[claytonjy]

> generates parameters that you can easily explain to someone with no background in math

I know it _seems_ that way, but there's a surprising amount of nuance there and I think we're both fooling and limiting ourselves by letting this idea fester.

For one, unlike linear regression, logistic regression estimates aren't collapsible, so you can NOT interpret them as "changing this input by X changes the output by Y". That's only true if your set of covariates is perfect, which is never true, though in practice this interpretation might not be _that_ far off.

Another issue I see is practitioners not being aware of scaled/unscaled estimates; I've seen real papers from AI groups use logistic regression estimates like feature importance rankings, but using estimates in the scale of the original features, and not understanding the distinction when confronted about it.

From a practical sense, I think practitioners are much better served using random forests as their initial exploratory models. Less effort for results that are in practice at least as good as a well-prepped logit. Plenty issues with feature importance there, but not any worse than with logistic regression.

[bunderbunder]

I don't think that's such a big deal in practice. See http://jakewestfall.org/blog/index.php/2018/03/12/logistic-r..., for example.

tl;dr: The upshot is that non-collapsibility means that I can't use LR coefficients for things that I don't really need to use them for, anyway. That doesn't feel like a crippling limitation to me.

(Well, also, I have to occasionally pause to cross my fingers and say, "ceteris paribus," under my breath, which does admittedly make people think I'm some sort of weird Harry Potter nut. Which is OK. They're not wrong, they're just right for the wrong reason.)

Nor does it render its coefficients less interpretable than those of most other models. "Less interpretable than OLS" can still be pretty darn interpretable.

[claytonjy]

I had exactly that post in mind, it really raised my awareness of these issues.

I agree with Jake's interpretation of the conditional interpretation of the estimates, but the practical issue is that virtually nobody not well-educated in statistics will do that correctly. In particular, people tend to do exactly what Jake concedes rarely makes any sense, which is comparing estimates across different model specifications.

You and I might interpret these betas just fine, but if we show them to a less stats-y audience, will they?

[bunderbunder]

I guess it depends. I have the luxury of working in a very "this is machine learning, which is not to be confused with statistical inference" problem domain. It doesn't really even really make sense to interpret most the models I build as describing any sort of causal relationship, and when people are looking at the parameter estimates, they're really just trying to figure out, "What does this model think is important?"

[claytonjy]

That sounds nice!

Feature ranking seems like a clearly safe interpretation of betas, though I've been bitten too often by letting glm (in R) scale my predictors, giving me back estimates on the original scales, and thus incomparable, and seen it happen to others even more. Easy to miss when your original scales aren't all that different.

[thanatropism]

It's not that difficult to compute true marginal effects from logistic regression using something like the bootstrap (if you have a distribution for your coefficients) or explicit differentiation. Every traditional stats app (Stata, SAS, etc) has this.

[claytonjy]

What do you mean by "true" marginal effect? Are you suggesting a post-hoc procedure can correct estimates such that they are close enough to the estimate that would have been produced with a more complete model specification?