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Re: st: Fixed effects in nonlinear least squares


From   "JVerkuilen (Gmail)" <jvverkuilen@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Fixed effects in nonlinear least squares
Date   Thu, 16 May 2013 09:06:57 -0400

On Thu, May 16, 2013 at 2:04 AM, Jacob Hansen <jacobmoller@gmail.com> wrote:
> Dear Statalist users,
>
> I would like to know if it is possible to include fixed effects in a
> nonlinear least squares regression. And if yes, how?
>
> It is not possible for me to simply create the dummy variables, as it
> would result in too many variables. I have 500 individuals and 24
> months resulting in 500*24=12.000 dummy variables.

I assume you wouldn't have that many dummies as that sounds like a
saturated model. I'd assume it would be 499 + 23 for person and year,
right? Not that that's any good either. The math that lets you sweep
out fixed effects by sweeping out the fixed effects doesn't really
apply to a nonlinear model. This is why nonlinear mixed models are
around and they are non-trivial to estimate.

I'm afraid I don't have a fantastic answer for you. I could think of a
number of reasonable "schemes" such as linearizing the model and using
a fixed effects estimation with updating but they wouldn't be trivial
and would require a good bit of checking (and even then, would they
make sense?). Many of the nice properties of fixed effects aren't
likely to carry over to a nonlinear model anyway, so I'm not sure
you'd get any benefit from fixed effects regardless.

Just how nonlinear is your model anyway? How important is the
nonlinearity? Can you get by with a nearby linear model built on
regression splines, fractional polynomials, or the like?


-- 
JVVerkuilen, PhD
jvverkuilen@gmail.com

"They were careless people, Tom and Daisy - they smashed up things and
creatures and then retreated back into their money of their vast
carelessness, or whatever it was that kept them together, and let
other people clean up the mess they had made." -- F. Scott Fitzgerald
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