There appear to be a bug in the estimation of significance in the binomial model in GLM. This bug apparently appears when the correlation between two variables is to strong. Such as this dummy example c(0,0,0,0,0,1,1,1,1,1)->a a->b m1<-glm(a~b, binomial) summary(m1) It is sufficient that all 1's correspond to 1's such as this example
Isn't this just the well-known failure of logistic regression (non-existence of maximum likelihood estimator) for linearly separable data? (b > 0.5 => a == 1)
c(0,0,0,0,0,1,1,1,1,1)->a c(0,0,0,0,1,1,1,1,1,1)->c m1<-glm(a~c, binomial) summary(m1)
This is not linearly separable, but almost, so the standard errors will be very large.