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# Re: st: Intepretation of interaction terms

 From lreine ycenna To statalist@hsphsun2.harvard.edu Subject Re: st: Intepretation of interaction terms Date Mon, 23 May 2011 13:33:16 +0100

```If I understood correctly, you saying that the interpretation of a, b,
and c are the same both  in (1) and (2)?
e.g. a is the effect of a, when the other variables =0. b is the
effect of b, when others =0. axb is the effect of both a and b when c
=0...etc.

On 23 May 2011 13:07, Maarten Buis <maartenlbuis@gmail.com> wrote:
> On Mon, May 23, 2011 at 1:45 PM, lreine ycenna wrote:
>> I have linear equations, all varables are numeric and I'm using
>> xtreg,rreg and pooled:
>>
>> (1) y = a + b + axb
>>
>> (2) y = a + b + c + axb + axc
>>
>>
>> In (1), the coefficient of a becomes the effect of a when b is zero;
>> coef of b becomes the effect of b when a is zero.
>> In (2), since not all variables are interacted, we cannot inteprete it
>> as we do in (2). Therefore, the coef of b is influenced by c, and the
>> coef of c is influenced by b.
>
> In (2) the coefficient of a (b1) is the effect of a (x1) when b (x2)
> and c (x3) are both 0. You can see this by rewriting (2) as (2a). Here
> I called a b and c as x1 x2 and x3 and explicitly added the
> coefficients (b1 till b5).
>
> (2a) y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x1 x2 + b5 x1 x3
>      y =  b0 + (b1 +  b4 x2 + b5 x3) x1  + b2 x2 + b3 x3
>
> So the effect of x1 is (b1 +  b4 x2 + b5 x3), which will become b1
> when both x2 and x3 are 0.
>
> The coefficient of b (b2) is the effect of b (x2) when a (x1) is 0.
> You can see this by rewriting (2) as (2b).
>
> (2b) y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x1 x2 + b5 x1 x3
>      y =  b0 + b1 x1 + (b2 +  b4 x1) x2 + b3 x3 +b5 x1 x3
>
> So the effect of x2 is (b2 +  b4 x1) , which will become b2 when x1 is 0.
>
> The coefficient of c (b3) is the effect of c (x3) when a (x1) is 0.
> You can see this by rewriting (2) as (2c)
>
> (2c) y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x1 x2 + b5 x1 x3
>      y =   b0 + b1 x1 + b2 x2 +( b3 +  b5 x1) x3 + b4 x1 x2
>
> So the effect of x3 is (b3 +  b5 x1) , which will become b3 when x1 is 0.
>
> Hope this helps,
> Maarten
>
> --------------------------
> Maarten L. Buis
> Institut fuer Soziologie
> Universitaet Tuebingen
> Wilhelmstrasse 36
> 72074 Tuebingen
> Germany
>
>
> http://www.maartenbuis.nl
> --------------------------
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