# Will the p value become useless in such case: logistic regression with perfect separation?

I think I understand the perfect separation problem in logistic regression and answered my own question in this post from optimization perspective.

Is there any intuitive explanation of why logistic regression will not work for perfect separation case? And why adding regularization will fix it?

However, I still do not understand the p-value in such case. I saw all the values in R is <2e-16 for thousands coefficients. For example

             Estimate Std. Error    z value Pr(>|z|)
c1       -1.524e+15  4.701e+07  -32413747   <2e-16 ***
c2       -4.226e+15  4.735e+07  -89262659   <2e-16 ***
c3       -2.932e+15  6.302e+07  -46524709   <2e-16 ***
c4       -2.808e+15  4.098e+07  -68505362   <2e-16 ***
c5        2.141e+15  7.796e+07   27470901   <2e-16 ***
c6       -5.617e+14  7.295e+07   -7699884   <2e-16 ***
c7       1.046e+15  7.135e+07   14654699   <2e-16 ***
c8       1.797e+15  4.161e+07   43176668   <2e-16 ***
c9       -1.443e+14  7.788e+07   -1852414   <2e-16 ***
c10      2.095e+15  9.287e+07   22557866   <2e-16 ***
c11      4.918e+14  3.600e+07   13659294   <2e-16 ***
c12      -1.293e+14  4.204e+07   -3076600   <2e-16 ***
...      ...        ...         ...         ...


Why would that happen? And Can I say the p-values are not longer valid in perfect separation case?

• This isn't answerable till you explain how you're fitting the model & calculating the p-values. The common schoolboy error is using maximum-likelihood fitting together with the Wald approximation to calculate p-values in the presence of separation, typically making them absurdly large. – Scortchi - Reinstate Monica Oct 25 '16 at 14:52