4 - Exploiting the Linear Model Framework

Summary

This chapter explores ways to set up a model matrix so that linear combinations of the columns can fit curves and multidimensional surfaces. These extend to methods, within a generalized additive model framework, that use a penalization approach to constrain over-fitting. A further extension is to fitting quantiles of the data. The methodologies are important both for direct use for modeling data, and for checking for pattern in residuals from models that are in a more classical parametric style. The methodology is extended, in later chapters, to include smoothing terms in generalized linear models and models that allow for time series errors.