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From |
Julian Runge <rungejuq@cms.hu-berlin.de> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Interpreting marginal effects for binary variables in multinomial logit |

Date |
Thu, 14 Jun 2012 13:19:39 +0200 |

Thanks for your comments. I agree on the "awkwardness" of fixing binary covariates at the mean. Best, Julian > > 2012/6/13 Austin Nichols <austinnichols@gmail.com>: >> Julian Runge <rungejuq@cms.hu-berlin.de>: >> Your interpretation sounds correct, but such atmeans marginal effects >> are meaningless. >> Consider the second command, or equivalently a logit of y==2 on x1 and >> x2 binary. >> The marginal effect is dp/dX for x1 evaluated at x2==0.7, say. >> No one in the data actually has x2==0.7, so comparing predicted probabilities >> for x1==0 and x2==0.7 to x1==1 and x2==0.7 makes no real sense. >> In practice, you often get something similar to a more sensible marginal effect, >> but that does not make it right to compute predictions for a nonlinear model at >> covariate patterns that are impossible to observe. >> >> It's not an "average marginal effect at the average" but simply >> a "marginal effect at the average" since the other x vars are fixed. >> The problem is that average of a vector of binary predictors is a >> terrible point at which to evaluate marginal effects. >> I.e. your use of the words "for a representative individual" >> implies such a person might be 70% a college graduate, or >> 10% pregnant, for example. >> >> Are the binary x vars related in any way? >> Include interactions or other logical dependencies? >> If so, you have even worse problems. >> >> On Wed, Jun 13, 2012 at 10:50 AM, Julian Runge >> <rungejuq@cms.hu-berlin.de> wrote: >>> Hello! >>> >>> Two brief (closely related) questions that I could not find a definite >>> answer to yet, neither in the literature nor in the discussion with peers. I >>> would really appreciate your input, especially on question 1: >>> >>> 1) >>> My model has a categorical dependent variable and all independent variables >>> are binary. I used a multinomial logit model with y={0, 1, 2} and 0 as base >>> outcome to estimate the model. After running the regression, I applied the >>> following commands to get marginal effects: >>> >>> margins, predict(outcome(1)) dydx( x1 x2 ... ) atmeans >>> margins, predict(outcome(2)) dydx( x1 x2 ... ) atmeans >>> >>> Now I am unsure how to interpret the marginal effects. I would do as >>> follows: >>> >>> It is the ceteris paribus mean effect for a discrete change in the >>> respective binary independent variable from zero to one for a representative >>> individual (in terms of “being average" on all variables, i.e. the >>> covariates are fixed at their mean) in the sample. Let us consider an >>> example to make this more accessible: The marginal effect on x1 for category >>> y=1 tells us that, ceteris paribus, a subject that answers “yes” (x1=1) >>> instead of “no” (x1=0) has a 0.0a (a%) higher probability to be part of >>> category y=1. >>> >>> --> Am I getting this right? >>> >>> >>> 2) >>> A credible online source noted the following: "The default behavior of >>> margins is to calculate average marginal effects rather than marginal >>> effects at the average or at some other point in the space of regressors." >>> Taking this into account I would think that I am calculating an "average >>> marginal effect at the average" above. Is that correct? >>> >>> >>> Thank you in advance, >>> Julian >> >> * >> * 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/ -- Julian Runge Student research assistant Institut für Entrepreneurship und Innovationsmanagement Prof. Christian Schade Dorotheenstr. 1, 1.OG 10117 Berlin Tel.: +49 (0)30 2093-99019 E-Mail: rungejuq@hu-berlin.de * * 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: Interpreting marginal effects for binary variables in multinomial logit***From:*David Hoaglin <dchoaglin@gmail.com>

**References**:**st: Interpreting marginal effects for binary variables in multinomial logit***From:*Julian Runge <rungejuq@cms.hu-berlin.de>

**Re: st: Interpreting marginal effects for binary variables in multinomial logit***From:*Austin Nichols <austinnichols@gmail.com>

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