# Complete separation in logistic regression with only one direction

In this paper Dealing with Separation in Logistic Regression Models some various types of complete separation are discussed:

direction of the separation is positive if and only if $s_i = 1 \Rightarrow y_i = 1$ or $s_i = 0 \Rightarrow y_i = 0$

direction of the separation is negative if and only if $s_i = 0 \Rightarrow y_i = 1$ or $s_i = 1 \Rightarrow y_i = 0$

I'm wondering if this can be also called complete separation:

$s_i = 0 \Rightarrow y_i = 1$ AND $s_i = 1 \Rightarrow y_i = 1$

I call this one direction to distinct it from the other two.

Here I have the corresponding showcases to make it clear:

posivite direction:

          out
group    0  1
ctrl  20  0
treat  0 20


negative direction:

          out
group    0  1
ctrl   0 20
treat  20 0


one direction

          out
group    0  1
ctrl   0 20
treat  0 20


My questions are:

• Can this be also called complete separation?
• May I use the same tools (for example bayesglm from R) to analyze this kind of complete separation?

The paper you linked do not have a correct definition of complete separation, it says that only occurs if it is caused by one variable $s_i$. That is not correct, complete separation can well occur without any single variable causing it. So maybe you should find some better source of basic information on LR, maybe https://www.amazon.com/Regression-Modeling-Strategies-Applications-Statistics/dp/0387952322 (there are also many good posts on this site).