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: $$ E(Y|U,T) = U^ \top \beta + m(T) $$ where β=(β₁,...,β _p )is a finite dimensional parameter and m(●) a smooth function. Here, we assume again a decomposition of the explanatory variables into two vectors, U and T. The vector U denotes a p-variate random vector which typically covers categorical explanatory variables or variables that are known to influence the index in a linear way. The vector T is a q-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 U or T, respectively.