Is it possible to customize a likelihood function for logit models using speedglm, biglm, and glm packages

Question

I am trying to fit a customized logistic regression/survival analysis function using the optim/maxBFGS functions in R and literally defining the functions by hand.

I was always under the impression that for the packages speedglm, biglm, and glm, the likelihood functions for logit models or whatever distribution were hardlocked. However, I was wondering if I was mistaken or if it was possible to specify my own likelihood functions. The reason being that optim/maxBFGS is a LOT slower to run than speedglm.

Answer 1

The R glm function is set up only to work with likelihoods from the exponential family. The fitting algorithms won't work with any other kind of likelihood, and with any other you're not in fact fitting a glm but some other kind of model.

The glm functions fit using iterated reweighted least squares; the special form of the likelihood function for the exponential families makes Newton's method for solving the max likelihood equations identical to fitting ordinary least squares regression repeatedly until convergence is achieved.

This is a faster process than generic nonlinear optimization; so if the likelihoods you want to use have been customized so that they are no longer from an exponential family, you are no longer fitting a generalized linear model. This means that the IRWLS algorithm isn't applicable, and the fit will be slower, as you are finding.