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Re: st: Interaction model

From   David Hoaglin <>
Subject   Re: st: Interaction model
Date   Wed, 8 Feb 2012 18:10:33 -0500

If the effect of the program can vary by all three of gender, SES, and
immigration status, you should use model (a).  And, if you have enough
data, you should consider including higher-order interactions, such as
program*rich*male.  In principle, your data contains 16 (= 2^4)
subgroups, corresponding to the possible combinations of values of
program, gender, SES, and immigration status.  If you are lucky, the
higher-order interactions will have small enough contributions that
you can omit them; interpretations in the presence of interactions are
more difficult.

Why is b4 the coefficient of both male and program*rich in model (a)?

In model (b) the definition of b1, b2, b3, and b4 is not the same in
the three models, because each model contains a different fifth
predictor.  It is difficult to imagine a situation in which model (b)
would be correct.

In model (a) the interpretation of each coefficient includes the fact
that the model is adjusting for the contributions of the other

David Hoaglin

> I want to examine if the effect of a program varies by gender, SES,
> and immigration status of the individuals. Income, the outcome, is a
> continuous variable. gender (male==1), SES (poor and rich==1) and
> immigration status (yes==1) all are dummies. I can examine the
> heterogeneous effect in the following different ways:
> (a) income= b1*program + b2*rich + b3*immi + b4*male + b4*program*rich
> +b5*program*male + b6*program*immi
> or estimate separate equations
> (b) income= b1*program + b2*rich + b3*immi + b4*male + b4*program*rich
>     income= b1*program + b2*rich + b3*immi + b4*male +b5*program*male
>     income= b1*program + b2*rich + b3*immi + b4*male + b6*program*immi
> I want to know which is the correct model (a) vs (b)  to estimate the
> heterogeneous effect and what is the difference between the two.

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