🚀 go-pugleaf

 Phillipe from American U. writes:

>   Let's now say that some theory leads me to believe that for
>   P, as it relates to Y, 50% is a special value, i.e., I suspect
>   that for the below-50% group and for the above-50% group of
>   observations, the regression slopes are the same but the
>   intercepts are different.
>
>   To model that "jump" in the values of Y around P=50, I decide
>   to add a second variable in my linear regression model, which
>   I call D. D is such that D=0 for P<50% and D=1 for P>=50%.
>
>   Thus, my model accounts for the trend (P) and for the jump (D).
>
>   The fact, however, that D is directly derived from P makes me
>   nervous about using both D and P in the same regression model.
>   Should I be nervous? After all, it is not unusual to use, say,
>   X and X^2 in the same set of independent variables? Is my model
>   okay as long as the correlation between P and D is not too high?
>   Would a similar approach be used when modeling a health condition,
> for instance, with its own trend, and the application of a
>   medical treatment expected to create a "jump" but no change in
>   the slope of the trend?
>
>   I'd appreciate any thoughts and comments about this.
>
    Jumps or discontinuities in data are discussed in Neter,
 Wasserman, and Kutner.  Applied Linear Regression Models.  They
 suggest an approach that is very similar to yours, but with some
 "rescaling" of the data so that the parameter estimates are more
 interpretable.

Robert Terry
Dept. of Psychology
Duke University
Durham, NC 27708
DOKIEM@DUKEMVS