[R] Threshhold Models in gnlm

[Ben Bolker]

Eliot McIntire <emcintire <at> forestry.umt.edu> writes:

> Hello,
> 
> I am interested in fitting a generalized nonlinear regression (gnlr) model  
> with negative binomial errors.
> 
> I have found Jim Lindsay's package that will do gnlr, but I have having  
> trouble with the particular model I am interested in fitting.
> 
> It is a threshhold model, where below a certain value of one of the  
> parameters being fitted, the model changes.
> 
>   [BIG SNIP]

Threshold models (also known as "piecewise linear", or more recently,
"hockey stick" models) are actually surprisingly challenging to fit
numerically.  There are papers on least-squares fitting going back
to Bacon and Watts (1971, Biometrika) and before to Quandt, and more
recent (2000) posts on the S-PLUS lists from Bill Venables, Mary Lindstrom,
and Nicholas Barrowman (who has a paper with Ram Myers on hockey stick
models in fisheries).  The basic trick is that, unless you do some kind
of numerical smoothing, it's very easy to get stuck in local minima.
I got a little carried away with the problem and am sending you some
code off-list ...

  cheers
    Ben Bolker