Re: Varying coefficients in (non)linear regression

In article <ef0f591.1@xxxxxxxxxxxxxxxx>,
Christopher <schw0516@xxxxxxxxxxxxx> wrote:

> > So how do they vary? What are you willing to assume
> > about that variation?
>
> I only assume that there is some continuous function that
> characterizes the variation. No model is assumed. What I need to do
> at the end of the day is have some function: b2 = f(X5|yfit). What
> you suggested does not do that. I know varying coefficient regression
> uses localized smoothes and cross validation based on data binning to
> get at how the model coeff. vary with some covariate that is not part
> of the model. Not sure if I'm getting my question across so please
> don't hesitate to ask for more info? I've been trying to solve this
> for some time with no luck...

Actually, what I suggested does do that, because you
can recover that parameterization of your coefficient
from the model I suggested that you try.

I'll concede that you can even build a model of the form

y = b0(x5) + b1(x5)*X1 + b2(x5)*X2 + b3(x5)*X3 + b4(x5)*X4 + e

where the b(i) are general spline models, or whatever
form you wish. In fact, my suggested model was in fact
an implicit first order spline model with exactly two
knots. You can also use binning techniques (if you have
adequate data) to produce models for the coefficients.
There are some subtle flaws/implicit assumptions in
such an approach.

However, if you don't understand how to do those things,
or you don't know how to implement and use the variety
of modeling tools that you refer to, then use of these
tools blindly is likely to produce foolish results.
It does not sound to me that you understand the subtle
differences between a model of the form I described and
a binned model, and how those differences would be
reflected in the fit. (I apologize if I'm wrong abut
that.) But if you don't know how to build such models,
then you don't really understand them. And building
models that you don't really understand from data that
you don't really understand - this is sure to result
in folly.

I think you want to invest some time in studying
modeling techniques. Study your data. Try some low
order models. Does estimation of a low order model
reduce the error variance? Are single data points
on the fringes your data driving the modeling? Are
these data points outliers? Noise? Bad data? Do some
plots of your data and look at what is happening.

Perhaps you don't have time to do these things -
nobody seems to. There are deadlines for results.
I wish you luck in your efforts and I'm sorry that
I can't help you more.

John


--
The best material model of a cat is another, or
preferably the same, cat.
A. Rosenblueth, Philosophy of Science, 1945
.

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