= Separation in logistic regression
{title2=$x_i^{\mathsf T}v>0\ (y_i=1),\quad x_i^{\mathsf T}v<0\ (y_i=0)$}
Complete separation means that a predictor direction $v$ strictly separates the binary outcomes as displayed. In <logistic regression>, replacing $\beta$ by $\beta+tv$ increases each observed-outcome <probability> as $t$ increases, so the <log-likelihood> has no finite maximizer. Weak inequalities with some equalities can similarly produce quasi-complete separation. Finite coefficient estimates and ordinary information-matrix inference therefore require an existence check rather than relying only on the formal score equations.
Back to article page
