This is not quite correct. The log probabilities are log p(y=1 | x; beta) = beta * x - log Z(x; beta) where Z(x) = p(y=0 | x; beta) + p(y=1 | x; beta) Thus,

This is not quite correct. The log probabilities are log p(y=1 | x; beta) = beta * x - log Z(x; beta) where Z(x) = p(y=0 | x; beta) + p(y=1 | x; beta) Thus, you can think of it as linear regression, but with an additional term log Z(x; beta) in the log likelihood.