6. Generalized Partial Linear Models

Marlene Müller
18 November 2003

A generalized linear model (GLM) is a regression model of the form

$\displaystyle E (Y\vert X) = G(X^T\beta ),$

where $ Y$ is the dependent variable $ Y$, $ X$ is a vector of explanatory variables, $ \beta$ an unknown parameter vector and $ G(\bullet)$ a known link function. The generalized partial linear model (GPLM) extends the GLM by a nonparametric component:

$\displaystyle E(Y\vert X,T) = G\{X^T\beta + m(T)\}.$

In the following we describe how to use the XploRe gplm quantlib for estimating generalized partial linear models. The gplm quantlib is highly related to the glm quantlib for GLM in XploRe . Names of routines and the functionality in both quantlibs correspond to each other. It is recommended to start reading with the GLM tutorial (Härdle, Klinke, and Müller; 2000, Chapter 7). Parts of the features which are also available in GLM are not explained in detail here.