marginal effects vs. odds ratios

[Josh Lee]

Hello,

I am currently trying to understand the pros and cons of using odds ratios vs. marginal effects for the interpretation of a multinomial logit. If anyone could enlighten me, or point me to a resource that could help with this decision, it would be greatly appreciated.

J

[Clyde Schechter]

If you search for literature and internet posts on this topic you will find a variety of opinions. Some of them put forth calmly, some put forth with the intensity of fundamentalist religion.

My own view is that any form of communication should be geared to the sensibilities of the audience. If you will be presenting your results to people who are unfamiliar with, or uncomfortable with odds ratios, then by all means explain your results with marginal effects. If you are presenting your results to whom odds ratios are as natural as breathing, use them: some of those people will never even have heard of marginal effects!

There is one factor that may tip the balance if your audience is mixed or equally facile with both approaches. If your results come from a logistic regression model, the results are more naturally presented as odds ratios. The reason is that in the logistic model, if there are no interaction terms, each predictor variable has a single associated odds ratio that is applicable at all values of all of the variables. In this same model, however, the marginal effect of any variable is a function of both the value of that variable and the values of the other variables in the model as well. So for describing logistic regression models, there is an inherent simplicity to the use of odds ratios. But, even then, if you are talking to people who simply don't understand odds ratios or are very unaccustomed to them, then marginal effects, which are in the more widely familiar probability metric, are a reasonable way to go.

It may also depend on the context. If you are analyzing a policy question, the policy analyst will want to know: if I do this, how will it change what happens. Do this typically means implement some policy. Change what happens usually means a change in the probability or rate of some outcome event. From a decision-making point of view, the relevant figure here is then the marginal effect, not the odds ratio. If, by contrast, we are not discussing policy but attempting to understand a mechanism of something in nature, the odds ratio is typically a better measure of the strength of association because it is usually not, as noted above, dependent on the baseline rate of occurrence or probability.

[Josh Lee]

Thank you very much. I will be presenting this as a thesis for an Applied Economics master's program. One of my committee members explained to me that generally in the context of economic research, marginal effects are chosen. However, I wasn't informed of any reasons as to why this was. Your explanation regarding policy analysis would seem to be the most prominent reason for this phenomenon. This was very helpful. Thank you for your time.