[R] Re: your mail

Jim Lindsey jlindsey at alpha.luc.ac.be
Fri Feb 4 12:30:42 CET 2000

> 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.

The Weibull distribution is a Box-Cox transform of an exponential
distribution and no one complains that it isn't a useful distribution.
Viewed as a distinct three-parameter distribution (when renormalized
as I do), Box-Coxed normal is as useful as the generalized gamma,
etc. For example, it allows one to distinguish parametrically between
normal and log normal. So I thought it was worth including and doing

> 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 am afraid that is not the way it works in PK. Kineticists want to
compare different compartment models. They would never dream of
investigating with linear models. My experience is the same in other
areas where nonlinear mechanistic models are used.

This is no more or less a question of scale of measurement than it is
for the Weibull.

> 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?

Except in chemistry (bioassays), I have no direct experience anywhere
where normal distributions (previously transformed to normality or
not) are appropriate. So I don't have any examples. My personal
private opinion is that the Box-Cox transformation is a thing of the
1960s and should be quickly and quietly forgotten.

> > 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.

It certainly makes a difference to the resulting transformation in the
cases I have tried. Jim

> 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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