Can you run a GLM using a logit link with a continuous DV (between 0 and 1)? Generally it’s suggested to use a binomial family with a logit link, but I’m guessing that is because the model assumes a binary DV. If we have a continuous DV would we want to use a Gaussian family instead of binomial?
I apologize if this question doesn’t make much sense: I have only a very basic knowledge of statistics, and am just trying to recalibrate a model specified by a colleague a number of years ago.
You seem to want to use a fractional logit, i.e. a quasi-likelihood model for a proportion. The key here is that it is a quasi-likelihood model, so the family refers to the variance function and nothing else. In quasi-likelihood that variance is a nuisance parameter, which does not have to be correctly specified in your model if your dataset is large enough. So I would stick with the usual family for a fractional logit model, and use the binomial family.