Winfried J. Steiner

Monotonic Regression Based on Bayesian P-Splines: An Application to Estimating Price Response Functions from Store-Level Scanner Data

In many practical situations, it is desirable to restrict the flexibility of nonparametric estimation to accommodate a presumed monotonic relationship between a covariate and the response variable. We follow a Bayesian approach using penalized B-splines and incorporate the assumption of monotonicity in a natural way by an appropriate specification of the respective prior distributions. We illustrate the methodology in an empirical application modeling demand for brands of orange juice and show that imposing monotonicity constraints for own- and cross-item price effects improves the predictive validity of the estimated sales response functions considerably.

Genetic Algorithms for product design: how well do they really work?

Recently, Balakrishnan and Jacob (1996) have proposed the use of Genetic Algorithms (GA) to solve the problem of identifying an optimal single new product using conjoint data. Here we extend and evaluate the GA approach with regard to the more general problem of product line design. We consider profit contribution as a firms economic criterion to evaluate product design decisions and illustrate how the genetic operators work to find the product line with maximum profit contribution. In a Monte Carlo simulation, we assess the performance of the GA methodology in comparison to Green and Kriegers (1985) greedy heuristic.

A Stackelberg-Nash model for new product design

Existing conjoint approaches to optimal new product design have focused on the Nash equilibrium concept to model competitive reactions. Whereas these approaches have treated all competing firms equally as Nash players, one firm may have an advantage over its rivals, e.g., more pre-experience on competitors’ behavior and/or a first-mover advantage. This paper proposes a Stackelberg-Nash (leader-followers) model which can accomodate such information for decision making. The optimal product design problem is formulated from the perspective of a profit-maximizing new entrant (the leader) who wants to launch a brand onto an existing product market and acts with foresight by anticipating price-design reactions of the incumbent firms (the Nash followers). In the absence of closed-form solutions, we use a sequential iterative procedure to compute a Stackelberg-Nash equilibrium and to establish its uniqueness. The new conjoint model is illustrated under several competitive scenarios and price, design and profit implications are compared to a simple Nash equilibrium model. We find that a Stackelberg leader strategy may not only yield a much higher profit for the new entrant than a Nash strategy, but may also lead to strong profit asymmetries between competitors with still higher profits for the incumbent firms. In other words, the incumbent firms may also benefit strongly from a new entrant choosing a Stackelberg leader strategy.

Accommodating heterogeneity and nonlinearity in price effects for predicting brand sales and profits

We propose a hierarchical Bayesian semiparametric approach to account simultaneously for heterogeneity and functional flexibility in store sales models. To estimate own- and cross-price response flexibly, a Bayesian version of P-splines is used. Heterogeneity across stores is accommodated by embedding the semiparametric model into a hierarchical Bayesian framework that yields store-specific own- and cross-price response curves. More specifically, we propose multiplicative store-specific random effects that scale the nonlinear price curves while their overall shape is preserved. Estimation is fully Bayesian and based on novel MCMC techniques. In an empirical study, we demonstrate a higher predictive performance of our new flexible heterogeneous model over competing models that capture heterogeneity or functional flexibility only (or neither of them) for nearly all brands analyzed. In particular, allowing for heterogeneity in addition to functional flexibility can improve the predictive performance of a store sales model considerably, while incorporating heterogeneity alone only moderately improved or even decreased predictive validity. Taking into account model uncertainty, we show that the proposed model leads to higher expected profits as well as to materially different pricing recommendations.

Produktliniengestaltung mit Genetischen Algorithmen

SummaryDesigning and pricing single products or product lines is one of the most important problem areas of a firm. In this contribution, a new conjoint-based optimal product line design model with special focus on profit maximizing firms is presented. The model allows the inclusion of consumers’ preferences, counterpart products of competitors as well as variable and fixed costs. Moreover, flexible probabilistic choice modeling is supported using the conditional multinomial logit model. A genetic algorithm is proposed for solving the product line design problem and, as a result of performance evaluation, is proved to be a promising solution technique. In particular, the performance of the genetic algorithm is compared with Green and Krieger’s well-known greedy heuristic which has received much application to realworld product line problems.

Conjointanalyse-basierte Produkt(linien)gestaltung unter Berücksichtigung von Konkurrenzreaktionen Conjoint-based product (line) design considering competitive reactions

Zusammenfassung. Ausgangspunkt unserer Untersuchungen zur Conjointanalyse-basierten wettbewerbsorientierten Produktgestaltung bilden segmentspezifische konditionale MNL-Modelle. Bisher auf diesem Gebiet entwickelte Ansätze, die sich mit der Bestimmung von Marktgleichgewichten befassen, beschränken sich ausschließlich auf den Single-Produkt-Fall (z.B. Choi u. DeSarbo, 1993; Green u. Krieger, 1997). Unser Beitrag setzt sich ebenfalls mit dem Single-Produkt-Fall (d.h. ein Produkt je Anbieter) auseinander, behandelt darüber hinaus erstmals aber auch den Wettbewerb mit Produktlinien. Gegenstand der Untersuchungen sind insbesondere die Existenz und Eindeutigkeit simultaner Positions-Preis- Gleichgewichte, die Existenz ineffizienter Marktgleichgewichte sowie der Differenzierungsgrad zwischen Konkurrenzprodukten.Abstract. Our analysis starts from segment-specific conjoint models of the conditional MNL type. Hitherto contributions deriving competitive equilibria that are based on conjoint models are limited to the single product case (e.g., Choi and DeSarbo, 1993; Green and Krieger, 1997). Here not only the single product problem (i.e., one product per firm), but also product line competition is dealt with. Problems studied comprise existence and uniqueness of simultaneous position-price-equilibria, existence of inefficient equilibria and degree of differentiation between products of different firms.

A comparison of semiparametric and heterogeneous store sales models for optimal category pricing

Category management requires sales response models helping to simultaneously estimate marketing mix effects for all brands of a product category. We, therefore, develop a general heterogeneity seemingly unrelated regression (SUR) model accommodating correlations between sales across brands. This model contains a latent class SUR model, the well-known hierarchical Bayesian SUR model and the homogeneous SUR model as special cases. We further propose a hierarchical Bayesian semiparametric SUR model based on Bayesian P-splines which comprises a homogeneous semiparametric SUR model as nested version. The results of an empirical application with store-level scanner data indicate that the flexible SUR approaches of modeling price response clearly outperform the various parametric (homogeneous and heterogeneous) SUR approaches with respect to not only predictive validity but also total expected category profits. In particular, functional flexibility turns out to be the primary driver for improving the predictive performance of a store sales model as heterogeneity pays off only once functional flexibility has been accounted for. Furthermore, since both flexible SUR models perform nearly equally well with respect to expected category profits, a uniform pricing strategy which is much less complex to implement than micromarketing can be recommended for our data.

Flexible estimation of time-varying effects for frequently purchased retail goods: a modeling approach based on household panel data

In most previous applications of brand choice models, possible time-varying effects in consumer behavior are ignored by merely imposing constant parameters. However, it is very likely that trends or short-term variations in consumers’ intrinsic brand utilities or sensitivities to marketing instruments occur. For example, preferences for specific brands or price elasticities in product categories such as coffee or chocolate may vary in the run-up to festive occasions like Easter or Christmas. In this paper, we employ flexible multinomial logit models for estimating time-varying effects in brand choice behavior. Time-varying brand intercepts and time-varying effects of covariates are modeled using penalized splines, a flexible, yet parsimonious, nonparametric smoothing technique. The estimation is data driven; the flexible functions, as well as the corresponding degrees of smoothness, are determined simultaneously in a unified approach. Our model further allows for alternative-specific time-varying effects of covariates and can mimic state-space approaches with random walk parameter dynamics. In an empirical application for ground coffee, we compare the performance of the proposed approach to a number of benchmark models regarding in-sample fit, information criteria, and in particular out-of-sample fit. Interestingly, the most complex P-spline model with time-varying brand intercepts and brand-specific time-varying covariate effects outperforms all other specifications both in- and out-of-sample. We further present results from a sensitivity analysis on how the number of knots and other P-spline settings affect the model performance, and we provide guidelines for the model building process about the many options for model specification using P-splines. Finally, the resulting parameter paths provide valuable insights for marketing managers.

The benefits of incorporating utility dependencies in finite mixture probit models

We propose an application of a new finite mixture multinomial conditional probit (FM-MNCP) model that accommodates preference heterogeneity and explicitly accounts for utility dependencies between choice alternatives considering both local and background contrast effects. The latter is accomplished by using a one-factor structure for segment-specific covariance matrices allowing for nonzero off-diagonal covariance elements. We compare the model to a finite mixture multinomial independent probit (FM-MNIP) model that as well accommodates heterogeneity but assumes independence. That way, we address the potential benefits of a model that additionally accounts for dependencies over a model that accommodates heterogeneity only. Our model comparison is based on empirical data for smoothies and is assessed in terms of fit, holdout validation, and market share predictions. One of the main findings of our empirical study is that allowing for utility dependencies may counterbalance the effects of considering heterogeneity, and vice versa. Additional findings from a simulation study indicate that the FM-MNCP model outperforms the FM-MNIP model with respect to parameter recovery.

Spieltheoretische Ansätze in der Conjointanalyse

Neuprodukt- und Preisgestaltung zahlen neben der Marktsegmentierung zu den wesentlichen Einsatzgebieten der Conjointanalyse (Cattin/Wittink 1982; Wittink/Cattin 1989; Wittink et al. 1994; Baier 1999). Bei Fragen der Neuproduktgestaltung hat sich die Conjointanalyse mittlerweile als dominierender methodischer Ansatz, was die Erfassung von Kauferpraferenzen fur Produkteigenschaften einerseits und die darauf basierende Ermittlung viel versprechender Neuproduktprofile andererseits betrifft, etabliert. Unter einem Produktprofil bzw. Produktdesign wird hierbei eine bestimmte Kombination von (i. d. R. diskreten) Auspragungen kaufrelevanter Produkteigenschaften verstanden. Dabei kann auch der Preis als Produkteigenschaft betrachtet und dem Produktdesign zugerechnet werden. Im Zusammenhang mit spieltheoretischen Ansatzen zur Neuproduktgestaltung ist aber auch die Unterscheidung zwischen Produktpreis und Produktposition gelaufig; letztere bezieht sich dann auf ein Produktdesign bestehend ausschlieslich aus nichtpreislichen Produkteigenschaften in der jeweils vorhandenen Auspragung.