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# Re: st: Interaction model

 From Shikha Sinha To statalist@hsphsun2.harvard.edu Subject Re: st: Interaction model Date Wed, 8 Feb 2012 15:47:32 -0800

```Thanks David.
b4 is not the coefficient for both male and program*rich- it was a mistake/typo.

I understand the model in (a) is a richer model compared to different
specifications in (b). What would be the interpretation of b1 in (a)?

Thanks,
Shikha

On Wed, Feb 8, 2012 at 3:10 PM, David Hoaglin <dchoaglin@gmail.com> wrote:
> 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
> predictors.
>
> 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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```