Semiparametric Stepwise Regression to Estimate Sales Promotion Effects

Kalyanam and Shively (1998) and van Heerde et al. (2001) have
proposed semiparametric models to estimate the influence of price
promotions on brand sales, and both obtained superior performance
for their models compared to strictly parametric modeling.
Following these researchers, we suggest another semiparametric
framework which is based on penalized B-splines to analyze sales
promotion effects flexibly. Unlike these researchers, we introduce
a stepwise procedure with simultaneous smoothing parameter choice
for variable selection. Applying this stepwise routine enables us
to deal with product categories with many competitive items without
imposing restrictions on the competitive market structure in
advance. We illustrate the new methodology in an empirical
application using weekly store-level scanner data.