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From |
Maarten buis <maartenbuis@yahoo.co.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: interaction between continuous variables |

Date |
Tue, 4 Sep 2007 18:10:04 +0100 (BST) |

--- alessia matano <alexis.rtd@gmail.com> wrote: > I am trying to perform a regression trying to put an interaction term > between two continuous variables. > In a first attempt I discretize one of them and then multiply the > relative dummy with the other variable, and I obtained some > interesting effect. > Then I red that this is not correct to be done and it is also > arbitrary (because I decide how descretize one variable...I was > calcultaing some threshold using the percentiles say p(33) p(66)) > getting three values. How to descretize a variable is just as arbitrary as assuming that the interaction is linear, so I would not worry about that. > Therefore I red some papers saying that you should centered the > continuous variables (becuase of problem of multicollinearity: is > that correct?) and then simply multiply them. In this way results > are not so interesting anymore. The main and interacted variables > together are never significant and it happens (and here I would > like your help) that in one case only the interacted is significant > while the main effect is not. Whta does it mean? Consider the following regression: y = b0 + b1*x1 + b2*x2 + b3*x1*x2 if x1 = 0: y = b0 + b1*0 + b2*x2 + b3*0*x2 y = b0 + b2*x2 effect of x2 is b2 if x1 = 1: y = b0 + b1*1 + b2*x2 + b3*1*x2 y = b0 + b1 + (b2 + b3)*x2 effect of x2 is b2 + b3, i.e. a unit increase in x1 resulted in b3 increase in the effect of x2 if x1 = 2: y = b0 + b1*2 + b2*x2 + b3*2*x2 y = b0 + 2*b1 + (b2 + 2*b3)*x2 effect of x2 is b2 + 2*b3, i.e. a unit increase in x1 resulted in 2*b3 increase in the effect of x2 So, the main effect of x2 (b2) is the effect of x2 when x1 = 0, and the interaction effect (b3) tells you how much the effect of x2 changes when x1 changes with one unit. Centering the variable makes sense because now the main effect is easier to interpret (Think what would happen if x1 was year of birth when it is non-centered: than the main effect would be the effect for someone who was bort 2007 years ago...). You don't have to center at the mean, as long as the value zero is meaningful in your data. Hope this helps, Maarten ----------------------------------------- Maarten L. Buis Department of Social Research Methodology Vrije Universiteit Amsterdam Boelelaan 1081 1081 HV Amsterdam The Netherlands visiting address: Buitenveldertselaan 3 (Metropolitan), room Z434 +31 20 5986715 http://home.fsw.vu.nl/m.buis/ ----------------------------------------- ___________________________________________________________ Want ideas for reducing your carbon footprint? Visit Yahoo! For Good http://uk.promotions.yahoo.com/forgood/environment.html * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: interaction between continuous variables***From:*"alessia matano" <alexis.rtd@gmail.com>

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