7. Generalized Additive Models

Stefan Sperlich and Jirí Zelinka
18 November 2003

Let's assume that we have independent random variables $ T_1$ and $ T_2$ and the response variable $ Y$ having the form

$\displaystyle Y=f_1(T_1)+f_2(T_2)+\varepsilon.
$

The functions $ f_1$, $ f_2$ are unknown and the random error $ \varepsilon $ is independent with $ T_1$ and $ T_2$. This situation can be simulated using XploRe very well:
  n   = 100
  t   = normal(n,2)               ; explanatory variable
  f1  = - sin(2*t[,1])            ; estimated functions
  f2  = t[,2]^2
  eps = normal(n,1) * sqrt(0.75)  ; error
  y   = f1 + f2 +eps              ; response variable


13579 XAGgam01.xpl

The data can come from praxis, too. Our task is to estimate the unknown functions $ f_1$ and $ f_2$.

This chapter deals with such problems and their solutions. It ought to demonstrate and to explain how to use XploRe for nonparametric regression and data analysis in generalized additive models (GAM). It describes all quantlets which belong to the gam quantlib which contains all routines of XploRe provided for estimation and testing in generalized additive models. It also has several links to the gplm quantlib for generalized partial linear models (GPLM) in XploRe thus many quantlets which are used in gam are fully described in Chapter 6 but not mentioned here.