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st: RE: Kernel regression


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Kernel regression
Date   Fri, 3 Oct 2008 20:14:15 +0100

One version of this question -- perhaps Nigussie's, perhaps not -- is smoothing a set of multivariate responses as a function of one or more predictors such that the sum of the responses is unity (100%, if you prefer). Many people on the list will know such data as being compositional data. 

Nigussie has shares of expenditure. I more often have fractions of sediment in different classes. It's the same problem, naturally. 

If we smooth (using kernel regression, or anything else) any one of those responses, or separately all of them, then the smoothing by default will take no account of the constraint that the responses are fractions of a total. That may not matter much, in so far as any reasonable smoother is some kind of average, but respecting the total is not guaranteed. 

Austin Nichols suggested his -locpr- from SSC, which nods respectfully at the fractional character of the response by producing c.i.s on the logit scale. But why stop there? Why not smooth on the logit scale too? (I hope I understand -locpr- correctly.) 

If anyone knows any work on smoothing a vector of compositional responses, w.r.t. a predictor, please do shout out. 

Nick 
n.j.cox@durham.ac.uk 

nigussie Tefera

I want to run kernel region for share of good j (rice, wheat etc) verses log total expenditure. Is there any better approach in STATA than lpoly command?

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