# Difference between generalized logistic regression and logistic regression

I have received a weird comment from a referee of pretty decent Journal. I stated in the methods section that "The association of the exposure with the outcome was investigated in terms of odds ratio (OR; 95% confidence interval, CI) using generalized logistic regression". Both outcome and exposure were binary.

Basically, this is what I did with R:

fit <- glm(outcome ~ exposure,  family =
data = df)


The referee commented this: “I would like to know why the authors used generalized logistic regression as opposed to conventional logistic regression. What is the extension part of the model (generalisation) doing? What was it used for? Were you trying to adjust for the clustering of participants within recruitment sites? You will need a multilevel model (not a GLM) for that."

What do you think is the true difference between generalized and conventional in this setting (also in code writing)?

There's generalised linear modelling GLM (a tool which is general in that it accomodates non-linear functions, in your case: logistic) and there's generalised logistic function (which is general in that it extends the "classical" logistic function). Mentioning the latter while meaning the former might have left the reviewer wondering about the priorities (elaborating on the logistic function while - from all the rev knew - the clustering of participants would've been prior concern, if any, to be addressed with a multi-level rather than GLM tool).

(sorry, I know this should go into a comment, for which I'd need 50 rep though)

• What do you mean by generalised logistic function? Commented Apr 23, 2022 at 18:33
• An extension of the initial logistic function, aka Richard's curve, which gives more flexibility to fitting a growth curve. The classical logistic function is a particular version of this general function in which one tuning parameter (v) remains effectively unused: en.wikipedia.org/wiki/Generalised_logistic_function
– I_O
Commented Apr 23, 2022 at 18:41
• Sorry, I didn't catch you! Could you be more didactic? Commented Apr 23, 2022 at 19:00
• Generalised linear model (a) and generalised logistic function (b) are two different beasts. However, it's easy to mix things up because the tool (a) is routinely used to do logistic regression (although not necessarily its "exotic" (b) variant). Anyhow, you wrote "generalised logistic regression" = (b) while you - presumably - did plain logistic regression with GLM = (a)? While the reviewer wondered about your apparent choice of a specialised logistic function, not the suitability of GLM for logistic regression.
– I_O
Commented Apr 23, 2022 at 19:25
• Thank you! Now I catched! Removing the term generalized would be sufficient! Commented Apr 23, 2022 at 19:35