to
> estimate both models, the graph shows that the quartic curve does show
> that wild behavior at the break, and the fractional polynomial model
> shows that that is due to overfitting the curve as in this case two
> linear curves will do just fine.
>
> *--------------- begin example -----------------
> sysuse uslifeexp, clear
> drop if year == 1918 // Spanish flu pandemic
> gen cyear = year - 1950 // center at break
>
> // 4th degree polynomial
> orthpoly cyear , gen(oyear*) degree(4)
> gen D = cyear > 0 if year < .
> forvalues i = 1/4 {
>        gen oyear`i'l = (1-D)*oyear`i'
> }
> forvalues i = 1/4 {
>        gen oyear`i'r = D*oyear`i'
> }
>
> // fit model
> reg le oyear?? D
>
> // predict outcome
> predict pol
>
> // fractional polynomial
> gen cyearl = (1-D)*cyear
> gen cyearr = D*cyear
>
> // fit model
> mfp, df(8) : reg le cyearl cyearr D
>
> // predict outcome
> predict mfp
>
> // Graph the models
> twoway line le pol mfp year,            ///
>       xline(1950)                      ///
>       lstyle(solid solid solid)        ///
>       lcolor(black red blue)           ///
>       legend(order( 1 "data"           ///
>                     2 "quartic"        ///
>                     3 "fractional"     ///
>                       "polynomial"  ))
> *---------------- end example ------------------
>  (For more on examples I sent to the Statalist see:
> http://www.maartenbuis.nl/example_faq )
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
>
> http://www.maartenbuis.nl
> --------------------------
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