# Logistic regression: Fisher's scoring iterations do not match the selected iterations in glm

it happened to me that in a logistic regression in R with glm the Fisher scoring iterations in the output are less than the iterations selected with the argument control=glm.control(maxit=25) in glm itself.

I see this as the effect of divergence in the iteratively reweighted least squares algorithm behind glm.

My question is: under which criteria does glm stop the iterations and provides with a partial output? I was thinking about something like "when the new coefficients-old coefficients < epsilon, then STOP". Is this the case? If not, what does make glm stop? Thanks, Avitus

• Hi @Avitus: The help page of glm.control says it: there you can specify an epsilon and the iterations converges when $|dev-dev_{old}|/(dev + 0.1) < \epsilon$. "dev" means Deviance. The maxit option specifies the maximum number of iterations. If the algorithm hasn't converged after maxit iterations, the partial output is given as well as an error message. – COOLSerdash Jun 5 '13 at 14:02
• Hi @COOLSerdash: your comment is actually an answer :-) I find it very helpful, thanks. One short silly question: what is the Deviance in glm.control? Is it the Deviance in en.wikipedia.org/wiki/Deviance_(statistics)? – Avitus Jun 5 '13 at 14:08
• Yes, that's exactly the Deviance. Maybe this and this will clarify Deviance further? – COOLSerdash Jun 5 '13 at 14:10
• @COOLSerdash: COOL links! Thank you very much. All I need now is to think about the choice of Deviance as parameter to stop or continue the iterations and gently ask you to edit your comment above into a question to upvote it :) – Avitus Jun 5 '13 at 14:15

In glm.control you can specify a positive $\epsilon$ which is used to decide whether the algorithm has converged or not. The documentation page of glm.control states that the algorithm converges if
$$\frac{|dev - dev_{old}|}{(|dev| + 0.1)} < \epsilon$$ Where "dev" means Deviance. These three resources maybe helpful in clarifying Deviance: first, second, third.