When using a binomial family, logit link for GLM (or GEE in my case), I notice that my model estimates diverge when my response variables (which are continuous probabilities with range 0 to 1) include 0 or 1 (or 0 <= y <= 1) as observed values, but the models with response variables that don't include 0 or 1 (or 0 < y < 1) are able to converge just fine.
- Why does this happen?
When running a logistic regression model (with 0 < y < 1) the model runs fine, as does the model when the response variable is dichotomous 0/1.
I suspect the following: say I have observations 0 < y <= 1. In this case, the algorithm sees my ones but not any zeros, and then craps out saying "some groups have fewer than x observations," the aforementioned group being the ones that are supposed to have zeros.
- If I exclude observations that are 0 or 1 in order to fit my models, am I biasing my results?
Here's an example: my response variable is graduation rate expressed as a percentage. For the logistic regression models, there are apparently schools that have 100% graduation rate (seen as a 1 in my dataset). Would it be a valid strategy to drop these schools from the model, and what are the implications in interpretation? Is this akin to dropping outliers willy-nilly?