Minor point: sometimes you write $g(u)$ and sometimes $g^{-1}(u)$ with the same letter $u$. Later in Section 15.2 page 267, $u$ is the exposure.
More importantly, you say " $g(u) = \exp(u)$ transforms a continuous linear predictor $X_i \beta$ to a positive $\hat{y}_i$", which is true, but a few lines above you defined $g()$ as the link function $\hat{y} = g^{-1}(X\beta)$. Then top of page 264 you say " $g$ is the inverse logit".
(It would also help in this section to define $\hat{y}$ because you define all other terms, is it meant to be $E[y|X]$ ?)
andrewgelman
commented
9 months ago
Minor point: sometimes you write $g(u)$ and sometimes $g^{-1}(u)$ with the same letter $u$. Later in Section 15.2 page 267, $u$ is the exposure.
More importantly, you say " $g(u) = \exp(u)$ transforms a continuous linear predictor $X_i \beta$ to a positive $\hat{y}_i$", which is true, but a few lines above you defined $g()$ as the link function $\hat{y} = g^{-1}(X\beta)$. Then top of page 264 you say " $g$ is the inverse logit".
(It would also help in this section to define $\hat{y}$ because you define all other terms, is it meant to be $E[y|X]$ ?)
Thanks ! Shira