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

[Prof Brian Ripley]

On Thu, 20 Nov 2003, Philippe Grosjean wrote:

> >Dear r-help members
> >I posted this message already yesterday, but don't know whether it
> >reached you since I joined the group only yesterday.
> >I would like to estimate the boxcox transformed model
> > (y^t - 1)/t ~ b0 + b1 * x.
> >Unfortunately, R returns with an error message when I try to
> >perform this with the call
> >nls( I((y^t - 1)/t) ~ I(b0 + b1*x),
> >	start = c(t=1,b0=0,b1=0), data = mydataframe)
> 
> >The error message is:  Object "t" not found
> 
> >Apparently R seems not to accept parameters on the left hand
> >side of a regression model. I know that my do-it-yourself
> >strategy is not necessary, since the package box-cox is
> >available. Unfortunately, I want the use the box-cox
> >transformation in a quantile regression, i.e. I have to replace
> >nls by nlrq in the call above.
> 
> >Any suggestions?
> 
> >Thanks and best regards,
> >	Johannes Ludsteck
> 
> You suggest the solution yourself: transform the equation to have all
> parameters at the right, thus:
> 
> y ~ ((b0 + b1 * x) * t + 1) ^ 1/t
> 
> (double check if this is correct)

But for nls that changes the fitting criterion from least-squares to
something completely different.

For the original problem, this is not the correct Box-Cox transformation,
as the normalizer has been omitted.  I am unaware of `package box-cox'
(and that is not a valid package name AFAIK), but function boxcox in MASS
computes the correct likelihood.

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.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595