Estimation bias in choice models with last choice feedback

The study compares two estimation methods for choice models with last choice feedback, using simulated and real data. The first method ignores the impact of unobserved heterogeneity on observed choices via presample choices, while the second method approximates this impact by a stochastic relationship. In panels with less than 10 choices per panelist, the first method overstates the impact of last choice on current choice and understates the impact of intrinsic preferences (i.e., brand intercepts). The second method performs significantly better than the first method. Under both methods, an increase in the number of heterogeneous coefficients in the model tends to increase the bias in the estimates. The largest bias occurs when lagged choice coefficients are heterogeneous.     

Data pruning in consumer choice models

Common, if not ubiquitous, Marketing practice when estimating models for scanner panel data is to: (a) observe the data, (b) prune the data to a “manageable” number of brands or SKUs, and (c) fit models to the remaining data. We demonstrate that such pruning practice can lead to significantly different (and potentially biased) elasticities, and hence different managerial/practical outcomes, especially in the context of model misspecification. We first justify our claims theoretically by writing the general problem in a classic missing-data framework and demonstrate that commonly used pruning mechanisms (gleaned from current academic Marketing literature) can lead to a nonignorable missing data mechanism. Secondly, we summarize an extensive set of simulations that were run to understand the driving factors of that bias. The results indicate much greater pruning bias in those cases where model fit is poor (small ), random utility errors are correlated with the covariates, or the model is misspecified (e.g., a homogeneous logit is specified when a mixed-logit is true). Empirically, we also demonstrate our findings on the well-cited and highly utilized fabric softener data of Fader and Hardie (1996). Our empirical findings suggest a number of estimates that vary according to the way in which the data is pruned including the magnitude of market mix and attribute elasticities, and purchase probabilities, but that the pruning effect is smaller for better fitting models.

Parameter nonstationarity in retail choice models

The question of spatial nonstationarity in retail choice models generally has been ignored in the literature. This paper discusses why such nonstationarity might arise and presents an empirical test of nonstationarity in grocery choice data collected from a midwestern city. Based on these findings a nonstationarity retail choice model is proposed. The nonstationary model predicts data from a hold-out sample better than the stationary model.     

Heterogeneity distributions of willingness-to-pay in choice models

We investigate direct and indirect specification of the distribution of consumer willingness-to-pay (WTP) for changes in product attributes in a choice setting. Typically, choice models identify WTP for an attribute as a ratio of the estimated attribute and price coefficients. Previous research in marketing and economics has discussed the problems with allowing for random coefficients on both attribute and price, especially when the distribution of the price coefficient has mass near zero. These problems can be avoided by combining a parameterization of the likelihood function that directly identifies WTP with a normal prior for WTP. We show that the typical likelihood parameterization in combination with what are regarded as standard heterogeneity distributions for attribute and price coefficients results in poorly behaved posterior WTP distributions, especially in small sample settings. The implied prior for WTP readily allows for substantial mass in the tails of the distribution and extreme individual-level estimates of WTP. We also demonstrate the sensitivity of profit maximizing prices to parameterization and priors for WTP.

The effect of attribute-based and alternative-based processing on consumer choice in context

The current research proposes that the extent to which consumer choices are affected by the decision process depends on the underlying nature of the choice problem. Specifically, choices resulting from substantial inter-brand comparisons and tradeoff analyses are vulnerable to whether product information is evaluated by attribute- or alternative-based processing. By contrast, choices resulting from a minimal cognitive processing are less sensitive to variations in the decision strategy employed. We test our theory in the well-known domain of choice context effects. Across three studies using multiple operationalizations of the decision process (i.e., information display format, product presentation mode, and processing goal), we find converging evidence that the more cognitively involving compromise choice increases when the environment facilitates attribute- versus alternative-based processing. Conversely, the choice of asymmetrically dominating option, which is characterized by relatively little analytical processing, does not depend on the type of decision strategy highlighted by the task.     

Incorporating choice dynamics in models of consumer behavior

This paper presents a framework for organizing and discussing factors influencing consumer choice dynamics, how these factors may be incorporated into models of buyer behavior and problems that may arise in estimating such models. The paper identifies research issues and delineates possible approaches. Proceedings of Session on Choice Dynamics at the Banff Symposium on Consumer Decision-Making and Choice Behavior. All authors share equally in content and remaining errors.     

Homogeneity and heterogeneity in stochastic models of brand choice behavior

Heterogeneity of consumers is one of the cornerstones of empirical findings and theories in marketing. It serves, for example, as the foundation for such areas as market segmentation and product differentiation. This paper attempts to trace and clarify the evolution over the last twenty years of the homogeneity assumptions in the area of stochastic models of brand choice behavior. In analyzing individual choice behavior by means of stochastic models, all individuals were often assumed to possess the same set of transition probabilities or follow the same stochastic process. However, empirical studies at the individual level indicate that individuals are actually non-homogeneous in those probabilities and processes. In this article we provide an analytical proof that if the behavior of individuals is specified to be homogeneous when it is not, wrong inferences about the type of stochastic process individuals follow and about the expected behavior of the total population will be drawn. Ways to remedy these problems by allowing for heterogeneity are reviewed. The implications of heterogeneity and our findings in the various application areas which utilize stochastic choice models are examined.     

Using stated response choice data to enrich revealed preference discrete choice models

There is growing interest in exploring the view that both revealed preference (RP) and stated preference (SP) data have useful information and that their integration will enrich the overall explanatory power of RP choice models. These two types of data have been independently used in the estimation of a wide variety of discrete choice applications in marketing. In order to combine the two data sources, each with independent choice outcomes, allowance must be made for their different scaling properties. The approach uses a full information maximum likelihood estimation procedure of the hierarchical logit form to obtain suitable scaling parameters to make one or more data sets comparable. We illustrate the advantages of the dual data strategy by comparing the results with those obtained from models estimated independently with RP and SP data. Data collected as part of a study of high speed rail is used to estimate a set of illustrative mode choice models.     

Cross-task validity comparisons of stated preference choice models

This paper uses a statistical test developed by Horowitz and Louviere (1993) to compare the parameters of several logit models estimated from different preference measures. This test shows that all models produce estimates of attribute effects that are equivalent up to a rescaling. Furthermore, models based on stated next purchase, the outcome of a purchase experiment, and a binary analysis of consideration set data produce equivalent estimates of all parameters.     

Integrating the Dirichlet-multinomial and multinomial logit models of brand choice

This paper discusses the interpretative benefits that arise from merging the Dirichlet-multinomial (DM) model as a loyalty variable in the multinomial logit (MNL) model of brand choice. The estimated parameters of this hybrid model compare favorably to those of a pure DM model (with no marketing mix variables) as well as those of a standard MNL model with an exponentially smoothed loyalty measure. The hybrid model offers an index of consumer heterogeneity and estimates of each brand's preference share, adjusted for the effects of price and promotional activities. We illustrate the unique interpretations offered by these parameters across four different product categories, showing how changes in heterogeneity (across categories or model specifications) are closely related to changes in the overall impact of marketing mix variables.The author is grateful to Bruce Hardie, Barbara Kahn, Jim Lattin, Len Lodish, Bob Meyer, and Don Morrison for their comments and suggestions. He appreciates the support of Doug Honnold and Information Resources, Inc., for providing the data and computational facilities used in this paper.     

Purchasing for someone else in a b-to-b context: Joint effects of choice overload and accountability

Purpose: The purpose of this paper is to examine whether the (negative) influence of assortment size identified in the business-to-consumer (B-to-C) literature also exists in business-to-business (B-to-B) settings and whether it is contingent on buyers’ accountability for their choices. Furthermore, it is examined if and to what extent assortment presentation in the form of color-coding may reduce the negative effects on decision satisfaction caused by large assortments.

Methodology/approach: In addition to a qualitative study (i.e., Study 1) including 16 semi-structured expert interviews, we conducted two experiments with real industrial buyers to further examine the interaction effect of assortment size and accountability on decision satisfaction as well as the moderating effect of color-coding. Specifically, in Study 2, we used a 2 (assortment size: small versus large) X 2 (accountability: informal versus official) between-subjects design. A 2 × 2 ANOVA revealed an interactive effect of assortment size and accountability on decision satisfaction. Furthermore, we ran a moderated mediation analysis to test for the underlying process. Study 3 used a 2 (color-coding: yes versus no) X 2 (accountability: informal versus official) between-subjects design. A comparison of the means across the experimental cells provided support for a positive influence of color-coding when industrial buyers are informally (rather than officially) accountable.

Findings: Our experiments show that when B-to-B buyers are held officially accountable, they experience equal decision satisfaction when choosing from small and large assortments. However, when buyers are held informally accountable, they experience a higher decision satisfaction when choosing from small rather than large assortments. These effects are mediated by decision justifiability. Furthermore, we show that color-coding the assortment influences buyers’ decision satisfaction positively when they are held informally accountable and are asked to choose from a large assortment.

Research implications: Our research contributes by demonstrating that overchoice effects exist in B-to-B settings. In addition, our studies show that potential overchoice effects are contingent on the specific form of accountability that industrial buyers experience. In this respect, our findings make an important contribution to the literature on B-to-B decision making and the role of accountability in these decisions.

Practical implications: Our research also has practical implications for managers that have to make assortment decisions as an appealing and easy to understand assortment is an important means to compete in the market. Many companies offer large assortments that, at the same time, are efficient in fulfilling customer needs and therefore do not have the potential to be reduced through the elimination of certain product variants. Assortment presentation (for example through color-coding) can be the key to offering a high number of variants while making the assortment mentally convenient at the same time.

Originality/value/contribution: To the best of our knowledge, ours is the first research to provide a more fine-grained analysis of official and informal accountability in a B-to-B context and to examine the differences between these two forms of accountability in an experimental setting with real industrial buyers.     

Advances in computation,statistical methods,and testing of discrete choice models

This paper gives a brief overview of recent developments in computation, estimation, and statistical testing of choice models, with marketing applications. Topics include statistical models for discrete panel data with heterogeneous decision-makers, simulation methods for estimation of high-dimension multinomial probit models, specification tests for model structure and for brand and purchase clustering, and innovations in numerical analysis for estimation and forecasting. In collaboration with Denis Bolduc, David Bunch, Michael Keane, Don Kridel, and Steve Stern.     

Sequential sampling models of choice: Some recent advances

Choice models in marketing and economics are generally derived without specifying the underlying cognitive process of decision making. This approach has been successfully used to predict choice behavior. However, it has not much to say about such aspects of decision making as deliberation, attention, conflict, and cognitive limitations and how these influence choices. In contrast, sequential sampling models developed in cognitive psychology explain observed choices based on assumptions about cognitive processes that return the observed choice as the terminal state. We illustrate three advantages of this perspective. First, making explicit assumptions about underlying cognitive processes results in measures of deliberation, attention, conflict, and cognitive limitation. Second, the mathematical representations of underlying cognitive processes imply well documented departures from Luce’s Choice Axiom such as the similarity, compromise, and attraction effects. Third, the process perspective predicts response time and thus allows for inference based on observed choices and response times. Finally, we briefly discuss the relationship between these cognitive models and rules for statistically optimal decisions in sequential designs.     

Business models and market entry mode choice of small software firms

So far the critical choice of the entry mode for a target country has been examined ignoring the special features of firms. Particularly, the impact of the wide variation of business models of software firms has been ignored. This multi case study investigates the relation between the business model and the entry mode, of eight software firms. The results imply that the product strategy and the service and implementation model of a software firm are closely connected to the entry mode choice, while the distribution model of intangible software products does not seem to have an impact on the operation mode.     

Efficient choice set designs for estimating availability cross-effects models

Batsell and Polking proposed a discrete choice model which incorporates the availability (presence or absence) of competing brands into the utility of each brand under study. The information on relative impacts of adding or deleting brands is of strategic interest, and models that do not incorporate such effects may be misleading. The designs suggested by Batsell and Polking have 2^m–m–1 choice sets. Even with as few as 10=m brands, this requires over 1000 choice sets. In this paper we provide a catalog of designs for estimating cross effects models in as few as 2m–1 choice sets. This will make cross effects modelling practical in a wide range of academic and commercial settings.     

Modeling preference evolution in discrete choice models: A Bayesian state-space approach

We develop discrete choice models that account for parameter driven preference dynamics. Choice model parameters may change over time because of shifting market conditions or due to changes in attribute levels over time or because of consumer learning. In this paper we show how such preference evolution can be modeled using hierarchial Bayesian state space models of discrete choice. The main feature of our approach is that it allows for the simultaneous incorporation of multiple sources of preference and choice dynamics. We show how the state space approach can include state dependence, unobserved heterogeneity, and more importantly, temporal variability in preferences using a correlated sequence of population distributions. The proposed model is very general and nests commonly used choice models in the literature as special cases. We use Markov chain monte carlo methods for estimating model parameters and apply our methodology to a scanner data set containing household brand choices over an eight-year period. Our analysis indicates that preferences exhibit significant variation over the time-span of the data and that incorporating time-variation in parameters is crucial for appropriate inferences regarding the magnitude and evolution of choice elasticities. We also find that models that ignore time variation in parameters can yield misleading inferences about the impact of causal variables. This paper is based on the first author's doctoral dissertation.     

Estimating choice models in data-sparse environments: Taking advantage of perceived similarity

Research suggests that choice models conditioned on correctly identified consideration sets outperform choice models conditioned on the awareness set (Hauser, 1978; Roberts and Lattin, 1991). However, in data-sparse environments, where purchase history information is not available or not relevant, choice models conditioned on the consideration set often yield nonunique or nonsignificant solutions. In these environments, we propose the use of similarity information to improve the performance of choice models. Support for this position is found in an empirical application involving automobiles.     

Advances in random utility models report of the workshop on advances in random utility models duke invitational symposium on choice modeling behavior

In recent years, major advances have taken place in three areas of random utility modeling: (1) semiparametric estimation, (2) computational methods for multinomial probit models, and (3) computational methods for Bayesian estimation. This paper summarizes these developments and discusses their implications for practice.