st: Re: st: Modelling of categorical-continuous variable interaction‏ - Follow-up

[David Hoaglin <dchoaglin@gmail.com>]

Dear Daniel,

The model that Maarten suggested is the same as your initial model, in
the sense that the two models produce the same fitted value of y for
each observation.

The two models, however, have different sets of predictors.  Thus, it
is important to remember that the definition of a regression
coefficient includes the list of the other predictors in the model.

What you refer to as "main effects" of X1, X2, and X3 in the second
model, I would prefer to call "linear terms in X1, X2, and X3."  Their
coefficients are slopes of y against those variables (after adjusting
for the contributions of the other predictors in the model).  Because
the second model contains interaction terms for D with X1, X2, and X3,
those slopes are for D == 1, and the coefficients of the interaction
terms are the additional slopes for D == 2 and D == 3.  In your
example, the slope of y against X3 for D == 2 is "a + b".  You can
assess the significance of that slope by using the -lincom- command.