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

[Daniel Yue <xyrixx@hotmail.com>]

Dear Statalisters,

as a follow-up to a previous question, the following issue continues to puzzle me
Defining D as a categorical with values 1-3 and X as continuous variables, I run the following model:

reg y i.D i.D#c.X1 i.D#c.X2 i.D#c.X3

While some of my interaction terms, e.g. i1.D#c.X3, are postive and significant with coefficient "a", others, e.g. i2.D#c.X3, are insignificant and the coefficient "b" of said interaction term is close to zero. I interpret this as "if D==1, then an increase in X3 has a significant effect of "a" on y, but if D==2, then an increase in X3 has no effect on y"

Then I run the following model, which Maarten Buis in a previous response had very helpfully pronounced essentially the same model, albeit with a different formulation:

reg y i.D##c.X1 i.D##c.X2 i.D##c.X3

This results in additional main effects X1-X3 and, surprise, some of the same interaction terms from earlier being significant, all of a sudden. For example: Main Effect X3 is significant (with base level D==1) with coefficient "a", but Interaction Effect i2.D#c.X3 is now significant, also, with coefficient "b". At the same time, if i add the coefficients from main effect X3 and i2.D#c.X3 together, the combined coefficient "a+b" is relatively close to zero. But Still, I would interpret this as "If D==1, an increase in X3 has a significant effect of "a" on y. if D==2, an increase in X3 has a significant effect of "a+b" on y.", even if "a+b" is very small/close to zero. How come the different formulation of the "same model" results in a different result? What am I missing?

Thanks so much for your consideration

Best,

Daniel 		 	   		  

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