Table 1 Link functions for linear, logistic and Poisson regression models in GLM, where different models have different A(∗), B(∗), and C(∗)
| GLM models | B(θ) | μ(θ)=B ′(θ) | Link θ(μ) | V(μ)=B ″(θ) |
|---|---|---|---|---|
| Linear regression | θ 2/2 | θ | Identity | 1 |
| Logistic regression | log(1+e θ) | \(\frac {1}{1 +e^{-{\theta }}}\) | logit | μ(1−μ) |
| Poisson regression | exp(θ) | exp(θ) | log | μ |