Interpretation of categorical variables in multinomial logit regressions

[Peter Barker]

Hi everyone,

I'm analyzing some experimental data and I have a hard time making sense of the interpretation of categorical variables in multinomial logit regressions when reporting relative risk ratios (RRR). I was hoping someone with more experience could help out.

Let's assume I have the following:
- three treatments: B, T1, T2
- dependent variable: happiness (dummy)
- one categorical variable (V) representing behavior: 1 (drink), 2 (eat), 3 (sleep)

Let's assume I run mlogit so that B becomes the reference treatment and I use "i.V" command in STATA to get separate coefficients for eat and sleep relative to drink and also use "rrr" to obtain relative risk ratios.

Now let's assume the coefficient of eat in T1 is 1.233*** --> would the interpretation be that when moving from drinking to eating, the likelihood of being happy in that particular treatment (T1) over-proportionally and significantly increases (by 23%) relative to the likelihood to be happy when one moves from drinking to eating in the Baseline? Essentially, does this mean that the likelihood for happiness increases by 23% more than it does increase in the Baseline?

I was reading up some stuff and the sense that I get is that the interpretation of those coefficients is similar to a diff-in-diff interpretation, but I'm not sure.

Thanks,
Peter

[Richard Williams]

If the dependent variable, happiness, is a dummy, why are you using mlogit rather than logit?

You might want to consider wheter the margins command can make interpretation easier. See

http://www3.nd.edu/~rwilliam/xsoc73994/Margins05.pdf

[Peter Barker]

Sorry, that was an error on my side. the DV is a categorical variable with 3 values: low, middle, high.
The reason I'm using RRRs is that it seems to me that their interpretation is similar to logit's odds ratios, which I find fairly intuitive. I just try to understand what their interpretation is in the case described above.

Unfortunately, when following your link I get an error "Service Temporarily Unavailable"

[Carlo Lazzaro]

Peter:
http://www3.nd.edu/~rwilliam/xsoc73994/Margins05.pdf is now available.

[Peter Barker]

Thank you.
I'm fine with the marginal effects approach. I'd still like to learn how to properly handle RRRs. I don't think I have an issue understanding it in general, but it seems to get a bit tricky for the case of categorical variables. Any help with respect to my example outlined above is appreciated.

[John Mullahy]

Peter: This is just one person's opinion, but I believe that working with average marginal effects on predicted conditional probabilities is much more straightforward—less "tricky," to use your term—in MNL models than working with RRRs.

With categorical RHS variables, the idea of the marginal effect is to compare the predicted outcome probabilities where all subjects are set at one category (say the baseline category, B) with the predicted probabilities where all subjects are set at one of the other categories (say T1 or T2), holding constant the values of all the other covariates. (Other "marginals effects" are possible to define, e.g. moving all subjects from their observed/actual categories to one of the other categories (e.g. B, T1, or T2), but these—in my experience, at least—are less commonly encountered.)

Among other things such average marginal effects have a nice adding-up property, i.e. for each subject they necessarily sum to zero across the categories of the outcome variable.

I realize that RRRs are more accepted in some disciplines, however, so these comments may be 100% unhelpful for your objectives.

[John Mullahy]

P.S. I just looked at Richard's very helpful assessment referred to in #2. It seems to me that the themes articulated there are consistent with what I suggested in #6.

[Richard Williams]

I'd still like to learn how to properly handle RRRs. I don't think I have an issue understanding it in general, but it seems to get a bit tricky for the case of categorical variables.

Personally I think categorical vars are easier to understand than continuous vars. With continuous you have to do this multiplication of effects. With categorical it is just one category versus the reference.

I also agree with John about marginal effects and adjusted predictions. I think it is simpler than trying to analyze all the zillions of effects you can get with an mlogit.

Possibly useful is listcoef, part of the spost13 package (findit spost13_ado). It lets you easily see what the coefficients are if you change the reference category for the DV. The mlogtest command that is also part of the package can be useful.