Effect Size for Multilevel Logit

[Andrea Arancio]

I'm using -meqrlogit- to run some multilevel logit models, with only random intercepts and not random slopes.

I'm now wondering what is the best way to calculate the effect size of each predictor, in this kind of model. For multilevel regression I usually calculate the Cohen's F-squared.

What do you recommend for mixed logit? And which is the best way to calculate it?

Thanks a lot!
Andrea

[Maarten Buis]

What about the odds ratio? Just add the or option of your meqrlogit command.

[Andrea Arancio]

Thanks Maarten. I considered that solution, but I was also wondering about the existence of some other method, to show togther with the model coefficients.
Is odds ratio the best?

[Maarten Buis]

What is best depends on your goals, so there can be no general answer to that question. However, the odds ratios follow naturally from that model, so it is often a good candidate.

[Weiwen Ng]

Odds ratios and change in predicted probability already can be interpreted as effect sizes. You said that you would calculate Cohen's f-squared for each predictor. Is that correct? Then, would you interpret the effect sizes based on Cohen's very rough guidelines as to what constitutes a small or medium one?

F-squared is based on the proportion of variation in the outcome that a covariate or group of covariates accounts for. Basically, f-squared is based on r-squared. If you really, really need something more than just odds ratios (or you can also present predicted probabilities from the margins command!), then perhaps a place to start would be understanding the various flavors of pseudo r-squared measures for logistic regression. I can see a few ways to get at the same issue that f-squared is trying to get at.

The problem is that while I suppose I could calculate a pseudo f-squared, I would have no way to interpret it, or even know how to think if what I was doing made sense. I don't think the underlying statistical theory is well developed for this. I think there's already no consensus on which pseudo r-squared measure is best in the first place.

Basically, unless you're a biostatistician and you're interested in actually proposing some sort of pseudo f-squared, I would stick to the odds ratios / marginal effects.