Re: st: Nonlinear regression command

[David Hoaglin <dchoaglin@gmail.com>]

Rick,

Removing the indicator Ds is not a mistake.  Because the indicator DL
and the interaction of DL with each of the other predictors are in the
model, the coefficients a0 through a9 are for the part of the sample
where the DL indicator is 0 (i.e., where the Ds indicator is 1).
Those coefficients are not for the whole sample.  They would be for
the whole sample if DL and the interactions involving DL were not in
the model.  In the model
Total Riskit = a0 + a1 Extentit + ... + a9 Exeopit + a10 DLi + a11
DLExtentit + ... + a19 DLExeopit + sigmait
you can think of the constant term and Extentit, ..., Exeopit as
interactions with Ds.

I described a11 as "the additional slope of Total Risk against Extent
when DL = 1."  The slope of Total Risk against Extent when DL = 1 is
equal to a1 + a11.  And the slope of Total Risk against Extent when DL
= 0 (i.e., Ds = 1) is equal to a1.

It may help to remember that, in a multi-predictor model, the
definition of each coefficient includes the list of other predictors
in the model.

For example, consider data that involve a dependent variable (y), two
groups (Group = 0 and Group = 1), and one continuous predictor (x).
The model
y = b0 + b1 x + b2 Group + b3 (Group * x) + e
provides a separate intercept and slope for each group.  The
intercepts are b0 for Group = 0 and b0 + b2 for Group = 1, and the
slopes are b1 for Group = 0 and b1 + b3 for Group = 1.  If we remove
the predictor Group * x, the lines for the two groups have a common
slope but separate intercepts.  Because the set of predictors has
changed, the definitions of the coefficients have changed, so we
should rewrite the model:
y = c0 + c1 x + c2 Group + e .

I hope this explanation helps.

David Hoaglin

On Mon, Jul 15, 2013 at 4:45 AM, Rick Kamphuis
<r.kamphuis@tilburguniversity.edu> wrote:
> Thanks for the comments!
> In the paper it is mentioned as a nonlinearity test, because of
> dividing the sample in two groups with a saturation.
> But indeed it is done with interactions. David,  I think you are
> almost right with the model, but you can not remove dummy Ds because
> than you get coefficients for the whole sample.
> The aim of this regression is to get the coefficients for group 1 with
> less than 20% and group 2 with more than 20% usage.
> Therefore I think I have to made interactions with Ds for all
> variables and with DL for all variables and then regress them all at
> the same time.
>
> Rick
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