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st: RE: matching percentiles technique


From   "Verkuilen, Jay" <JVerkuilen@gc.cuny.edu>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: matching percentiles technique
Date   Thu, 25 Jun 2009 12:02:43 -0400

Juanita Riaño wrote:

>I was wondering if any of you have experience working with the "matching percentiles" technique to aggregate indicators with different distributions. I am just using the pctile command for each indicator and then merging the datasets using the resulting percentile distribution. But I am not sure if this is the correct approach.<

The problem has in fact been studied extensively in the psychometrics literature under the name "equipercentile equating." It doesn't work very well as the ECDF is a rather poor estimator of the CDF for this purpose, and the equating curve ends up being rather biased as a consequence. Usually some kind of smoothing of the ECDF is needed to get a good equating curve. This is typically done using kernel smoothing but I'm sure that other methods are possible and may be better in your particular problem. 

See:

Kolen, M.J.  & Brennan, R.L. Test equating, scaling, and linking. Methods and practices, 2nd ed. New York: Springer-Verlag, 2004.

von Davier, A.A., Holland, P.W., & Thayer, D.T. The Kernel Method of Test Equating. New York: Springer-Verlag, 2004.



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