Table 1 The Link function [42]
From: Big data ordination towards intensive care event count cases using fast computing GLLVMS
Link Name | Link | Inverse | 1st Derivative |
|---|---|---|---|
Gaussian/Normal | \(\mu\) | \(\eta\) | 1 |
Binomial (Bernoulli: m=1) | \(\text{l}\text{n}(\mu /(m-\mu \left)\right)\) | \(m/(1+\text{exp}\left(-\eta \right))\) | \(m/\left(\mu \left(m-\mu \right)\right)\) |
Logit Probit | \({{\Phi }}^{-1}(\mu /m)\) | \(m{\Phi }\left(\eta \right)\) | \(m/\varphi \left\{{{\Phi }}^{-1}(\mu /m)\right\}\) |
Log-log | \(\text{ln}(-\text{ln}(1-\mu /m))\) | \(m(1-\text{exp}(-\text{exp}\left(\eta \right)\left)\right)\) | \((m\left(1-\mu /m\right)\text{ln}{\left(1-\mu /m\right)}^{-1}\) |
Poisson *Log | \(\text{ln}\left(\mu \right)\) | \(\text{exp}\left(\eta \right)\) | \(1/\mu\) |
Negatif Binomial *NB-C | \(\text{l}\text{n}(\mu /(\mu +1/\alpha \left)\right)\) | \(\text{exp}\left(\eta \right)/\left(\alpha \left(1-\text{exp}\left(\eta \right)\right)\right)\) | \(1/(\mu +\alpha {\mu }^{2})\) |
Negatif Binomial *log | \(\text{ln}\left(\mu \right)\) | \(\text{exp}\left(\eta \right)\) | \(1/\mu\) |
Gamma *Inverse | \(1/\mu\) | \(1/\eta\) | \(-1/{\mu }^{2}\) |
Inverse Gaussian *Inv Quad | \(1/{\mu }^{2}\) | \(1/\sqrt{\eta }\) | \(-1/{\mu }^{3}\) |