Is it plausible to have a positive coefficient with a negative marginal / impact effect after running multinomial logit model?
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gung - Reinstate Monica
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Tano
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I wrote a follow-up question to this question: https://stats.stackexchange.com/questions/520009/the-interpretation-of-a-positive-glm-coefficient-with-a-negative-marginal-effec – Tom Apr 16 '21 at 12:26
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This is a version of a frequently asked question. The answer is that your variable is correlated with the other variables that are in the model. As a result, the estimates for the variable can be positive when the other variables are included even though the marginal association is negative. The basic story is discussed in many places on CV, but if you want a generic introduction, it may help you to read my answer here: Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?
gung - Reinstate Monica
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I don't think that that is the problem here, as I don't see any mention of additional control variables. I suspect that Tano ran one multinomial logit model, than computed marginal effects, and than saw that a raw coefficient was positive, but the corresponding marginal effect was negative. – Maarten Buis Aug 29 '14 at 11:49
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That's a fair interpretation, @MaartenBuis, you could be right. I guess the question is a little ambiguous. Maybe the OP will clarify it. – gung - Reinstate Monica Aug 29 '14 at 15:01
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This can happen. Remember that the raw coefficients in a mlogit refer to changes in the log of the probability of one outcome divided by the probability of the baseline outcome (the logarithm of an odds), while the marginal effects refer to changes in the probability of one outcome. A variable can influence the one probability and the baseline probability so that it has a positive effect on the ratio, but a negative effect on the the one probability.
Maarten Buis
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