# Is it technically “valid” to fit a logistic regression with a dependent variable that is a proportion?

Several posts (here and here) suggest that beta regression is more appropriate when the dependent variable is naturally bounded between 0 and 1. My question is, leaving appropriateness aside, is it technically incorrect to fit a logistic regression to proportional response variable? R will throw a warning but still produce a result.

It seems to me that the likelihood function will not be a valid likelihood when the response variable is proportional instead of binary, but mathematically speaking, it can still be minimized to give a solution. I wonder what violation/mistake, if any, is made when fitting a logistic regression to proportional data.

• In addition to the answers below: Here is another post dealing with this question. – COOLSerdash Jun 29 '13 at 9:35

• (+1) Maarten, another question: I read that binomial GLM can be used for fraction/proportion responses if the total number of trials is provided for each fraction/proportion (in R this is done with a weights argument to glm), see e.g. here stats.stackexchange.com/a/26779/28666. How does "fractional logit" with "robust standard errors" relate to this approach? Is it the same thing or not? – amoeba says Reinstate Monica Sep 5 '16 at 11:40