Ahhh, good catch! I just went in and fixed it.

]]>Well, invlogit is a special case of the logistic in which the maximum value is 1. In this special case the situation is indeed a bit confusing:

Logit: [0, 1] -> R // qlogis(x)

Invlogit: R -> [0, 1] // plogis(x)

Logistic: R -> [0, 1]

Inverse logistic: [0, 1] -> R

So here the logit is the inverse of logistic which in self is the inverse logit which is the inverse of the inverse logistic.

]]>Thanks Andrew. Indeed I fail to see what’s special about invlogit versus writing out the function. Using the function shows the student can convert an odds to a probability, that’s plus.

I stand corrected about the distances. I assumed there would be some distance to a safe well, if wells are 50m apart they drain the same water table and will have the same arsenic content.

I guess what bothers me about the divide by 4 (not really a) rule is that it disregards the nature of a multiplicative model. The absolute difference cannot be constant across values of other (non null) covariates. I would pass a student who answered “I cannot answer that, it all depends on the distance to the well”.

]]>Jd:

Just to clarify: In the last paragraph of my above post, when I say “Invlogit is invlogit,” I mean, use invlogit() (or, in default R, plogis()). Do not write it as exp(x)/(1 + exp(x)) or as 1/(1 + exp(-x)) because that misses the point that invlogit() is its own function. If you want to use logistic regression, you should understand logit and invlogit as functions in their own right, not as complicated formulas involving exponentials. My point is not mathematical accuracy or speed of computation—all these formulas are indeed the same thing—but, rather, understanding.

]]>I think maybe anon’s question was – why are you saying to use invlogit() rather than 1/(1+exp(-x)) (which is the invlogit function) ?

]]>Anon:

There’s no prohibition of anything. It’s find to use invlogit. It’s also fine to divide by 4 if the probability is close to 1/2. An advantage of dividing by 4 is that if you have a table of regression coefficients, it’s easy to divide by 4 and see what they are.

The bigger picture is that I want students to understand regression models quantitatively, not just qualitatively. The usual story is that people look at coefficients and just see whether they’re positive or negative and whether they’re statistically significant. I think that’s a mistake, so I train students to be able to see a fitted regression model and interpret it quantitatively.

]]>Thomas:

First, you missed the point of the last paragraph of my post. It’s invlogit(…) ,not exp/(1+exp).

Second, you missed the point of the last sentence before the last paragraph, that the probabilities of switching are indeed not far from 50%. Almost nobody in that area in Bangladesh lives as far as 300m from the nearest safe well. The distances are mostly much less, mostly less than 50m from the nearest safe well.

I agree that if probabilities are not close to 1/2, you shouldn’t use the divide-by-4 rule, you should just work with invlogit directly. But the divide-by-4 rule is often useful, I think it’s usually a good starting point, and in this particular example it works just fine.

]]>Imagine the clean well is at 300m. The 1st person has a probability of exp(0.46-2.7)/(1+exp(idem)) = 0.096, the 2nd person exp(0.23-2.7)/(1+exp(idem)) = 0.078, difference = 0.018. Not even in the ballpark of 0.055. ]]>