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The following is an excellent example for your condition (you'll get the same error message when you run logistic regresson on the following data)
Consider the following data
y x z
1 1 1
1 2 2
1 3 3
1 4 4
1 5 5
0 6 5
0 7 6
0 8 6
0 9 7
0 9 8
Consider X as a single predictor of Y. There is a situation
in these data called separability. Note that a cutpoint on
X of 5.5 separates the Ys. Try a logistic regression of
Y on X, and you get Bs and Standard errors that blow up.
Likewise, consider Z as a single predictor. Here, Z=5
straddles the boundary of Y being 0 or 1. A similar thing
happens with Z as a single predictor.
X and Z are highly but not perfectly correlated. When you
do a logistic regression of Y on both X and Z, Logistic Regression prints
the kind of messages that you report.
So, take a closer look at your data, and look for situations
of separability or near-separability (complete or near-complete separation) and/or high correlation
in your predictors.
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