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I run logistic regression models where the event rate is generally very low. In my models I get a large intercept term. What bothers me is the exceptionally high chi-square of the intercept term. How do I interpret this condition?

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The intercept term is the parameter estimate when all the independent variables are 0. One way that you could get the results you describe is if 0 is not a meaningful value for the IVs. E.g. suppose one of your IVs is annual income in $. Then a 0 value is far outside the data.

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    $\begingroup$ I like year of birth as an example $\endgroup$ – Maarten Buis Jan 15 '16 at 13:30
  • $\begingroup$ What about the high chi-square? Does it indicate that the intercept has an exceptional contribution in the model? And the independent variables poorly explain the target? $\endgroup$ – Ujjwal Agrawal Jan 15 '16 at 13:36
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    $\begingroup$ It doesn't mean anything. $\endgroup$ – Peter Flom - Reinstate Monica Jan 15 '16 at 23:47

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