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

 From Julian Runge 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?
>>>
>>>
>>> Julian
>>
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--
Julian Runge
Student research assistant
Institut für Entrepreneurship und Innovationsmanagement
Dorotheenstr. 1, 1.OG
10117 Berlin
Tel.: +49 (0)30 2093-99019
E-Mail: rungejuq@hu-berlin.de

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```