# Threshold for and Variations of Exact logistic regression

According to this UCLA tutorial exact logistic regression (elrm::elrm in R) should be prefered to the logistic regression glm(... ,family = binomial)in R if

• the sample size is small AND/OR
• Some cells are empty

My questions:

1. What does small sample mean in this case (e.g. n<30 or n < 300 or n<3 000)
2. If exact logistic regression performs better than logistic regression in some cases why don't we always use exact logistic regression? I know that exact logistic regression is often more computationally expensive because of the Monte Carlo Markov Chain Algorithm. Is this the only reason?
3. Are there also multinomial/ordered and probit versions of the exact logistic regression?