While reviewing King & Zeng paper on rare event data in logistic regression, I'm wondering what this term means?
Beta hat of the class 0.
While reviewing King & Zeng paper on rare event data in logistic regression, I'm wondering what this term means?
Beta hat of the class 0.
It is the estimated intercept in the logistic regression. I.e.,
$$E(Y\vert \vec{x}) = p(\vec{x}), \qquad \log\left(\frac{p(\vec{x})}{1-p(\vec{x})}\right) = \beta_0+\vec{\beta}_1^\top\vec{x} $$
See appendix B.4 and write $\tilde{\vec{x}} = (1, \vec{x}^\top)^\top$ and $\vec{\beta} = (\beta_0,\vec\beta_1^\top)^\top$