# 7. Generalized Partial Linear Models

As indicated in the overview in Chapter 5, a partial linear model (PLM) consists of two additive components, a linear and a nonparametric part:

where is a finite dimensional parameter and a smooth function. Here, we assume again a decomposition of the explanatory variables into two vectors, and . The vector denotes a -variate random vector which typically covers categorical explanatory variables or variables that are known to influence the index in a linear way. The vector is a -variate random vector of continuous explanatory variables which is to be modeled in a nonparametric way. Economic theory or intuition should guide you as to which regressors should be included in or , respectively.

Obviously, there is a straightforward generalization of this model to the case with a known link function . We denote this semiparametric extension of the GLM

 (7.1)

as generalized partial linear model (GPLM).