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Statistics for Applications Chapter 10: Generalized Linear Models (GLMs). 1/52. Linear model A Linear model assumes Y |X N ( (X), 2 I), And IE(Y |X) = (X) = X , 2/52. Components of a Linear model The two components (that we are going to relax) are 1. Random component: the response variable Y |X is continuous and normally distributed with mean = (X) = IE(Y |X). 2. Link: between the random and covariates X = (X (1) , X (2) , , X (p) ) : (X) = X . 3/52. Generalization A Generalized Linear model (GLM) generalizes normal Linear regression Models in the following directions. 1. Random component: Y some exponential family distribution 2.

A generalized linear model (GLM) generalizes normal linear regression models in the following directions. Random component: ∼ some exponential family distribution. Link: between the random and covariates: where. g μ(X) = X⊤β. g called link function and μ …

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