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Investigating the competitive assumption of Multinomial Logit models of brand choice by nonparametric modeling
Abstract
Summary The Multinomial Logit (MNL) model is still the only viable option to study nonlinear responsiveness of utility to covariates
nonparametrically. This research investigates whether MNL structure of inter-brand competition is a reasonable assumption,
so that when the utility function is estimated nonparametrically, the IIA assumption does not bias the result. For this purpose,
the authors compare the performance of two comparable nonparametric choice models that differ in one aspect: one assumes MNL
competitive structure and the other infers the pattern of brands» competition nonparametrically from data.
... It is has been well-known for quite some time that incorrect assumptions regarding household-level heterogeneity can seriously bias estimates of the impact of marketing mix elements upon brand choice (Gonul and Srinivasan 1993). Since then, numerous papers have successfully applied the Guadagni-Little loyalty measure { for example, Bell and Lattin (2000) to study loss aversion and reference pricing, Abe et al. (2003) in competitive pricing, Seetharaman (2003) for state dependence { and it has been found not only to perform well, but to be relatively robust in terms of parameter bias (Abram et al. 2000). Because the measure is so easily applied, it will certainly continue to nd wide use, and so a deeper understanding of its statistical properties is called for. ...
... Note that this assumption does not imply that P j A jkt is independent of A jkt , nor does the reverse implication hold. 1 This assumption has an important application in the problem at hand; because, ikt and P j A jkt are uncorrelated, we can write: ...
Fred Feinberg is Michael R. and Mary Kay Hallman Fellow and Associate Professor of Marketing at the University of Michigan Business School. Gary J. Russell is Henry B. Tippie Research Fellow and Professor of Marketing at the Henry B. Tippie College of Business, University of Iowa. The names of the authors are listed alphabetically; both contributed equally. Send correspondence to the rst author at University of Michigan Business School, 701 Tappan St., Ann Arbor, MI 48109-1234, phone: (734) 764-4711, fax: (781) 459-6052, e-mail: feinf@umich. edu.
... 1 According to Van Heerde et al. (2002), managers should rely on models which provide the most accurate predictions. Besides, more flexible nonparametric estimation methods have also become established in choice modeling, see, e.g., Abe (1991), Abe (1995), Abe et al. (2004), or Boztuğ et al. (2014). ...
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.
... Using flexible regression methods (e.g., kernel estimators, spline estimators, or k-nearest neighbor estimators) is not new in marketing (see Leeflang et al., 2000 for an overview). Several papers analyze nonlinear pricing and promotional effects on aggregated brand sales or market shares (see, e.g., Kalyanam & Shively, 1998;Van Heerde, Leeflang, & Wittink, 2001;Hruschka, 2002;Martínez-Ruiz, Mollá-Descals, Gómez-Borja, & Rojo-Álvarez, 2006;Steiner, Brezger, & Belitz, 2007;Brezger & Steiner, 2008;Lang, Steiner, Weber, & Wechselberger, 2015;Weber, Steiner, & Lang, 2017), some others non-linear effects in brand choice models (Abe, 1995;Abe, 1999;Abe, Boztuğ, & Hildebrandt, 2004; Table 1 Overview of discrete choice models with time-varying parameters. ...
Nowadays, brand choice models are standard tools in quantitative marketing. In most applications, parameters representing brand intercepts and covariate effects are assumed to be constant over time. However, marketing theories, as well as the experience of marketing practitioners, suggest the existence of trends or short-term variations in particular parameters. Hence, having constant parameters over time is a highly restrictive assumption, which is not necessarily justified in a marketing context and may lead to biased inferences and misleading managerial insights.
In this paper, we develop flexible, heterogeneous multinomial logit models based on penalized splines to estimate time-varying parameters. The estimation procedure is fully data-driven, determining the flexible function estimates and the corresponding degree of smoothness in a unified approach. The model flexibly accounts for parameter dynamics without any prior knowledge needed by the analyst or decision maker. Thus, we position our approach as an exploratory tool that can uncover interesting and managerially relevant parameter paths from the data without imposing assumptions on their shape and smoothness.
Our approach further allows for heterogeneity in all parameters by additively decomposing parameter variation into time variation (at the population level) and cross-sectional heterogeneity (at the individual household level). It comprises models without time-varying parameters or heterogeneity, as well as random walk parameter evolutions used in recent state space models, as special cases. The results of our extensive model comparison suggest that models considering parameter dynamics and household heterogeneity outperform less complex models regarding fit and predictive validity. Although models with random walk dynamics for brand intercepts and covariate effects perform well, the proposed semiparametric approach still provides a higher predictive validity for two of the three data sets analyzed.
For joint estimation of all regression coefficients and hyperparameters, we employ the publicly available software BayesX, making the proposed approach directly applicable.
... In this regard future research could start a from a homogeneous flexible choice model (which can be found in e. g., Briesch et al. 2002;Abe et al. 2004;Hruschka et al. 2004) and add heterogeneity of parameters in a manner similar to what has been done to arrive at the heterogeneous logit model. Of course, estimation of heterogeneous logit models with flexible indirect utility function will be more involved. ...
... Kalyanam and Shively 1998;van Heerde et al. 2001;Hruschka 2001Hruschka , 2002Steiner et al. 2007;Brezger and Steiner 2008;Weber and Steiner 2012), to brand choice models (see e.g. Abe 1999; Abe et al. 2004;Briesch et al. 2002;Kneib et al. 2007;Schindler et al. 2007), or to the field of allocating catalogs to customers (see e.g. Baumgartner and Hruschka 2005). ...
There is consensus in the marketing literature that satisfaction of customers concerning the perceived quality and pricing of products or services is critical for customer retention. In contrast, there is lack of empirical evidence about the exact functional relationship. Using parametric and nonparametric regression, this contribution empirically investigates whether and to what extent nonlinear effects of and interaction effects between both satisfaction dimensions affect customer retention. The empirical results do not only reveal complex nonlinear effects for those satisfaction-retention relationships, respectively, but also indicate strong interaction effects of both satisfaction dimensions on customer retention. Furthermore, nonparametric approaches prove to be more flexible than parametric approaches to model complex interactions.
China has provided hundreds of billions of dollars in loans to developing countries. Researchers and pundits have focused on China’s motivations for allocating development finance, particularly in Africa, due to debt sustainability concerns. This paper aims to contribute to the understanding of the ways in which creditworthiness impacts the Chinese government’s development finance allocation decisions. In doing so, it examines the impact of African countries’ creditworthiness levels on Chinese development finance commitments. It also explores the impact of African country creditworthiness on Chinese loan cancellations and forgiveness. This paper finds that a disproportionate share of Chinese government loan commitments to African countries are made to governments with high credit risk levels. It also finds that, as African countries’ creditworthiness decreases, their likelihood of having Chinese loan commitments canceled increases. This underscores the importance of greater transparency from—and coordination with—China in its approach to debt sustainability and its attitude toward risk on the African continent, as well as the importance of building African debt management and capacity to ensure responsible borrowing. Finally, the paper finds negative, though weak, relationship between creditworthiness and Chinese loan forgiveness. In other words, as opposed to what the debt trap diplomacy hypothesis would suggest, Chinese loans to risky countries are more likely to be forgiven.
The multinomial logit model (MNL) is one of the most frequently used statistical models in marketing
applications. It allows one to relate an unordered categorical response variable, for example representing
the choice of a brand, to a vector of covariates such as the price of the brand or variables characterising
the consumer. In its classical form, all covariates enter in strictly parametric, linear form into the
utility function of the MNL model. In this paper, we introduce semiparametric extensions, where smooth
effects of continuous covariates are modelled by penalised splines. A mixed model representation of
these penalised splines is employed to obtain estimates of the corresponding smoothing parameters, leading
to a fully automated estimation procedure. To validate semiparametric models against parametric models,
we utilise different scoring rules as well as predicted market share and compare parametric and semiparametric
approaches for a number of brand choice data sets.
Marketing scholars commonly characterize market structure by studying the patterns of substitution implied by brand switching. Though the approach is useful, it typically ignores the destabilizing role of marketing variables (e.g., price) in switching behavior. The authors propose a flexible choice model that partitions the market into consumer segments differing in both brand preference and price sensitivity. The result is a unified description of market structure that links the pattern of brand switching to the magnitudes of own- and cross-price elasticities. The approach is applied in a study of competition between national brands and private labels in one product category.
The authors present a Bayesian approach to the estimation of household parameters. Applied to the standard logit model, the procedure produces household-level estimates of all model parameters, enabling researchers to identify differences in household reaction to all variables in the marketing mix. Simulated data are used to study the small-sample performance of the estimator. The estimator can be easily implemented with standard algorithms used to maximize likelihood functions. In application to tuna scanner panel data, strong evidence of heterogeneity in price, display, and feature response (slope) parameters is detected. Approaches that fail to take into account slope heterogeneity are shown to underestimate the value of feature advertising and in-store displays in this dataset. In addition, the household price sensitivity estimates are strongly related to coupon usage and demonstrate how the estimates can be used to implement a targeted household drop.
Generalized additive models have the form η(x) = α + σ fj(xj), where η might be the regression function in a multiple regression or the logistic transformation of the posterior probability Pr(y = 1 | x) in a logistic regression. In fact, these models generalize the whole family of generalized linear models η(x) = β′x, where η(x) = g(μ(x)) is some transformation of the regression function. We use the local scoring algorithm to estimate the functions fj(xj) nonparametrically, using a scatterplot smoother as a building block. We demonstrate the models in two different analyses: a nonparametric analysis of covariance and a logistic regression. The procedure can be used as a diagnostic tool for identifying parametric transformations of the covariates in a standard linear analysis. A variety of inferential tools have been developed to aid the analyst in assessing the relevance and significance of the estimated functions: these include confidence curves, degrees of freedom estimates, and approximate hypothesis tests.The local scoring algorithm is analogous to the iterative reweighted least squares algorithm for solving likelihood and nonlinear regression equations. At each iteration, an adjusted dependent variable is formed and an additive regression model is fit using the backfitting algorithm. The backfitting algorithm cycles through the variables and estimates each coordinated function by smoothing the partial residuals.