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

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Poisson model with interaction term |

Date |
Tue, 26 Feb 2008 10:49:03 +0000 (GMT) |

Just to make things more complicated, I have a problem with the approach by Norton and collegues. Say we have two explanatory variables, called x1 and x2, than an interaction effect is, how much does the effect of x1 change when x2 changes. Norton et al. deal with the case when we have non-linear model and we are interested in the effect on the untransformed dependent variable than the computation. The problem I have is this: In the case of non-linear models you would expect the effect of x1 to change when x2 changes even if we do not enter the interaction term. This is most easily seen in a graph. In case of a logistic regression the marginal effect of x1 is the slope of the curve of the probability against x1 (In case of poisson it the the slope of the curve of the rate against x1) In the graph that is created by the code below you can see the marginal effects of x1 when x1 == 0 when x2==0 and x2 == 1 when the logistic regression equation is: invlogit(pr) = x1 - 2*x2 I think (but I am not sure) that the method by Norton et al. gives the combined change in the effect of x1, i.e. the change in effect of x1 that would have occured anyhow and the change in effect due to the interaction term together. I think that in many case this would be reasonable, but I can also imagine situations where you just want to know the effect of the interaction term net of the change in effect that would occur anyhow. -- Maarten *-------------- begin graph ---------------------------- // Marginal effects at x = 0 local marg1 = invlogit(-2)*invlogit(2)*2 local marg2 = invlogit(0)*invlogit(0)*2 // graph twoway function y = invlogit(2*x-2), range(-2 2) /// lpattern(shortdash) || /// function y = invlogit(2*x), range(-2 2) || /// function y = invlogit(-2) + `marg1'*x, /// range(-.5 .5) lpattern(solid) || /// function y = invlogit(0) + `marg2'*x, /// range(-.5 .5) lpattern(solid) xline(0) /// xtitle(x1) ytitle(probability) /// legend(order( 1 "effect when" "x2==1" /// 2 "effect when" "x2==0" /// 3 "marginal" "effects" )) *--------------- end graph ----------------------------- (To see the graph, run this in Stata as described in http://home.fsw.vu.nl/m.buis/stata/exampleFAQ.html#work ) --- Maarten buis <maartenbuis@yahoo.co.uk> wrote: > The formulas can be found in section 2.3 here: > http://www.unc.edu/%7Eenorton/NortonWangAi.pdf > > Where in case of a poisson with a standard link function: > F(u)=exp(u); f(u)=F'(u)=exp(u); f'(u)=F''(u)=exp(u) > > Hope this helps, > Maarten > > --- Lloyd Dumont <lloyddumont@yahoo.com> wrote: > > > Actually, I am running count models on panel data > > using xtpoisson and xtnbreg, but have the exact same > > question. (But mine really does include a count as a > > dep var.) How do I make sense of the interaction > > term? I am fairly sure I cannot just add the > > coefficients of main effects and two-way interactions > > in this case. I don't even think I can take the > > significance of the coefficient on the interaction > > term seriously. > > > > Thanks as always. Lloyd Dumont > > --- agostino@unical.it wrote: > > > > > thank you Maarten, hence I can simply apply the > > > linear case formulas... > > > > > > thanks again > > > Maria > > > Citazione Maarten buis <maartenbuis@yahoo.co.uk>: > > > > > > > --- agostino@unical.it wrote: > > > > > I’m estimating a Poisson model, which includes > > > an interaction term > > > > > and I need to compute the impact (marginal > > > effect) of x1 on lnY. > > > > > > > > > > I have found on SJ an article “Computing > > > interaction effects and > > > > > standard errors in Logit and Probit models”, by > > > Norton, Wang and Ai > > > > > (2004), who warn that for nonlinear models > > > > <snip> > > > > > Please notice that my interest is computing > > > the effect of x1 on lnY > > > > > , I’m not interested in the marginal effect of > > > the interaction term, > > > > > nor in the effect of x1 on E(Y), because my > > > dependent variable is > > > > > not a count. > > > > <snip> > > > > > > > > If you are only interested in the effect on ln(y) > > > than it is no longer > > > > a non-linear model, so the article by Norton et > > > al. is no longer > > > > relevant. > > > > > > > > -- 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/ ----------------------------------------- __________________________________________________________ Sent from Yahoo! Mail. A Smarter Inbox. http://uk.docs.yahoo.com/nowyoucan.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/

**Follow-Ups**:**Re: st: Poisson model with interaction term***From:*Phil Schumm <pschumm@uchicago.edu>

**Re: st: Poisson model with interaction term***From:*Lloyd Dumont <lloyddumont@yahoo.com>

**References**:**Re: st: Poisson model with interaction term***From:*Maarten buis <maartenbuis@yahoo.co.uk>

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