[R] nls, nlrq, and box-cox transformation

Roger Koenker roger at ysidro.econ.uiuc.edu
Thu Nov 20 17:51:17 CET 2003

On Thu, 20 Nov 2003, Prof Brian Ripley wrote:

> Now nlrq uses a different criterion and Philippe's suggestion may work
> there.  I can't tell quickly: the help page does not say what the
> criterion is.  But if those are the same, then I suspect the criterion is
> uninteresting as a way to choose t, since two of the three aims of
> Box-Cox are to stabilize the distribution of lhs - rhs.

One of the advantages of the quantile regression fitting criterion in
this circumstance is that it is only _trying_ to accomplish one objective
instead of three, i.e. to deal with the nonlinearity.  One still needs,
as in the Gaussian case to worry about the Jacobian of the transformation
from u -> y, but this can be fixed by the usual rescaling of the response
by its geometric mean as in e.g. Atkinson, Plots, Transformations, and
Regression, p 86-7.

url:	www.econ.uiuc.edu/~roger/my.html	Roger Koenker
email	rkoenker at uiuc.edu			Department of Economics
vox: 	217-333-4558				University of Illinois
fax:   	217-244-6678				Champaign, IL 61820

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