Spline Regression in the Presence of Categorical Predictors

We consider the problem of estimating a relationship nonparametrically using regression splines when there exist both continuous and categorical predictors. We combine the global properties of regression splines with the local properties of categorical kernel functions to handle the presence of categorical predictors rather than resorting to sample splitting as is typically done to accommodate their presence. The resulting estimator possesses substantially better nite-sample performance than either its frequency-based peer or cross-validated local linear kernel regression or even additive regression splines (when additivity does not hold). Theoretical underpinnings are provided and Monte Carlo simulations are undertaken to assess nite-sample behavior, and two illustrative applications are provided. An implementation in R (R Core Team (2012)) is available; see the R package 'crs' for details (Racine & Nie (2012)).