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From |
David Hoaglin <dchoaglin@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: positive interaction - negative covariance |

Date |
Fri, 22 Feb 2013 15:17:50 -0500 |

Dear Andrea, The basis for a statement about the interaction is the estimate of b3 and its standard error: After taking into account the contributions of X and Z, the interaction is not significant (p = .245). Thus, X has a positive impact on Y when Z is present and when Z is absent, but those contributions are not significantly different. That is, the interaction is essentially absent. A negative covariance between b1 and b3 is to be expected. You may want to remove XZ from the model. Regards, David Hoaglin On Fri, Feb 22, 2013 at 12:32 PM, andrea pedrazzani <andrea.pedrazzani.piter@gmail.com> wrote: > Hello, > > I have a simple regression model with an interaction: Y = b0 + (b1)X + > (b2)Z + (b3)XZ. > Z is a dummy (0 or 1). > > b1 = .0021067 (SE= .0008513 and p=0.013) > b2 = -.3692713 (SE= .2329837 and p=0.113) > b3 = -.0010758 (SE= .000926 and p=0.245) > > Hence, the combined coefficient (i.e., the coefficient on X when Z=1) > is positive: > b1+b3 = .0021067 + -.0010758 = .0010309 > > with SE = sqrt( var(b1) + var(b3)*(Z^2) + 2Z*cov(b1,b3) ) > = sqrt( .0000007246 + .0000008574*1 + -.0000007079*2 ) > = .00040768 > > To get the p-value for the combinet coefficient, I did > .0010309/.00040768 = 2.528699. The corresponding p = 0.0114. > > Summing up, X has a positive impact on Y when the condition Z is > present (.0010309), and a positive impact also when the condition Z is > not present (.0021067). > So, what can I say about the interaction? What kind of interaction is > it when the impact of X is positive both when the condition is present > and when it is absent? Moreover, the coefficients b1 and (b1+b3) are > very similar to each other. > Also, both b1 and the combined coefficient (b1+b3) are positive, but > the covariance between b1 and b3 is negative. It sounds strange to > me... > > Sorry, these are probably trivial questions. I would be really > grateful if someone can help me. > > Best, > > Andrea Pedrazzani * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: positive interaction - negative covariance***From:*andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>

**Re: st: positive interaction - negative covariance***From:*andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>

**References**:**st: positive interaction - negative covariance***From:*andrea pedrazzani <andrea.pedrazzani.piter@gmail.com>

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