GeneralizedLinearModels (GLMs)

In these models, the response variable y is assumed to follow an exponential family distribution with mean μi, which is assumed to be some (often nonlinear) function of x^tβ It is considered to be linear, because the covariates affect the distribution of yionly through the linear combination x^tβ

Random Component – set by setFamily, refers to the probability distribution of the response variable (Y); e.g. normal distribution for Y in the linear regression, or binomial distribution for Y in the binary logistic regression. Also called a noise model or error model. How is random error added to the prediction that comes out of the link function?

Systematic Component - specifies the explanatory variables (X1, X2, ... Xk) in the model, more specifically their linear combination in creating the so called linear predictor;

Link Function, η or g(μ) - set by setLink The link function provides the relationship between the linear predictor and the mean of the distribution function. specifies the link between random and systematic components. It says how the expected value of the response relates to the linear predictor of explanatory variables; e.g., η = g(E(Yi)) = E(Yi) for linear regression, or η = logit(π) for logistic regression.

iteratively reweighted least squares method for maximum likelihood estimation of the model parameters Notes