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From |
Maarten Buis <maartenlbuis@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Intepretation of interaction terms |

Date |
Mon, 23 May 2011 14:07:09 +0200 |

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 -------------------------- * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: Intepretation of interaction terms***From:*lreine ycenna <lreine.ycenna@gmail.com>

**References**:**st: Intepretation of interaction terms***From:*lreine ycenna <lreine.ycenna@gmail.com>

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