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

[Daniel Yue <xyrixx@hotmail.com>]

Dear David,

thanks so much for your response, although, unfortunately, result-wise it was not the answer I was hoping for. :)

Best,

Daniel
----------------------------------------
> Date: Mon, 8 Jul 2013 10:35:35 -0400
> Subject: st: Re: st: Modelling of categorical-continuous variable interaction‏ - Follow-up
> From: dchoaglin@gmail.com
> To: statalist@hsphsun2.harvard.edu
>
> 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.
> From what you have said, the result will be that "a + b" does not
> differ significantly from zero. You seem to be basing your
> interpretation of an increase in X3 when D == 2 on the significance of
> "b"; that is incorrect. The correct interpretation is based on the
> significance of "a + b". It would say, "If D == 2, an increase in X3
> (after adjusting for the contributions of the other predictors) does
> not have a significant effect on y." It would be a good idea to
> include the confidence interval for "a + b" (available in the output
> from -lincom-).
>
> David Hoaglin
>
> On Mon, Jul 8, 2013 at 9:59 AM, Daniel Yue <xyrixx@hotmail.com> wrote:
>> 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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