How can I read a three-way # interaction with dummies and a "constant"?

[Alexandra Gourjon]

Hi,

I was wondering how I could read a three-way interaction with one #, two dummies (0,1) and a "constant"? There are a lot of documents for regressions with ## interactions but I have found none for #. I have the following regression:
xi: areg trans i.classage#i.group1#c.school, absorb(urban)
| Robust
transanmoy | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------------------------------------+----------------------------------------------------------------
I_nbre_classe11_2plus#I_bp# |
c.tot_scol_prim1 |
0 0 | 95304.22 345818 0.28 0.784 -593307.5 783915.9
0 1 | 136654.4 183444.6 0.74 0.459 -228630.4 501939.2
1 0 | 24511.88 380467.3 0.06 0.949 -733095.2 782119
1 1 | -89434.71 115478.5 -0.77 0.441 -319381.8 140512.3

I thought each coefficient corresponded to the regression of the "constant", c.school_rate, with my dependent variable for the combination of each subgroup (that is reg trans school if group==0 and classage==0 which gives the coefficient 95304.22 etc.) but as I took the opposite dummy for i.group I got a completely different result, which shouldn't be according to my understanding:

| Robust
transanmoy | Coef. Std. Err. t P>|t| [95% Conf. Interval]
----------------------------------------+----------------------------------------------------------------
I_nbre_classe11_2plus#I_nobp# |
c.tot_scol_prim1 |
0 0 | 9053.467 280265.4 0.03 0.974 -548285 566391.9
0 1 | -156647.6 253266.7 -0.62 0.538 -660296.2 347001
1 0 | -250002 157739.8 -1.58 0.117 -563684.8 63680.83
1 1 | -359902.2 477793.8 -0.75 0.453 -1310047 590243.1

How is that? How do I interpret these results?

Thank you very much,

Alexandra

[Maarten Buis]

First off, don't use the xi: prefix. As to your question, see: http://maartenbuis.nl/publications/ref_cat.html

[Carole J. Wilson]

Maarten Buis : FYI, the webpage you link is empty.

[Maarten Buis]

The server appears to be down.

[Carole J. Wilson]

Alexandra, Let's be sure we are speaking the same language here. Take a look at help fvvarlist which describes the operators # and ##.

i.classage#i.group1#c.school
*expands to
i.classage*i.group*c.school


i.classage##i.group1##c.school
*expands to
i.classage + i.group + c.school + i.classage#i.group + i.classage#c.school + i.group#c.school + i.classage#i.group#c.school

Unless you have a very good theoretical reason, you should include all constituent parts of interaction terms. Therefore, you should use the ## operator instead of the # operator.

Please place the [CODE] [/CODE] around any Stata code or output. Your results in #1 are not readable.

[Alexandra Gourjon]

Ah ok thanks a lot for your answers!

[Maarten Buis]

[QUOTE=Carole J. Wilson;n1338758]

i.classage#i.group1#c.school
*expands to
i.classage*i.group*c.school

That is not quite true. It makes all possible combinations of classage, group, and school. If you include the constant in your model, it will remove one of those as a reference category, otherwise it includes all of them. It gets a bit more complicated if you also manually include the main effects. So you can use this and get somewhat meaningful results. At least you won't run into the problem of including interactions without including the main effects.

[Carole J. Wilson]

Thanks for clarifying, Maarten.

The actual expansion is:

classage0*group0*school +
classage0*group1*school+
classage1*group0*school+
classage1*group1*school

Even with a constant, it will give you coefficients for all.

clear
sysuse auto
gen tr=0
replace tr=1 if trunk>=14
reg price i.foreign#i.tr#c.rep78 , coefleg

In this case, I guess you would interpret the constant as the value of yhat when the values of the factor variables are at the baseline and the continuous variable is 0 (which is not possible in this case)?