Identity link

Topic of Introduction to generalised linear models, part of Generalised linear models

Identity link

Type	Topic
Taught in	Introduction to generalised linear models
Part	Generalised linear models

g(\mu)=\mu, the canonical link for normal responses: the mean is the linear predictor itself. With a normal random component the GLM is the normal linear model.

In Introduction to generalised linear models

From Introduction to generalised linear models

The normal linear model is the GLM with identity link and normal random component: \mu_i={\boldsymbol{X}}_i^\top\boldsymbol{\beta} and \mathrm{Var}(Y_i)=\sigma^2. Logistic regression is the GLM with Bernoulli random component and the logit link Equation (5) in Introduction to generalised linear models. Writing those two out is not a new model. It is the definition, specialised.

Used in

• Taught in Introduction to generalised linear models
• Also used in Linear regression · Standard errors, and models for counts
• All 9 questions on Introduction to generalised linear models

See also

Logit link · Probit link · Complementary log-log link · Log link · Inverse link · Canonical link · Linear predictor · Random component · Generalised linear model · Normal linear model

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