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# st: Interpreting marginal effects for binary variables in multinomial logit

 From Julian Runge <[email protected]> To [email protected] Subject st: Interpreting marginal effects for binary variables in multinomial logit Date Wed, 13 Jun 2012 16:50:06 +0200

```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?