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Re: st: types and codes of the non-linear models


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: types and codes of the non-linear models
Date   Thu, 21 Feb 2013 11:05:20 -0500

On Thu, Feb 21, 2013 at 10:25 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> With a function like this, the parameters usually no longer have
> simple interpretations.
>
> There is an exception for -b3-. -b3- is in effect a kind of origin on
> the time axis for your model and it is estimated as about 2010. In
> this case, the very high t statistic and very low P-value are just a
> side-effect of the usual null hypothesis that the origin is "really
> zero", i.e. 0 AD. That hypothesis is not of scientific interest, or so
> I presume.

Rescaling a variable is also important in a nonlinear model. 0 AD is a
silly number and thus years should never be coded as years in a model
because doing so creates an automatic and totally avoidable source of
ill-conditioning that a nonlinear regression will probably not be able
to cope with. Pick a reference year such as 2010, set that to 0 and
code everything relative to that.

Also, not all parameters need to be estimated. Sometimes just having a
reasonable stand-in to represent a feature like the lower or upper
asymptote is more important than having the "right" value. With
asymptotes you almost never have much information about them, and in
practice would need to use regularization/a priori information to get
it to work anyway, or do a sensitivity analysis by holding the other
ones constant and grid searching.




> This kind of modelling is usually lose-lose, unfortunately. One or
> two-parameter models miss important features of the data. More
> complicated models are more difficult to fit, or converge
> unsatisfactorily.

Truly nonlinear models require that the user know quite a bit of
mathematics to get sensible answers, and even then it may be a long
and complex trip to get things to work, if they ever do.

I wonder if the original poster would be able to map the problem onto
some generalized linear model and avoid the complexity of nonlinear
regression all together
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