Generalized additive model

A generalized additive model has linear predictor $g({\mu }_i)=\alpha +{\sum }_j{s}_j(x_{ij})$. Centering the smooth functions identifies the intercept. The response family and link function remain part of the model; an unspecified software family must not be inferred from the response name.

A generalized additive mixed model supplements smooth population effects with latent random effects. Given these effects, responses follow a specified response family; integrating them out induces dependence between related observations.