Predicting with a GLM I wanted to check my understanding of predicting with a GLM:
A binomial/logistic regression model predicts the binomial parameter = p = P(success). To convert the probability into classes, we have to add a threshold or cutoff.
The same idea applies for a multinomial logistic regression model.
A poisson regression model predicts the poisson parameter = rate. To convert into counts, I use a threshold again?
A gamma model predicts the scale and rate parameters. I do not need a threshold because the response is continuous.

Quoting from Wikipedia:

The GLM consists of three elements:

*

*An exponential family of probability distributions.

*A linear predictor $\eta=X \beta$

*A link function $g$ such that $E(Y|X)=\mu=g^{-1}(\eta)$

There is no threshold inherent in a GLM. Once you have the model, you can make predictions of $\mu$ (sometimes called the "mean function") for any set of covariates $X$. For a binomial model that could be translated into a probability of class membership. For a Poisson model, you are modeling counts directly.
Your application of a binomial GLM might then involve a threshold for making class predictions. Your application of a Poisson count model might involve translating counts into a rate per unit time, length, or area.  But those applications should be thought of as outside the GLM itself.
