mlogit - coefficent and marginal effects with different sings

[Amy Duma]

Hi,

I am running a multinational logistic regression with the mlogit command. I have noticed that the coefficient of one of the independent variables (a dummy) takes a negative sign, which i interpret as the dummy having a negative impact on the probability of (let's say) outcome 1 with reference to the base outcome.

but when I estimate the marginal effects as follows:

margins x, post pr (out(1))

I get the opposite result, that is, a change from 0 to 1 in the independent variable has a positive impact on the probability of outcome 1.

Can someone explain to me why that could happen?

Thanks!

Amy

[German Rodriguez]

This can happen in multinomial logit models because you are modeling relative probabilities. Basically your predictor is associated with a decline in the probability of outcome 1 relative to the baseline (say outcome 3). But the same predictor could be associated with an even greater decline in the probability of outcome 2 relative to the baseline. As a result, the actual probability of outcome 1 could go up when you go from category 0 to 1 of the predictor. This is why one should always look at marginal effects in multinomial logit models. For a more detailed discussion and an example see https://data.princeton.edu/wws509/stata/mlogit.

[Amy Duma]

This can happen in multinomial logit models because you are modeling relative probabilities. Basically your predictor is associated with a decline in the probability of outcome 1 relative to the baseline (say outcome 3). But the same predictor could be associated with an even greater decline in the probability of outcome 2 relative to the baseline. As a result, the actual probability of outcome 1 could go up when you go from category 0 to 1 of the predictor. This is why one should always look at marginal effects in multinomial logit models. For a more detailed discussion and an example see https://data.princeton.edu/wws509/stata/mlogit.

Thank you - that makes perfect sense!