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From |
"Stephen P. Jenkins" <stephenj@essex.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: probit with interaction dummies (significance and marginal effects) |

Date |
Mon, 28 Jul 2008 09:49:57 +0100 |

> ---------------------------------------------------------------------- > Date: Sun, 27 Jul 2008 05:44:28 -0400 > From: "Erasmo Giambona" <e.giambona@gmail.com> > Subject: Re: st: probit with interaction dummies > (significance and marginal effects) > > Dear Tony, Stephen and Allan, > > Thanks very much for your insightful contributions. I am still unclear > on how to intepret the simple coefficient on the interaction of two > continuos variables after logit in relation to the marginal effects. > Any thoughts on this would be appreciated. > Thanks, > Erasmo You appear to be seeking a one number quick fix. There isn't one. I recommend going back to first principles. A "marginal effect" (ME) can be defined in a number of ways according to taste, but one way of thinking about it in context of binary depvar models is: ME = change in Pr(y=1) given a one unit change in x (one of the RHS vbles) with appropriate redefinition in the case of binary/categorical x. You tell us that x is interacted with another variable, call it z. If the model is a probit Pr(y=1|x, z, ...) = Normal(a + b*x + c*xz + ....) then you can calculate the predicted probabilities Pr(y=1|x = x_1, z = z_1, ...) = Normal(a + b*x_1 + c*(x_1)*(z_1) + ....) and Pr(y=1|x = x_2, z = z_1, ...) = Normal(a + b*x_2 + c*(x_2)*(z_1) + ....) where x_2 = x_1 + 1, and the parameters are now understood to be estimated values. Change "Normal()" to -invlogit- for the Logit model. So, we can calculate: ME = Pr(y=1|x = x_2, z = z_1, ...) - Pr(y=1|x = x_1, z = z_1, ...), and this depends on the value of z_1, and also on the values of the other covariates ... Observe that there is no single unique "marginal effect" in non-linear models (logit, probit, poisson, etc.) regardless of whether interaction terms are included or not as covariates. Whatever ME you calculate depends on the values of the covariates. This is also true when there are interaction effects. Indeed, in the expression above, you would get another ME estimate were z held at a different value from z_1. Expressions like ME = Pr(y=1|x = x_1, z = z_1, ...) - Pr(y=1|x = x_2, z = z_1, ...) can be calculated, together with associated standard errors, using -nlcom-. The Norton et al. Stata Journal article that you cited simply canned some of these calculations. (Scott Long's NASUG presentation that I referred to last message is a clear demonstration of the predicted probability approach, together with associated graphs to illustrate the results. (He uses some of his own programs, but understand the principles.)) To me, the principal lessons of the Norton et al. article are a reminder of the following about non-linear models: * Some researchers wish to conclude that an "interaction effect is significant" by eyeballing the absolute t-ratio of the coefficient on an interaction term in a non-linear model (e.g. checking whether the |t| on coefficient c in the model above is greater than 1.96) * This is problematic because we are usually interested in concepts like MEs rather than a coefficient per se. * The value of an ME depends on the values of the covariates at which evaluated and, moreover, so too does the SE of the ME. * In particular an ME may not differ significantly from zero, even in cases where the coefficient on the interaction term is statistically significant. * So, interpretation of estimates from non-linear models can be trickier than interpretation of estimates from linear models Stephen ------------------------------------------------------------- Professor Stephen P. Jenkins <stephenj@essex.ac.uk> Director, Institute for Social and Economic Research University of Essex, Colchester CO4 3SQ, U.K. Tel: +44 1206 873374. Fax: +44 1206 873151. http://www.iser.essex.ac.uk Survival Analysis using Stata: http://www.iser.essex.ac.uk/teaching/degree/stephenj/ec968/ Downloadable papers and software: http://ideas.repec.org/e/pje7.html Learn about the UK's new household panel survey, the United Kingdom Household Longitudinal Study: http://www.iser.essex.ac.uk/ukhls/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**Re: st: probit with interaction dummies (significance and marginal effects)***From:*"Erasmo Giambona" <e.giambona@gmail.com>

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