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From |
andrea pedrazzani <andrea.pedrazzani.piter@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Fri, 22 Feb 2013 23:50:11 +0100 |

Thank you very much Nick, Jay and David. My -x- is -dur-, whose range is from 1 to 1764. I plotted the two curves as you suggested me: local b0 = 1.663478 local b1 = .0021067 local b2 = -.3692713 local b3 = -.0010758 twoway function `b0' + `b1'*dur, ra(1 1764) || /// function `b0' + (`b1' + `b3')*dur + `b2', ra(1 1764) The two functions have the same shape and are very close to each other. Both tend to slightly increase as -x- increases (the functions are really jagged, because -dur- has many values). The first one (where the condition Z is absent) is always a bit higher than the second (where the condition is present). If I am not wrong, this indicates that the impact of both on my dependent variable goes in the same (positive) direction. To Jay: my dependent variable is a proportion (I am using flogit) To David: > 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. Thank you for clarifying the point. Indeed, if I compare the confidence interval of b1 to the confidence interval of (b1+b3), they are not statistically different. Is it the same? In a book I read, the authors make this comparison. Thanks again. Best, Andrea Pedrazzani 2013/2/22 David Hoaglin <dchoaglin@gmail.com>: > 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/ * * 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:*Nick Cox <njcoxstata@gmail.com>

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

**Re: st: positive interaction - negative covariance***From:*David Hoaglin <dchoaglin@gmail.com>

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