Quasibinomial regression
= Quasibinomial regression
The logit mean model $p_i=(1+e^{-x_i^T\beta})^{-1}$ with working <variance function> $\phi p_i(1-p_i)$ has the same coefficient estimates as ordinary binomial <logistic regression>, but estimates dispersion from residuals. For an actual individual binary random variable, $Y^2=Y$ forces <variance> $p(1-p)$, so a nonunit dispersion is a working specification rather than a new independent binary distribution.