ABSTRACT
A generalized additive model is an extension of a nonparametric linear regression model. Suppose we obtain a sample of n independent observations of k predictor variables x1; : : : ;xk and a response y. A generalized additive regression model is used to connect through a link function g() the mean response m = E(yjx1; : : : ;xk) and an additive function of the predictors of the form s0+ s1(x1)+ + sk(xk) where s0 is the intercept, and s1(); : : : ;sk() are loess or univariate spline smoothers. The equation of the generalized additive model is
g(m) = s0+ s1(x1)+ + sk(xk): In this chapter we focus on two cases: when y is a binary variable and when it is a count variable. With the parametric generalized linear model approach, if y is binary, an ordinary logistic regression model should be fit. If y is a count variable, a Poisson regression model is appropriate. If the linearity of the regression terms may not hold, a nonparametric generalized additive model is a solution.
