Interpretation of a Relative Risk Ratio in the case of a continuous variable (in log)?

[Killian Foubert]

Hello everyone

I am conducting a mlogit regression with three possible outcomes (the first one being my base), and my variable of interest is continuous and in log (more precisely, it's the log of the number of victims in a conflict). I also include a set of control variables. I use the option eform in my esttab command in order to obtain Relative Risk Ratios for my variables of interest (log victims and other controls).

On google I mostly found how to interpret these RRR in the case of dummy variables. However I found nothing about the interpretation of RRR in the case of a continuous variable, and nothing neither in the case of a continuous variable in log.

By interpretation, I mean the interpretation of magnitudes. I understand that if I find a significant and >1 RRR, it means that the likelihood of the outcome occuring relative to the base increases as the variable increases. What I miss is the interpretation in terms of magnitude. If my RRR is, let's say, 1.05, what does it mean in terms of "quantitative" change in the likelihood of my outcome relative to the base one?

Thank you in advance for your help

[Clyde Schechter]

So, in your case, it means that given two conflicts that differ by an order of magnitude (meaning a factor of 10 if you used log base 10, or a factor of e if you used natural logarithms) in number of victims, the probability of whatever outcome is associated with that RRR (you don't say what it is) is approximately 5% greater in the one with more victims.

I suspect you are also wondering how you could phrase that in terms of a per-victim increase. It is possible, and there have been many threads here on Statalist dealing with that issue (usually with logit instead of mlogit, but the reasoning and calculations are exactly the same) that you can look up if you really want to. But I would prefer to discourage you from doing that in this situation. I say that because the specific variable you log transformed is number of victims in a conflict. In that case, I suspect the reason for using a log-transform is that the range of the number of victims is extremely large, so that a one-victim difference between conflicts would be essentially meaningless. So if that's the case, explaining the RRR in terms of a marginal effect per additional victim would be equally pointless.

[Killian Foubert]

Thank you very much for your message,, it's perfect. Have a good day.