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From |
Lloyd Dumont <[email protected]> |

To |
[email protected] |

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

Date |
Tue, 26 Feb 2008 07:53:47 -0800 (PST) |

Thanks, Maarten. After a lot of thinking about this and looking over which parts of the code generated which parts of the graph and trying to recall how marginal changes are computed with a logit, I think I get your example. But, I'm still not sure how to translate that back to a poisson or negative binomial context---and if the panel nature of the data make it even more complex. --- Maarten buis <[email protected]> wrote: > 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 <[email protected]> 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 <[email protected]> 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 > > > --- [email protected] wrote: > > > > > > > thank you Maarten, hence I can simply apply > the > > > > linear case formulas... > > > > > > > > thanks again > > > > Maria > > > > Citazione Maarten buis > <[email protected]>: > > > > > > > > > --- [email protected] 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/ > ____________________________________________________________________________________ Be a better friend, newshound, and know-it-all with Yahoo! Mobile. Try it now. http://mobile.yahoo.com/;_ylt=Ahu06i62sR8HDtDypao8Wcj9tAcJ * * 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:*Maarten buis <[email protected]>

**References**:**Re: st: Poisson model with interaction term***From:*Maarten buis <[email protected]>

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