I was reading this post


and found that the author adjusted a glm with binomial family and log link. As far as I remember, the inverse of the link function should be a function which return values in the range [0,1] for the case of the binomial family. The inverse of the log function, the exponential function don't have this property.

Is this correct? Log link is a valid link for the binomial family in a glm?


1 Answer 1


The log link is a valid link function for the binomial family, but as you point out, its use may lead to numerical/convergence problems. So there is no guarantee that it will work well in any given case, although it often does.

There are multiple examples on this site, for instance Why isn't it 'wrong' to use a log link instead of a logit one when doing GLM with a binomial family? (really a dup!), What to Do When a Log-binomial Model's Convergence Fails and two simple examples that both also contain R code: Manipulating Binomial Distribution and Confidence interval on binomial effect size

If interest is in relative risk not in odds ratios this seems a natural way to go, see Relative Risk Regression in Medical Research: Models, Contrasts, Estimators, and Algorithms. But, as the question alludes to, there is multiple problems, not the least numerical, with fitting a binomial model with log link. There is now a dedicated R package on CRAN with multiple special algorithms trying to solve this numerical problems, see logbin: An R Package for Relative Risk Regression Using the Log-Binomial Model.

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    $\begingroup$ This is pretty weird, the development of glm was aimed to restrict the values of the linear predictor in the domain of the parameter space using the link function. I cannot understand why some one would use a link that is not guarantee to give values inside the parameter space. Why would one use a Poisson distribution with the identity link, or the Gamma distribution with the identity link? this makes no sense at all for me (as statistician). However it seems that there are people doing this outside, I am totally shocked. $\endgroup$ Commented Sep 2, 2020 at 17:48
  • $\begingroup$ You could ask that as a more general (also historical) question. But in simple cases (as in one of the examples linked to above), with only predictor a treatment/control indicator, there should never be any convergence problems. $\endgroup$ Commented Sep 2, 2020 at 17:57

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