Estimating time-varying parameters in brand choice models: A semiparametric approach

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.     

A New Look at Constructed Choice Processes

Normative models of choice assert axiomatically that preferences are consistent, coherent, and determined only by relevant alternatives. In contrast to this classical economic perspective, behavioral models derived from research in psychology and consumer behavior assert that preferences are not guided by an internal, stable utility function but are constructed during the choice process. The current paper is based on a session on constructed choice processes (CCP) at the 2004 Choice Symposium that focused on how the standard CCP model can be enriched by bringing theories and tools from modern research in social cognition to bear on choice phenomenon. The richer conceptual framework presented by new, currently unpublished empirical work provides a novel perspective on choice construction by integrating the roles of subjective construal, experiential information, attribution, goals, and satisfaction in understanding preference construction processes in choice.     

A multi-category customer base analysis

Customer base analysis is an essential tool to measure and develop relationships with customers. While various models have been proposed in a noncontractual setting, they focus primarily on analyzing transactional patterns associated with a single product category or a firm-level activity, such as the times at which purchases are made at a particular retailer. This research proposes a modeling framework for customer base analysis in a multi-category context. Specifically, we model the time between a customer's purchases at the firm and the product categories that comprise her shopping basket arising from multi-category choice decisions. The proposed model uses a latent space approach that parsimoniously captures the dynamics of multi-category shopping behavior due to the interplay between purchase timing and shopping basket composition. We also account for interdependence among multiple categories, temporal dependence across category choices, and latent customer attrition. Using category-level transaction data, we show that the proposed model offers excellent fit and performance in predicting customer purchase patterns across multiple categories. The forecasts and inferences afforded by our model can assist managers in tailoring marketing efforts across categories.     

Conjunctive screening in models of multiple discreteness

Consumer demand for products often result in the purchase of multiple goods at the same time. Corner solutions, or the non-purchase of items, occur when consumers have strong preference for some goods that do not satiate and weak preference for other goods. However, if non-purchase arises because a consumer finds particular brands and attributes unacceptable, leading to the formation of consideration sets, then estimates of preference will be too extreme and biased. In this paper, we extend the work on consideration sets and discrete choices to a wider class of models, and develop a model of multiple discreteness with conjunctive screening of the alternatives that remove offerings from consideration. We propose a method for consideration set formation that does not require one to specify a partitioned space of the augmented variable, and that can be adapted into the class of choice models in which an outcome variable is removed. We explore implications for disentangling non-purchase due to consideration set formation using two data sets of ice cream and frozen pizza purchases. The ice cream data, in which responses are both discrete and volumetric, allow us to compare differences in how screening affect purchase incidence versus volumetric demand per incidence. Screening reduces the estimated number of customers with positive demand but leads to an increase in demand for those not screened. In the frozen pizza data, we find that conjunctive screening accounts for many of the observed corner solutions and leads to estimates of preference and satiation that differs from traditional models of multiple-discreteness without screening.     

Integrating Time-Preferences into E-Negotiation Systems: A Model,Elicitation Approach and Experimental Implications

Researchers have advocated that the acquisition of user preferences is important to the successful adoption of electronic negotiation systems. In this paper, we focus on one such preference, namely time preference, wherein the price of a good/service varies according to the delivery/consumption time. Time preference is a behavioral aspect that varies across buyers. We discuss how different types of preferences can be elicited, represented and integrated with electronic negotiations. We discuss three experiments to study the effect of time preferences on negotiation. The first is a preference elicitation experiment involving 36 subjects. The next two are agent-to-agent negotiation experiments, one based on the individual preferences obtained earlier and the other based on an expanded dataset on both individual preferences as well as negotiation parameters. The agent-based experiment compares outcomes and efficiencies between the standard exponential discounting model and two behavioral models of time preference. Our results bring out the preferences of subjects, as well as the extent to which negotiation is affected and enhanced by the incorporation of time-preferences.     

A Micromodel of New Product Adoption with Heterogeneous and Forward-Looking Consumers: Application to the Digital Camera Category

We develop an empirical model for the adoption process of a new durable product that accounts for consumer heterogeneity as well as consumers forward-looking behavior. Accounting for heterogeneity is important for two reasons. As the mix of consumers with different preferences and price sensitivities could change over time, firms need to update their marketing strategies. Further, it allows for a variety of shapes for the aggregate adoption process over time. As prices for durable and technology products fall over time with firms continually introducing enhanced products, consumers may anticipate these prices and improvements and delay their purchases in the product category. Forward-looking consumers optimize purchase timing by trading off their utilities from buying the product and their expectations on future prices, quality levels, and brand availability. Such forward-looking behavior will result in price dynamics in the marketplace as price changes today influence future purchases. And it results in different shapes of the new product sales pattern over time by influencing the time to take-off. We show how the parameters of our model can be estimated using aggregate data on the sales, prices, and attributes of brands in a product category. We apply our model to market data from the digital camera category. Our data are consistent with the presence of both heterogeneity and forward looking behavior among consumers. At the product category level, we are able to decompose the effects of the entry of Sony into primary demand expansion and switching from other brands. At the brand level, we find that there exist several segments in the market with different preferences for the brands and different price sensitivities leading to differences in adoption timing and brand choice across segments. For a given brand, we show how the changing customer mix over time has implications for that brands pricing strategies. We characterize how price effects vary across brands and over time and how price changes in a given time period influence sales in subsequent periods. Model comparison and validation results are also provided.     

Knows Me and My Business: The Association between Preference for Relational Governance and Owners' Choice of Banks

We explore the relative importance of relational and economic preferences in small business owners' choice of a primary bank. We measured preferences directly at three points within 14 years and found that business owners' preference for relational versus economic governance was associated with the type of bank chosen and that the effect of relational preference remained relatively stable over time. Our findings support the idea that a preference for social relations might shape even the most straightforward economic decisions and suggest that variation in this preference is large, persistent enough to support business opportunities for small firms, including small banks.     

A simple method for estimating preference parameters for individuals

This paper demonstrates a method for estimating logit choice models for small sample data, including single individuals, that is computationally simpler and relies on weaker prior distributional assumptions compared to hierarchical Bayes estimation. Using Monte Carlo simulations and online discrete choice experiments, we show how this method is particularly well suited to estimating values of choice model parameters from small sample choice data, thus opening this area to the application of choice modeling. For larger sample sizes of approximately 100–200 respondents, preference distribution recovery is similar to hierarchical Bayes estimation of mixed logit models for the examples we demonstrate. We discuss three approaches for specifying the conjugate priors required for the method: specifying priors based on existing or projected market shares of products, specifying a flat prior on the choice alternatives in a discrete choice experiment, or adopting an empirical Bayes approach where the prior choice probabilities are taken to be the average choice probabilities observed in a discrete choice experiment. We show that for small sample data, the relative weighting of the prior during estimation is an important consideration, and we present an automated method for selecting the weight based on a predictive scoring rule.     

Recent Progress on Endogeneity in Choice Modeling

We describe recent progress in several areas related to endogeneity, including: choice set formation and attention to attributes; interactions among decision-makers; respondents' strategic behavior in answering stated preference choices; models of multiple discrete/continuous choice; distributions of willingness-to-pay; and methods for handling traditionally endogenous explanatory variables.     

Means matter, but variance matter too: Decomposing response latency influences on variance heterogeneity in stated preference experiments

Response time latencies have been shown to influence consumer’s choice behaviour in choice-based-conjoint studies. The literature has shown that response time latencies affect the mean outputs of parameter estimates derived from models of discrete choice. In this paper, we add further insight into the influences response time latencies have on such models by modelling latent response information associated with the variance of random parameter distributions through parameterisation of variance heterogeneity (or heteroskedasticity). We demonstrate that response time latencies influence not only the means of random parameter distributions, but also the variances, and that failure to account for both may result in incorrect model inferences being drawn.     

Generalized Reverse Discrete Choice Models

Marketing practitioners and academics have shown a keen interest in the processes that drive consumers’ choices since the early work of Guadagni and Little (1982). Over the past decade or so, a number of alternative models have been proposed, implemented and analyzed. The common behavioral assumption that underlines these models of discrete choice is random utility maximization (RUM). The RUM assumption, in its simplest form, posits that a consumer with a finite set of brands to choose from chooses the brand that gives her the maximum amount of utility. An alternative approach would be to assume that consumers choose the alternative that offers them the least disutility. Our paper proposes and tests a broad class of generalized extreme value models based on this hypothesis. We model the decision process of the consumer the assumption random disutility minimization (RDM) and derive a new class of discrete choice models based on this assumption. Our findings reveal that there are significant theoretical and econometric differences between the discrete choice models derived from a RUM framework and the RDM framework proposed in this paper. On the theoretical front we find that the class of discrete choice models based on the assumption of disutility minimization is structurally different from the models in the literature. Further, the models in this class are available in closed form and exhibit the same flexibility as the GEV models proposed by McFadden (1978). In fact, the number of parameters are identical to and have the same interpretation as those obtained via RUM based GEV models. In addition to the theoretical differences we also uncover significant empirical insights. With the computing effort and time for both models being roughly the same this new set of models offers marketing academics and researchers a viable new tool with which to investigate discrete choice behavior.JEL Classification: C25, C35, M37, D12     

Tradeoffs between sensory attributes and organic labels: the case of orange juice

Researchers have investigated the role of sensory attributes and organic labels on consumers’ preferences and perceptions of food, but few has examined whether sensory attributes are relevant for consumers who prefer organic food and the extent to which sensory attributes influence consumer's marginal willingness to pay for organic food. The objective of this study is to determine how sensory attributes and organic label work together to influence consumer's stated preference and marginal willingness to pay for orange juice. To achieve this, we conducted a blind sensory evaluation of two orange juices followed by a discrete choice experiment to determine the extent to which consumer's stated preference for orange juice labelled as organic is affected by sensory experience preceding the choice experiment. Random parameter logit models and latent class conditional logit models are used to explain stated preference. Results indicate that the effect of sensory attributes on consumer's marginal willingness to pay differed by organic juice and conventional juice.     

Combining Sources of Preference Data for Modeling Complex Decision Processes

We review current state-of-the-art practices for combining preference data from multiple sources and discuss future research possibilities. A central theme is that any one data source (e.g., a scanner panel source) is often insufficient to support tests of complex theories of choice and decision making. Hence, analysts may need to embrace a wider variety of data types and measurement tools than traditionally have been considered in applied decision making and choice research. We discuss the viability of preference-stationarity assumptions usually made when pooling data, as well as random-utility theory-based approaches for combining data sources. We also discuss types of models and data sources likely to be required to make inferences about and estimate models that describe choice dynamics. The latter discussion is speculative insofar as the body of literature on this topic is small.     

AN EQUILIBRIUM GUIDE TO DESIGNING AFFINE PRICING MODELS

The paper examines equilibrium models based on Epstein–Zin preferences in a framework in which exogenous state variables follow affine jump diffusion processes. A main insight is that the equilibrium asset prices can be computed using a standard machinery of affine asset pricing theory by imposing parametric restrictions on market prices of risk, determined inside the model by preference and model parameters. An appealing characteristic of the general equilibrium setup is that the state variables have an intuitive and testable interpretation as driving the consumption and dividend dynamics. We present a detailed example where large shocks (jumps) in consumption volatility translate into negative jumps in equilibrium prices of the assets as agents demand a higher premium to compensate for higher risks. This endogenous “leverage effect,” which is purely an equilibrium outcome in the economy, leads to significant premiums for out‐of‐the‐money put options. Our model is thus able to produce an equilibrium “volatility smirk,” which realistically mimics that observed for index options.     

Dynamic Influences on Individual Choice Behavior

Research examining the process of individual decision making over time isbriefly reviewed. We focus on two major areas of work in choice dynamics:research that has examined how current choices are influenced by the historyof previous choices, and newer work examining how choices may be made toexploit expectations about options available in the future. A central themeof the survey is that if a general understanding of choice dynamics is toemerge, it will come through the development of boundedly-rational models ofdynamic problem solving that lie on the interface between economics andpsychology.     

Modeling and Forecasting the Sales of Technology Products

Managers in technology product markets require sales response models that provide substantive insights into the effects of marketing activities as well as reliable sales forecasts. Such markets are characterized by frequent introductions and withdrawals of multiple models by different companies. Thus, the data available on the performance of any individual model is scarce. A second characteristic is that the effects of product attributes and marketing activities could change over time as different types of consumers participate in the market at different points in time. Given sparse data, it becomes critical to specify a model that allows pooling of information across brand-models while at the same time providing brand-model specific parameters. We accomplish this via a hierarchical Bayesian model specification. Further, to capture the effects of changing consumer preferences over time, we specify a time varying parameter model. Our modeling framework therefore, integrates a hierarchical Bayesian model within a time varying parameter framework to develop a dynamic hierarchical Bayesian model. We employ data on digital cameras in the U.S. market to estimate the parameters of our proposed model. We use thirty-three months of national level data on the digital camera market with the data series beginning very close to the inception of this product category. We find that while there is little variation in reliance of benefits by early adopters, the second wave of adopters focus on Ease of Use followed by later adopters who rely on Storage and Image Quality. Looking at the elasticities of demand with respect to the various benefits, we find that at around the halfway point of our data series, the industry as a whole would have been better off investing in increasing image quality rather than storage if costs associated with the two are equal. However, at the end of the time horizon both benefits appear to have about equal impact. Further, the relative benefits of improving these attributes vary across brands and points in time. We then generate single period and multiple period ahead sales forecasts. We make different assumptions about information availability and find that the average (across brand-models and time) MAPE ranges from 7.5 to 14.5% for the model. We provide extensive comparisons of our model with 4 potential alternatives and find that our model outperforms these alternatives on the nature of substantive insights obtained as well as in forecasting out-of-sample especially when there is a very short time window of data.     

How to generalize from a hierarchical model?

Models of consumer heterogeneity play a pivotal role in marketing and economics, specifically in random coefficient or mixed logit models for aggregate or individual data and in hierarchical Bayesian models of heterogeneity. In applications, the inferential target often pertains to a population beyond the sample of consumers providing the data. For example, optimal prices inferred from the model are expected to be optimal in the population and not just optimal in the observed, finite sample. The population model, random coefficients distribution, or heterogeneity distribution is the natural and correct basis for generalizations from the observed sample to the market. However, in many if not most applications standard heterogeneity models such as the multivariate normal, or its finite mixture generalization lack economic rationality because they support regions of the parameter space that contradict basic economic arguments. For example, such population distributions support positive price coefficients or preferences against fuel-efficiency in cars. Likely as a consequence, it is common practice in applied research to rely on the collection of individual level mean estimates of consumers as a representation of population preferences that often substantially reduce the support for parameters in violation of economic expectations. To overcome the choice between relying on a mis-specified heterogeneity distribution and the collection of individual level means that fail to measure heterogeneity consistently, we develop an approach that facilitates the formulation of more economically faithful heterogeneity distributions based on prior constraints. In the common situation where the heterogeneity distribution comprises both constrained and unconstrained coefficients (e.g., brand and price coefficients), the choice of subjective prior parameters is an unresolved challenge. As a solution to this problem, we propose a marginal-conditional decomposition that avoids the conflict between wanting to be more informative about constrained parameters and only weakly informative about unconstrained parameters. We show how to efficiently sample from the implied posterior and illustrate the merits of our prior as well as the drawbacks of relying on means of individual level preferences for decision-making in two illustrative case studies.

     

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.     

The Joint identification of utility and discount functions from stated choice data: An application to durable goods adoption

We present a survey design that generalizes static conjoint experiments to elicit inter-temporal adoption decisions for durable goods. We show that consumers’ utility and discount functions in a dynamic discrete choice model are jointly identified using data generated by this specific design. In contrast, based on revealed preference data, the utility and discount functions are generally not jointly identified even if consumers’ expectations are known. The separation of current-period preferences from discounting is necessary to forecast the diffusion of a durable good under alternative marketing strategies. We illustrate the approach using two surveys eliciting Blu-ray player adoption decisions. Both model-free evidence and the estimates based on a dynamic discrete choice model indicate that consumers make forward-looking adoption decisions. In both surveys the average discount rate is 43 percent, corresponding to a substantially higher degree of impatience than the rate implied by aggregate asset returns. The estimates also reveal a large degree of heterogeneity in the discount rates across consumers, but only little evidence for hyperbolic discounting.