Generalized Additive Models; Some Applications

Generalized additive models have the the form η(x)=α+Σfj(Xj), where η might be the regression function in a multiple regression, or the logistic transformation of the posterior probability p(y=l/ x) in logistic regression. In fact, these models generalize the whole family of GLIM models η(x)=β’x where η(x)=g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions, which uses a scatterplot smoother as a building block. The models are demonstrated in a non-parametric logistic regression. A variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions. The procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis.