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?