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

Model selection in generalised structured additive regression models

In recent years data sets have become increasingly more complex requiring more flexible instruments for their analysis. Such a flexible instrument is regression analysis based on a structured additive predictor which allows an appropriate modelling for different types of information, e.g.~by using smooth functions for spatial information, nonlinear functions for continuous covariates or by using effects for the modelling of cluster--specific heterogeneity. In this thesis, we review many important effects. Moreover, we place an emphasis on interaction terms and introduce a possibility for the simple modelling of a complex interaction between two continuous covariates. \\ Mainly, this thesis is concerned with the topic of variable and smoothing parameter selection within structured additive regression models. For this purpose, we introduce an efficient algorithm that simultaneously selects relevant covariates and the degree of smoothness for their effects. This algorithm is even capable of handling complex situations with many covariates and observations. Thereby, the validation of different models is based on goodness of fit criteria, like e.g.~AIC, BIC or GCV. The methodological development was strongly motivated by case studies from different areas. As examples, we analyse two different data sets regarding determinants of undernutrition in India and of rate making for insurance companies. Furthermore, we examine the performance or our selection approach in several extensive simulation studies

Simultaneous selection of variables and smoothing parameters in structured additive regression models

In recent years, considerable research has been devoted to developing complex regression models that can deal simultaneously with nonlinear covariate effects and time trends, unit- or cluster specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different types. Much less effort, however, has been devoted to model and variable selection. The paper develops a methodology for the simultaneous selection of variables and the degree of smoothness in regression models with a structured additive predictor. These models are quite general, containing additive (mixed) models, geoadditive models and varying coefficient models as special cases. This approach allows one to decide whether a particular covariate enters the model linearly or nonlinearly or is removed from the model. Moreover, it is possible to decide whether a spatial or cluster specific effect should be incorporated into the model to cope with spatial or cluster specific heterogeneity. Particular emphasis is also placed on selecting complex interactions between covariates and effects of different types. A new penalty for two-dimensional smoothing is proposed, that allows for ANOVA-type decompositions into main effects and an interaction effect without explicitly specifying the main effects. The penalty is an additive combination of other penalties. Fast algorithms and software are developed that allow one to even handle situations with many covariate effects and observations. The algorithms are related to backfitting and Markov chain Monte Carlo techniques, which divide the problem in a divide and conquer strategy into smaller pieces. Confidence intervals taking model uncertainty into account are based on the bootstrap in combination with MCMC techniques.

Flexible Estimation of Price Response Functions Using Retail Scanner Data

Kalyanam and Shively [1998. Estimating irregular pricing effects: a stochastic spline regression approach. Journal of Marketing Research 35 (1), 16–29] and van Heerde et al. [2001. Semiparametric analysis to estimate the deal effect curve. Journal of Marketing Research 38 (2), 197–215] have demonstrated the usefulness of nonparametric regression to estimate pricing effects flexibly. The empirical results of these two studies, however, also revealed that nonparametric regression may suffer from too much flexibility leading to nonmonotonic shapes for price effects. In this paper, we show how the problem of nonmonotonicity can be dealt with without losing the power of flexible estimation techniques. We propose a semiparametric approach based on Bayesian P-splines with monotonicity constraints imposed on own- and cross-price effects. In an empirical application, we illustrate that flexible estimation of own- and cross-price effects can improve the predictive validity of a sales response model substantially, even when price response curves were constrained to show a monotonic shape, as suggested by economic theory. We also discuss the consequences from an unconstrained estimation of price effects

Semiparametric Stepwise Regression to Estimate Sales Promotion Effects

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

with contributions by supported by

developed at developed b