Semiparametric Stepwise Regression to Estimate Sales Promotion Effects

  • Winfried J. Steiner
  • Christiane Belitz
  • Stefan Lang
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)


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.


Product Category Semiparametric Model Sales Promotion Price Promotion Start Model 
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  1. BLATTBERG, R.C. and GEORGE, E.I. (1991): Shrinkage Estimation of Price and Promotional Elasticities. Journal of the American Statistical Association, 86(414), 304–315.Google Scholar
  2. DE BOOR, C. (1978): A Practical Guide to Splines. Springer, New York.Google Scholar
  3. EILERS, P.H.C. and MARX, B.D. (1996): Flexible smoothing using B-splines and penalized likelihood (with comments and rejoinder). Statistical Science, 11(2), 89–121.CrossRefMathSciNetGoogle Scholar
  4. FOEKENS, E.W. (1995): Scanner Data Based Marketing Modelling: Empirical Applications. Labyrinth Publications, The Netherlands.Google Scholar
  5. HANSSENS, D.M., PARSONS L.J. and SCHULTZ, R.L. (2001): Market Response Models: Econometric and Time Series Analysis. Chapman & Hall, London.Google Scholar
  6. HASTIE, T. and TIBSHIRANI, R. (1990): Generalized Additive Models. Chapman & Hall, London.Google Scholar
  7. HRUSCHKA, H. (2004): Relevance of Functional Flexibility for Heterogeneous Sales Response Models. A Comparison of Parametric and Seminonparametric Models. Discussion Paper 394, Faculty of Economics, University of Regensburg.Google Scholar
  8. KALYANAM, K., SHIVELY, T.S. (1998): Estimating Irregular Pricing Effects: A Stochastic Spline Regression Approach. Journal of Marketing Research, 35(1), 16–29.Google Scholar
  9. LANG, S. and BREZGER, A. (2004): Bayesian P-splines. Journal of Computational and Graphical Statistics, 13, 183–212.CrossRefMathSciNetGoogle Scholar
  10. MONTGOMERY, A.L. (1997): Creating Micro-Marketing Pricing Strategies Using Supermarket Scanner Data. Marketing Science, 16(4), 315–337.Google Scholar
  11. VAN HEERDE, H.J., LEEFLANG, P.S.H. and WITTINK, D.R. (2001): Semiparametric Analysis to Estimate the Deal Effect Curve. Journal of Marketing Research, 38(2), 197–215.Google Scholar
  12. VAN HEERDE, H.J., LEEFLANG, P.S.H. and WITTINK, D.R. (2002): How Promotions Work: SCAN*PRO-Based Evolutionary Model Building. Schmalenbach Business Review, 54(3), 198–220.Google Scholar

Copyright information

© Springer Berlin · Heidelberg 2006

Authors and Affiliations

  • Winfried J. Steiner
    • 1
  • Christiane Belitz
    • 2
  • Stefan Lang
    • 3
  1. 1.Department of MarketingUniversity of RegensburgRegensburgGermany
  2. 2.Department of StatisticsUniversity of MunichMunichGermany
  3. 3.Institute of Empirical Economic ResearchUniversity of LeipzigLeipzigGermany

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