As discussed in this post, perfect separation (algorithm did not converge) is a separate issue aside from "fitted probabilities numerically 0 or 1 occurred".

As suggested in @gung's example, the model can be perfectly fine, even fitted probabilities numerically 0 or 1 occurred.

So, why R is giving such warning? Because it might be overfitting involved?

  • $\begingroup$ In my experience when R gives me this warning it means I have done something truly stupid. It is a bit like: Did you really mean ...? $\endgroup$ – mdewey May 24 '17 at 15:51
  • $\begingroup$ @mdewey ye, that is exactly my question. if you check gung's example, it can be perfectly fine, why it is warning me? $\endgroup$ – Haitao Du May 24 '17 at 15:52
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    $\begingroup$ Hints: what are the logits of $0$ and $1$? How would they be represented in floating point? What does that imply about the reliability of those representations? $\endgroup$ – whuber May 24 '17 at 18:19

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