[R] Re: your mail

[Bill Venables]

OK, this is not R, but my curiosity has got the better of me.

> > On Wed, 2 Feb 2000, Adriane Leal wrote:
> > 
> > > I'd like to perform a box-cox transformation to a data set and also plot
> > > lambda versus L(lambda) using R. Does anybody knows how can I do such a
> > > thing? 
> 
> gnlr3 in my gnlm library does both linear and nonlinear models with
> Box-Cox transformation. 

I'm really curious to know why you would want to do a box-cox
transformation model on top of a non-linear model.

It seems to me linear models are often used as a local,
investigative tool and the box-cox transformation is really an
extension of this aspect of linear models to look for a scale of
measurement where some sort of simplicity of structure is
apparent, like homogeneity of variance, additivity and so on.

By contrast I regard non-linear models as appropriate where the
investigative phase is well and truly over.  I would never fit a
non-linear model unless I had some pretty clear idea that it was
going to be appropriate, preferably with a solid theory behind
it, beginning with the scale of measurement.  If you need to hunt
around for a scale of measurement in which your non-linear model
looks reasonable, I become very skeptical about whether there was
any solid basis for a specific non-linear model in the first 
place.

I must admit, though, I have seen papers on fitting box-cox
transformed non-linear models before (at least in tech report
form) so am I missing something?  Does anyone have a good example
of where a box-cox transformed non-linear model is clearly an
appropriate thing to use?

> However, it is somewhat nonstandard as it
> renormalizes to obtain a true density whereas the standard
> transformation creates a function that is not a density because of the
> constraint that only positive values can be transformed but the normal
> distribution is on the whole real line. Jim

Again, under my contention that box-cox transformed models are
largely investigative tools, I wonder if this refinement is going
to pay off very much.

Brian Ripley wrote the first version of our box-cox and I did
some fiddling with it to make it a bit slicker.  At the time I
thought about this kind of extension but decided against any on
the grounds (a) that I could not see much use for them and (b)
they could send the wrong message to users.  I have to say I
still think so.

-- 
Bill Venables,      Statistician,     CMIS Environmetrics Project
CSIRO Marine Labs, PO Box 120, Cleveland, Qld,  AUSTRALIA.   4163
Tel: +61 7 3826 7251           Email: Bill.Venables at cmis.csiro.au    
Fax: +61 7 3826 7304      http://www.cmis.csiro.au/bill.venables/



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