I have a data set where the response variable Y is a rate between 0 and 1, where the histogram of Y is bimodal. So I feel the linear regression is not suitable.s I have been reading papers about inflated beta regression.
My question is, just as in OLS, we check the plot of Y at a given level of X to se if it is normal, do I need to ensure that the conditional plots of Y given X for each of my predictors is also bimodal?
Also, I have read that R-square isn't applicable for GLMs such as beta regression, and instead I need to use deviance residuals. If I want to ensure that the model fits well(all variance is explained), should I be looking for a deviance residual plot that is normally distributed?
A preliminary run in SAS showed strong hetero-skedasticity in my model's residuals (the raw residuals, i.e., Y - Yhat) ----however, I want to confirm that this is okay, since in non-linear regression the variance depends on the mean (specifically okay for beta regression) ?