Examples: Generalized Linear Models

Abstract

In chapter 6 we described briefly our implementation of two conjugate gradient algorithms in GLIM. Here we describe a number of other details necessary to adapt GLIM to fit generalized linear models by conjugate gradients. When GLIM fits a model, it stops iterating when the relative change in the log likelihood function is less than 10⁻⁴. If the log likelihood is small, this is replaced by an absolute criterion involving ( n-rank(X) ). Other than replacing this with¹ max(n-r, 1) we adopted this as our convergence criterion. We chose Fisher’s scoring algorithm2 for the line search algorithm. Most of the quantities necessary to implement Fisher scoring are computed during evaluation of the likelihood function. The extra cost (typically a few arithmetic operations) is small compared to the cost of generating the rows of X. We used a relative convergence criterion based on the relative change in the log likelihood for the current iteration of the search measured against the total change during the search.