Apologies to all for my delay in summarizing. A sudden family medical
situation prohibited a speedy reply.
Many thanks to Douglas Bates for his detailed and informative explanations
regarding the SAS vs S-Plus convergence issue. Additional thanks to Bruce
McCullogh (yes, Bruce, I did receive the papers and thanks again), Max Kuhn,
Don MacQueen and James Roger for their experiences and suggestions.
My primary concern was why SAS's PROC NLIN converged when nls didn't when
confronted with data not well suited for a particular model (in my case
modeling rather linear data with a biexponential model) as suggested in the
statement below.
> ...However, I was somewhat surprised to find that SAS's
> PROC NLIN did fit these models without difficulty...
However, after additional private communication, Professor Bates showed how
PROC NLIN in fact did not converge, despite the message saying that the
convergence criteria had been met. Investigation of the log file reveals
that the model collapsed to a singular model and that PROC NLIN had fixed
one of the rate parameters (with a corresponding standard error of
infinity). So, in this case PROC NLIN altered the model being fit without
mention and simply reported the results of the simplified model. Further,
for the data in question the resulting model fit was quite good (consequence
of the data set and specified model, where some of the parameters have
little apparent impact on the model fit). Hence, with notification of
convergence and estimated parameters which provide a reasonable fit to the
data it would be easy to conclude that PROC NLIN had been successful. The
lesson here is that it pays to be careful when interpreting the results
issued by this SAS routine.
Conversely, with the same data nls refused to converge at all (issuing
messages about singular gradient matrix or step size reduced below minimum).
nls then expects the modeler (and rightly so) to investigate any
difficulties encountered during the fitting process and does not without
mention simplify the model and report convergence results from this
simplified situation.
There are no doubt many strong feelings regarding the approaches taken by
SAS and S-Plus. I will not enter into that dispute, but will certainly
consider the results from PROC NLIN with a bit more scrutiny in the future.
A secondary question posted in my original message concerned the
appropriateness of including the "time zero" point in the regression when
that point has been defined to be 100 (or any given value) and then forcing
the model through that point. Understanding that there are situation
specific exceptions, the general counsel has been to exclude this point as
it really provides no additional information and artificially inflates
degrees of freedom.
Best regards,
Peter Scherer
Dow AgroSciences
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