Better initial guesses for logistic regression

[dcwuser]

We do a full-on multi-dimensional optimization to get logistic regression parameters via likelihood maximization. I don't see any alternatives in the literature, but we should at least be able to make a better initial guess to feed into that algorithm than "all zeros", which is what we currently do.

[dcwuser]

For the bivariate case, here is a simple idea I found online. Call x_T and x_F the mean values of x for the true and false cases. Assume
\sigma(a + b x_T) = 3/4
\sigma(a + b x_F) = 1/4
Then b = \frac{\sigma^{-1}(3/4) - \sigma^{-1}(1/4)}{x_T - x_F}. This should get the sign right, and the order of magnitude if we are lucky.