{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T17:15:49Z","timestamp":1781111749774,"version":"3.54.1"},"reference-count":64,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2024,3,1]],"date-time":"2024-03-01T00:00:00Z","timestamp":1709251200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T00:00:00Z","timestamp":1711670400000},"content-version":"vor","delay-in-days":28,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100018933","name":"Technische Universit\u00e4t Clausthal","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100018933","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["OR Spectrum"],"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We combine nonparametric price response modeling and dynamic pricing. In particular, we model sales response for fast-moving consumer goods sold by a physical retailer using a Bayesian semiparametric approach and incorporate the price of the previous period as well as further time-dependent covariates. All nonlinear effects including the one-period lagged price dynamics are modeled via P-splines, and embedding the semiparametric model into a Hierarchical Bayesian framework enables the estimation of nonlinear heterogeneous (i.e., store-specific) immediate and lagged price effects. The nonlinear heterogeneous model specification is used for price optimization and allows the derivation of optimal price paths of brands for individual stores of retailers. In an empirical study, we demonstrate that our proposed model can provide higher expected profits compared to competing benchmark models, while at the same time not seriously suffering from boundary problems for optimized prices and sales quantities. Optimal price policies for brands are determined by a discrete dynamic programming algorithm.<\/jats:p>","DOI":"10.1007\/s00291-024-00756-0","type":"journal-article","created":{"date-parts":[[2024,3,29]],"date-time":"2024-03-29T17:01:35Z","timestamp":1711731695000},"page":"29-72","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Dynamic pricing using flexible heterogeneous sales response models"],"prefix":"10.1007","volume":"46","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0491-1699","authenticated-orcid":false,"given":"Philipp","family":"Aschersleben","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Winfried J.","family":"Steiner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2024,3,29]]},"reference":[{"issue":"3","key":"756_CR1","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1177\/002224379102800308","volume":"28","author":"M Abe","year":"1991","unstructured":"Abe M (1991) A moving ellipsoid method for nonparametric regression and its application to logit diagnostics with scanner data. J Mark Res 28(3):339\u2013346. https:\/\/doi.org\/10.1177\/002224379102800308","journal-title":"J Mark Res"},{"issue":"3","key":"756_CR2","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1287\/mksc.14.3.300","volume":"14","author":"M Abe","year":"1995","unstructured":"Abe M (1995) A nonparametric density estimation method for brand choice using scanner data. Mark Sci 14(3):300\u2013325. https:\/\/doi.org\/10.1287\/mksc.14.3.300","journal-title":"Mark Sci"},{"issue":"4","key":"756_CR3","doi-asserted-by":"publisher","first-page":"635","DOI":"10.1007\/BF02753916","volume":"19","author":"M Abe","year":"2004","unstructured":"Abe M, Boztu\u011f Y, Hildebrandt L (2004) Investigating the competitive assumption of multinomial logit models of brand choice by nonparametric modeling. Comp Stat 19(4):635\u2013657. https:\/\/doi.org\/10.1007\/BF02753916","journal-title":"Comp Stat"},{"issue":"1\u20133","key":"756_CR4","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/0304-4076(93)90061-9","volume":"57","author":"MM Ali","year":"1993","unstructured":"Ali MM, Sharma SC (1993) Robustness to nonnormality of the durbin-watson test for autocorrelation. J Econ 57(1\u20133):117\u2013136. https:\/\/doi.org\/10.1016\/0304-4076(93)90061-9","journal-title":"J Econ"},{"issue":"1","key":"756_CR5","doi-asserted-by":"publisher","first-page":"22","DOI":"10.1016\/j.ijresmar.2007.10.001","volume":"25","author":"RL Andrews","year":"2008","unstructured":"Andrews RL, Currim IS, Leeflang PSH, Lim J (2008) Estimating the SCAN*PRO model of store sales: HB, FM or just OLS? Int J Res Mark 25(1):22\u201333. https:\/\/doi.org\/10.1016\/j.ijresmar.2007.10.001","journal-title":"Int J Res Mark"},{"issue":"4","key":"756_CR6","doi-asserted-by":"publisher","first-page":"591","DOI":"10.1007\/s11573-022-01083-y","volume":"92","author":"P Aschersleben","year":"2022","unstructured":"Aschersleben P, Steiner WJ (2022) A semiparametric approach to estimating reference price effects in sales response models. J Bus Econ 92(4):591\u2013643. https:\/\/doi.org\/10.1007\/s11573-022-01083-y","journal-title":"J Bus Econ"},{"issue":"5","key":"756_CR7","doi-asserted-by":"publisher","first-page":"866","DOI":"10.1509\/jmkr.47.5.866","volume":"47","author":"MB Ataman","year":"2010","unstructured":"Ataman MB, Van Heerde HJ, Mela CF (2010) The long-term effect of marketing strategy on brand sales. J Mark Res 47(5):866\u2013882. https:\/\/doi.org\/10.1509\/jmkr.47.5.866","journal-title":"J Mark Res"},{"issue":"4","key":"756_CR8","doi-asserted-by":"publisher","first-page":"533","DOI":"10.2307\/2297285","volume":"49","author":"A Bhargava","year":"1982","unstructured":"Bhargava A, Franzini L, Narendranathan W (1982) Serial correlation and the fixed effects model. Rev Econ Stud 49(4):533. https:\/\/doi.org\/10.2307\/2297285","journal-title":"Rev Econ Stud"},{"issue":"1","key":"756_CR9","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1007\/s00291-012-0313-4","volume":"36","author":"Y Boztu\u011f","year":"2014","unstructured":"Boztu\u011f Y, Hildebrandt L, Raman K (2014) Detecting price thresholds in choice models using a semi-parametric approach. OR Spectr 36(1):187\u2013207. https:\/\/doi.org\/10.1007\/s00291-012-0313-4","journal-title":"OR Spectr"},{"issue":"1","key":"756_CR10","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1198\/073500107000000223","volume":"26","author":"A Brezger","year":"2008","unstructured":"Brezger A, Steiner WJ (2008) Monotonic regression based on Bayesian P-splines: An application to estimating price response functions from store-level scanner data. J Bus Econ Stat 26(1):90\u2013104. https:\/\/doi.org\/10.1198\/073500107000000223","journal-title":"J Bus Econ Stat"},{"key":"756_CR11","doi-asserted-by":"publisher","unstructured":"Brezger A, Kneib T, Lang S (2005) BayesX: Analyzing Bayesian structured additive regression models. J Stat Softw 14(11):1\u201322. https:\/\/doi.org\/10.18637\/jss.v014.i11, http:\/\/bayesx.org","DOI":"10.18637\/jss.v014.i11"},{"key":"756_CR12","first-page":"374","volume-title":"Activity analysis of production and allocation","author":"GW Brown","year":"1951","unstructured":"Brown GW (1951) Iterative solutions of games by fictitious play. In: Koopmans TC (ed) Activity analysis of production and allocation. Wiley, New York, pp 374\u2013376"},{"issue":"346","key":"756_CR13","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1080\/01621459.1974.10482955","volume":"69","author":"MB Brown","year":"1974","unstructured":"Brown MB, Forsythe AB (1974) Robust tests for the equality of variances. J Am Stat Assoc 69(346):364\u2013367. https:\/\/doi.org\/10.1080\/01621459.1974.10482955","journal-title":"J Am Stat Assoc"},{"issue":"1","key":"756_CR14","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1023\/A:1023534028314","volume":"1","author":"PK Chintagunta","year":"2003","unstructured":"Chintagunta PK, Dub\u00e9 JP, Singh V (2003) Balancing profitability and customer welfare in a supermarket chain. Quant Mark Econ 1(1):111\u2013147. https:\/\/doi.org\/10.1023\/A:1023534028314","journal-title":"Quant Mark Econ"},{"issue":"3","key":"756_CR15","doi-asserted-by":"publisher","first-page":"322","DOI":"10.1177\/002224379703400302","volume":"34","author":"M Christen","year":"1997","unstructured":"Christen M, Gupta S, Porter JC, Staelin R, Wittink DR (1997) Using market-level data to understand promotion effects in a nonlinear model. J Mark Res 34(3):322\u2013334. https:\/\/doi.org\/10.1177\/002224379703400302","journal-title":"J Mark Res"},{"issue":"6","key":"756_CR16","doi-asserted-by":"publisher","first-page":"1115","DOI":"10.1287\/mksc.1110.0666","volume":"30","author":"P Ebbes","year":"2011","unstructured":"Ebbes P, Papies D, van Heerde HJ (2011) The sense and non-sense of holdout sample validation in the presence of endogeneity. Mark Sci 30(6):1115\u20131122. https:\/\/doi.org\/10.1287\/mksc.1110.0666","journal-title":"Mark Sci"},{"issue":"2","key":"756_CR17","doi-asserted-by":"publisher","first-page":"89","DOI":"10.1214\/ss\/1038425655","volume":"11","author":"PHC Eilers","year":"1996","unstructured":"Eilers PHC, Marx BD (1996) Flexible smoothing with $$B$$-splines and penalties. Stat Sci 11(2):89\u2013102. https:\/\/doi.org\/10.1214\/ss\/1038425655","journal-title":"Stat Sci"},{"issue":"5","key":"756_CR18","doi-asserted-by":"publisher","first-page":"721","DOI":"10.1287\/opre.51.5.721.16758","volume":"51","author":"G Fibich","year":"2003","unstructured":"Fibich G, Gavious A, Lowengart O (2003) Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects. Oper Res 51(5):721\u2013734. https:\/\/doi.org\/10.1287\/opre.51.5.721.16758","journal-title":"Oper Res"},{"issue":"1\u20132","key":"756_CR19","doi-asserted-by":"publisher","first-page":"249","DOI":"10.1016\/S0304-4076(98)00063-3","volume":"89","author":"EW Foekens","year":"1999","unstructured":"Foekens EW, Leeflang PSH, Wittink DR (1999) Varying parameter models to accommodate dynamic promotion effects. J Econ 89(1\u20132):249\u2013268. https:\/\/doi.org\/10.1016\/S0304-4076(98)00063-3","journal-title":"J Econ"},{"issue":"3","key":"756_CR20","doi-asserted-by":"publisher","first-page":"443","DOI":"10.1509\/jmkr.43.3.443","volume":"43","author":"D Fok","year":"2006","unstructured":"Fok D, Horv\u00e1th C, Paap R, Franses PH (2006) A hierarchical Bayes error correction model to explain dynamic effects of price changes. J Mark Res 43(3):443\u2013461. https:\/\/doi.org\/10.1509\/jmkr.43.3.443","journal-title":"J Mark Res"},{"issue":"1","key":"756_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0169-2070(98)00053-3","volume":"15","author":"PH Franses","year":"1999","unstructured":"Franses PH, Ghijsels H (1999) Additive outliers, GARCH and forecasting volatility. Int J Forecast 15(1):1\u20139. https:\/\/doi.org\/10.1016\/S0169-2070(98)00053-3","journal-title":"Int J Forecast"},{"issue":"477","key":"756_CR22","doi-asserted-by":"publisher","first-page":"359","DOI":"10.1198\/016214506000001437","volume":"102","author":"T Gneiting","year":"2007","unstructured":"Gneiting T, Raftery AE (2007) Strictly proper scoring rules, prediction, and estimation. J Am Stat Assoc 102(477):359\u2013378. https:\/\/doi.org\/10.1198\/016214506000001437","journal-title":"J Am Stat Assoc"},{"key":"756_CR23","volume-title":"Econometric analysis","author":"WH Greene","year":"2008","unstructured":"Greene WH (2008) Econometric analysis, 6th edn. Pearson Prentice Hall, Upper Saddle River, NJ","edition":"6"},{"issue":"1","key":"756_CR24","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1287\/mksc.14.1.82","volume":"14","author":"EA Greenleaf","year":"1995","unstructured":"Greenleaf EA (1995) The impact of reference price effects on the profitability of price promotions. Mark Sci 14(1):82\u2013104. https:\/\/doi.org\/10.1287\/mksc.14.1.82","journal-title":"Mark Sci"},{"key":"756_CR25","unstructured":"Hanssens DM, Parsons LJ, Schultz RL (2002) Market Response Models: Econometric and Time Series Analysis, vol 12, 2nd Edn. Kluwer Academic Publishers, Boston"},{"key":"756_CR26","doi-asserted-by":"publisher","DOI":"10.1017\/CCOL0521382483","volume-title":"Applied nonparametric regression","author":"W H\u00e4rdle","year":"1990","unstructured":"H\u00e4rdle W (1990) Applied nonparametric regression, vol 19. Cambridge University Press, Cambridge"},{"issue":"5","key":"756_CR27","doi-asserted-by":"publisher","first-page":"470","DOI":"10.1016\/j.jretconser.2012.06.002","volume":"19","author":"H Haupt","year":"2012","unstructured":"Haupt H, Kagerer K (2012) Beyond mean estimates of price and promotional effects in scanner-panel sales-response regression. J Retail Consum Serv 19(5):470\u2013483. https:\/\/doi.org\/10.1016\/j.jretconser.2012.06.002","journal-title":"J Retail Consum Serv"},{"issue":"6","key":"756_CR28","doi-asserted-by":"publisher","first-page":"1007","DOI":"10.1002\/jae.2347","volume":"29","author":"H Haupt","year":"2014","unstructured":"Haupt H, Kagerer K, Steiner WJ (2014) Smooth quantile-based modeling of brand sales, price and promotional effects from retail scanner panels. J Appl Econ 29(6):1007\u20131028. https:\/\/doi.org\/10.1002\/jae.2347","journal-title":"J Appl Econ"},{"issue":"1","key":"756_CR29","doi-asserted-by":"publisher","first-page":"127","DOI":"10.1287\/mksc.1120.0748","volume":"32","author":"C Horv\u00e1th","year":"2013","unstructured":"Horv\u00e1th C, Fok D (2013) Moderating factors of immediate, gross, and net cross-brand effects of price promotions. Mark Sci 32(1):127\u2013152. https:\/\/doi.org\/10.1287\/mksc.1120.0748","journal-title":"Mark Sci"},{"issue":"8","key":"756_CR30","first-page":"845","volume":"67","author":"H Hruschka","year":"1997","unstructured":"Hruschka H (1997) Sch\u00e4tzung und normative Analyse ausgew\u00e4hlter Preis-Absatz-Funktionen. Z Betriebswirtsch 67(8):845\u2013864","journal-title":"Z Betriebswirtsch"},{"key":"756_CR31","doi-asserted-by":"publisher","unstructured":"Hruschka H (2000) Specification, estimation, and empirical corroboration of Gutenberg\u2019s kinked demand curve. In: Albach H, Brockhoff KKL, Eymann E, et\u00a0al (Eds) Theory of the Firm. Springer, Berlin and Heidelberg, p 153\u2013168, https:\/\/doi.org\/10.1007\/978-3-642-59661-2_8","DOI":"10.1007\/978-3-642-59661-2_8"},{"issue":"2","key":"756_CR32","doi-asserted-by":"publisher","first-page":"1009","DOI":"10.1016\/j.ejor.2005.05.003","volume":"174","author":"H Hruschka","year":"2006","unstructured":"Hruschka H (2006a) Relevance of functional flexibility for heterogeneous sales response models: A comparison of parametric and semi-nonparametric models. Eur J Oper Res 174(2):1009\u20131020. https:\/\/doi.org\/10.1016\/j.ejor.2005.05.003","journal-title":"Eur J Oper Res"},{"issue":"12","key":"756_CR33","doi-asserted-by":"publisher","first-page":"94","DOI":"10.15358\/0344-1369-2006-JRM-2-94","volume":"28","author":"H Hruschka","year":"2006","unstructured":"Hruschka H (2006b) Statistical and managerial relevance of aggregation level and heterogeneity in sales response models. Mark ZFP \u2013 J Res Manag 28(12):94\u2013102. https:\/\/doi.org\/10.15358\/0344-1369-2006-JRM-2-94","journal-title":"Mark ZFP \u2013 J Res Manag"},{"issue":"4","key":"756_CR34","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1007\/s00291-006-0075-y","volume":"29","author":"H Hruschka","year":"2007","unstructured":"Hruschka H (2007) Clusterwise pricing in stores of a retail chain. OR Spectr 29(4):579\u2013595. https:\/\/doi.org\/10.1007\/s00291-006-0075-y","journal-title":"OR Spectr"},{"key":"756_CR35","doi-asserted-by":"publisher","unstructured":"Hruschka H (2017) Functional flexibility, latent heterogeneity and endogeneity in aggregate market response models. Mark ZFP \u2013 J Res Manag 39(3):17\u201331. https:\/\/doi.org\/10.15358\/0344-1369-2017-3-17","DOI":"10.15358\/0344-1369-2017-3-17"},{"key":"756_CR36","doi-asserted-by":"publisher","DOI":"10.5445\/IR\/1000063629","author":"A Jordan","year":"2016","unstructured":"Jordan A (2016) Facets of forecast evaluation. PhD dissertation, Karlsruher Institut f\u00fcr Technologie, Karlsruhe. https:\/\/doi.org\/10.5445\/IR\/1000063629","journal-title":"PhD dissertation, Karlsruher Institut f\u00fcr Technologie, Karlsruhe"},{"key":"756_CR37","doi-asserted-by":"publisher","DOI":"10.18637\/jss.v090.i12","author":"A Jordan","year":"2019","unstructured":"Jordan A, Kr\u00fcger F, Lerch S (2019) Evaluating probabilistic forecasts with scoringrules. J Stat Softw. https:\/\/doi.org\/10.18637\/jss.v090.i12","journal-title":"J Stat Softw"},{"issue":"1","key":"756_CR38","doi-asserted-by":"publisher","first-page":"16","DOI":"10.1177\/002224379803500104","volume":"35","author":"K Kalyanam","year":"1998","unstructured":"Kalyanam K, Shively TS (1998) Estimating irregular pricing effects: A stochastic spline regression approach. J Mark Res 35(1):16\u201329. https:\/\/doi.org\/10.1177\/002224379803500104","journal-title":"J Mark Res"},{"issue":"3","key":"756_CR39","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1287\/mksc.18.3.317","volume":"18","author":"PK Kopalle","year":"1999","unstructured":"Kopalle PK, Mela CF, Marsh L (1999) The dynamic effect of discounting on sales: empirical analysis and normative pricing implications. Mark Sci 18(3):317\u2013332. https:\/\/doi.org\/10.1287\/mksc.18.3.317","journal-title":"Mark Sci"},{"key":"756_CR40","unstructured":"Krishnamurthi L, Raj SP, Selvam R (1990) Statistical and managerial issues in cross-sectional aggregation, working paper, Northwestern University"},{"issue":"2","key":"756_CR41","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1111\/insr.12405","volume":"89","author":"F Kr\u00fcger","year":"2021","unstructured":"Kr\u00fcger F, Lerch S, Thorarinsdottir T, Gneiting T (2021) Predictive inference based on Markov chain Monte Carlo output. Int Stat Rev 89(2):274\u2013301. https:\/\/doi.org\/10.1111\/insr.12405","journal-title":"Int Stat Rev"},{"issue":"1","key":"756_CR42","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1198\/1061860043010","volume":"13","author":"S Lang","year":"2004","unstructured":"Lang S, Brezger A (2004) Bayesian P-splines. J Comput Graph Stat 13(1):183\u2013212. https:\/\/doi.org\/10.1198\/1061860043010","journal-title":"J Comput Graph Stat"},{"issue":"1","key":"756_CR43","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1016\/j.ejor.2015.02.047","volume":"246","author":"S Lang","year":"2015","unstructured":"Lang S, Steiner WJ, Weber A, Wechselberger P (2015) Accommodating heterogeneity and nonlinearity in price effects for predicting brand sales and profits. Eur J Oper Res 246(1):232\u2013241. https:\/\/doi.org\/10.1016\/j.ejor.2015.02.047","journal-title":"Eur J Oper Res"},{"key":"756_CR44","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-4050-2","volume-title":"Building models for marketing decisions","author":"PSH Leeflang","year":"2000","unstructured":"Leeflang PSH, Wittink DR, Wedel M, Naert PA (2000) Building models for marketing decisions, vol 9. Springer, Boston, MA"},{"key":"756_CR45","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1016\/S0167-2231(76)80003-6","volume":"1","author":"RE Lucas","year":"1976","unstructured":"Lucas RE (1976) Econometric policy evaluation: a critique. Carnegie-Rochester Conf Ser Public Policy 1:19\u201346. https:\/\/doi.org\/10.1016\/S0167-2231(76)80003-6","journal-title":"Carnegie-Rochester Conf Ser Public Policy"},{"issue":"10","key":"756_CR46","doi-asserted-by":"publisher","first-page":"1087","DOI":"10.1287\/mnsc.22.10.1087","volume":"22","author":"JE Matheson","year":"1976","unstructured":"Matheson JE, Winkler RL (1976) Scoring rules for continuous probability distributions. Manag Sci 22(10):1087\u20131096. https:\/\/doi.org\/10.1287\/mnsc.22.10.1087","journal-title":"Manag Sci"},{"key":"756_CR47","volume-title":"Applied computational economics and finance","author":"MJ Miranda","year":"2002","unstructured":"Miranda MJ, Fackler PL (2002) Applied computational economics and finance. MIT Press, Cambridge, MA"},{"issue":"4","key":"756_CR48","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1287\/mksc.16.4.315","volume":"16","author":"AL Montgomery","year":"1997","unstructured":"Montgomery AL (1997) Creating micro-marketing pricing strategies using supermarket scanner data. Mark Sci 16(4):315\u2013337. https:\/\/doi.org\/10.1287\/mksc.16.4.315","journal-title":"Mark Sci"},{"issue":"1","key":"756_CR49","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1287\/mksc.20.1.1.10197","volume":"20","author":"VR Nijs","year":"2001","unstructured":"Nijs VR, Dekimpe MG, Steenkamps JBEM, Hanssens DM (2001) The category-demand effects of price promotions. Mark Sci 20(1):1\u201322. https:\/\/doi.org\/10.1287\/mksc.20.1.1.10197","journal-title":"Mark Sci"},{"issue":"4","key":"756_CR50","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1287\/mksc.1120.0718","volume":"31","author":"S Park","year":"2012","unstructured":"Park S, Gupta S (2012) Handling endogenous regressors by joint estimation using copulas. Mark Sci 31(4):567\u2013586. https:\/\/doi.org\/10.1287\/mksc.1120.0718","journal-title":"Mark Sci"},{"key":"756_CR51","unstructured":"R Core Team (2022) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria, https:\/\/www.R-project.org\/"},{"key":"756_CR52","doi-asserted-by":"publisher","DOI":"10.1515\/9781400850303","volume-title":"Bayesian non- and semi-parametric methods and applications","author":"PE Rossi","year":"2014","unstructured":"Rossi PE (2014) Bayesian non- and semi-parametric methods and applications. Princeton University Press, Princeton"},{"issue":"3","key":"756_CR53","doi-asserted-by":"publisher","first-page":"274","DOI":"10.1287\/mksc.18.3.274","volume":"18","author":"JM Silva-Risso","year":"1999","unstructured":"Silva-Risso JM, Bucklin RE, Morrison DG (1999) A decision support system for planning manufacturers\u2019 sales promotion calendars. Mark Sci 18(3):274\u2013300. https:\/\/doi.org\/10.1287\/mksc.18.3.274","journal-title":"Mark Sci"},{"issue":"6","key":"756_CR54","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1016\/j.jretconser.2007.02.008","volume":"14","author":"WJ Steiner","year":"2007","unstructured":"Steiner WJ, Brezger A, Belitz C (2007) Flexible estimation of price response functions using retail scanner data. J Retail Consum Serv 14(6):383\u2013393. https:\/\/doi.org\/10.1016\/j.jretconser.2007.02.008","journal-title":"J Retail Consum Serv"},{"key":"756_CR55","volume-title":"Models for sales promotion effects based on store-level scanner data","author":"HJ Van Heerde","year":"1999","unstructured":"Van Heerde HJ (1999) Models for sales promotion effects based on store-level scanner data. Labyrint Publication, Capelle a\/d IJssel"},{"issue":"3","key":"756_CR56","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1509\/jmkr.37.3.383.18782","volume":"37","author":"HJ Van Heerde","year":"2000","unstructured":"Van Heerde HJ, Leeflang PSH, Wittink DR (2000) The estimation of pre- and postpromotion dips with store-level scanner data. J Mark Res 37(3):383\u2013395. https:\/\/doi.org\/10.1509\/jmkr.37.3.383.18782","journal-title":"J Mark Res"},{"issue":"2","key":"756_CR57","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1509\/jmkr.38.2.197.18842","volume":"38","author":"HJ Van Heerde","year":"2001","unstructured":"Van Heerde HJ, Leeflang PSH, Wittink DR (2001) Semiparametric analysis to estimate the deal effect curve. J Mark Res 38(2):197\u2013215. https:\/\/doi.org\/10.1509\/jmkr.38.2.197.18842","journal-title":"J Mark Res"},{"issue":"3","key":"756_CR58","doi-asserted-by":"publisher","first-page":"198","DOI":"10.1007\/BF03396653","volume":"54","author":"HJ Van Heerde","year":"2002","unstructured":"Van Heerde HJ, Leeflang PSH, Wittink DR (2002) How promotions work: SCAN*PRO-based evolutionary model building. Schmalenbach Bus Rev 54(3):198\u2013220. https:\/\/doi.org\/10.1007\/BF03396653","journal-title":"Schmalenbach Bus Rev"},{"issue":"3","key":"756_CR59","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1287\/mksc.1040.0061","volume":"23","author":"HJ Van Heerde","year":"2004","unstructured":"Van Heerde HJ, Leeflang PSH, Wittink DR (2004) Decomposing the sales promotion bump with store data. Mark Sci 23(3):317\u2013334. https:\/\/doi.org\/10.1287\/mksc.1040.0061","journal-title":"Mark Sci"},{"issue":"12","key":"756_CR60","doi-asserted-by":"publisher","first-page":"1337","DOI":"10.1007\/s11573-012-0638-0","volume":"82","author":"A Weber","year":"2012","unstructured":"Weber A, Steiner WJ (2012) Zur Ber\u00fccksichtigung von Heterogenit\u00e4t versus funktionaler Flexibilit\u00e4t in Absatzreaktionsmodellen: Eine empirische Studie auf Basis von Handelsdaten. Z Betriebswirtsch 82(12):1337\u20131365. https:\/\/doi.org\/10.1007\/s11573-012-0638-0","journal-title":"Z Betriebswirtsch"},{"issue":"3","key":"756_CR61","doi-asserted-by":"publisher","first-page":"843","DOI":"10.1016\/j.ejor.2020.07.055","volume":"294","author":"A Weber","year":"2021","unstructured":"Weber A, Steiner WJ (2021) Modeling price response from retail sales: An empirical comparison of models with different representations of heterogeneity. Eur J Oper Res 294(3):843\u2013859. https:\/\/doi.org\/10.1016\/j.ejor.2020.07.055","journal-title":"Eur J Oper Res"},{"issue":"2","key":"756_CR62","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1007\/s00291-016-0459-6","volume":"39","author":"A Weber","year":"2017","unstructured":"Weber A, Steiner WJ, Lang S (2017) A comparison of semiparametric and heterogeneous store sales models for optimal category pricing. OR Spectr 39(2):403\u2013445. https:\/\/doi.org\/10.1007\/s00291-016-0459-6","journal-title":"OR Spectr"},{"issue":"4","key":"756_CR63","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1509\/jmkr.41.4.448.47017","volume":"41","author":"M Wedel","year":"2004","unstructured":"Wedel M, Zhang J (2004) Analyzing brand competition across subcategories. J Mark Res 41(4):448\u2013456. https:\/\/doi.org\/10.1509\/jmkr.41.4.448.47017","journal-title":"J Mark Res"},{"issue":"43","key":"756_CR64","doi-asserted-by":"publisher","first-page":"1686","DOI":"10.21105\/joss.01686","volume":"4","author":"H Wickham","year":"2019","unstructured":"Wickham H, Averick M, Bryan J et al (2019) Welcome to the tidyverse. J Open Sourc Softw 4(43):1686. https:\/\/doi.org\/10.21105\/joss.01686","journal-title":"J Open Sourc Softw"}],"container-title":["OR Spectrum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-024-00756-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00291-024-00756-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00291-024-00756-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,5]],"date-time":"2024-04-05T16:04:46Z","timestamp":1712333086000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00291-024-00756-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,3]]},"references-count":64,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2024,3]]}},"alternative-id":["756"],"URL":"https:\/\/doi.org\/10.1007\/s00291-024-00756-0","relation":{},"ISSN":["0171-6468","1436-6304"],"issn-type":[{"value":"0171-6468","type":"print"},{"value":"1436-6304","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,3]]},"assertion":[{"value":"31 March 2022","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 February 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"29 March 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}