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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

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

Date |
Wed, 13 Jun 2012 13:54:53 -0400 |

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/

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

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