Sequential choice designs to estimate the heterogeneity distribution of willingness-to-pay

Two prominent approaches exist nowadays for estimating the distribution of willingness-to-pay (WTP) based on choice experiments. One is to work in the usual preference space in which the random utility model is expressed in terms of partworths. These partworths or utility coefficients are estimated together with their distribution. The WTP and the corresponding heterogeneity distribution of WTP is derived from these results. The other approach reformulates the utility in terms of WTP (called WTP-space) and estimates the WTP and the heterogeneity distribution of WTP directly. Though often used, working in preference space has severe drawbacks as it often leads to WTP-distributions with long flat tails, infinite moments and therefore many extreme values. By moving to WTP-space, authors have tried to improve the estimation of WTP and its distribution from a modeling perspective. In this paper we will further improve the estimation of individual level WTP and corresponding heterogeneity distribution by designing the choice sets more efficiently. We will generate individual sequential choice designs in WTP space. The use of this sequential approach is motivated by findings of Yu et al. (2011) who show that this approach allows for superior estimation of the utility coefficients and their distribution. The key feature of this approach is that it uses Bayesian methods to generate individually optimized choice sets sequentially based on prior information of each individual which is further updated after each choice made. Based on a simulation study in which we compare the efficiency of this sequential design procedure with several non-sequential choice designs, we can conclude that the sequential approach improves the estimation results substantially.     

Extentions of probabilistic perceptual maps with implications for competitive positioning and choice

Perceptual product positioning maps which are derived from probabilistic scaling models possess some distinct advantages over their deterministic counterparts. However, many probabilistic models still labor under a number of restrictive mathematical conditions. This paper describes an anisotropic space extension that alleviates some of these limitations by explicitly modeling the dimensional variances and covariances of each brand in a product positioning map. To clarify the decisions necessary when using probabilistic scaling models and to illustrate some of their attractive properties, two sets of convenience goods data are analyzed. The applications focus on the model's implications for the understanding of brand positioning and choice probabilities.     

Accommodating the effects of brand unfamiliarity in the multidimensional scaling of preference data

This paper presents a multidimensional scaling (MDS) methodology (vector model) for the spatial analysis of preference data that explicitly models the effects of unfamiliarity on evoked preferences. Our objective is to derive a joint space map of brand locations and consumer preference vectors that is free from potential distortion resulting from the analysis of preference data confounded with the effects of consumer-specific brand unfamiliarity. An application based on preference and familiarity ratings for ten luxury car models collected from 240 consumers who intended to buy a luxury car within a designated time frame is presented. The results are compared with those obtained from MDPREF, a popular metric vector MDS model used for the scaling of preference data. In particular, we find that the consumer preference vectors obtained from the proposed methodology are substantially different in orientation from those estimated by the MDPREF model. The implications of the methodology are discussed.The authors gratefully acknowledge helpful comments from the editor and two anonymous reviewers, and also from Michael D. Johnson and Robert J. Meyer. They also thank Michael Kusnick and Robert Kleinbaum for their assistance in conducting the survey.     

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.     

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.     

Combining revealed and stated preferences data

Our objective is to develop a unifying framework for the incorporation of different types of survey data in individual choice models. We describe statistical methodologies that combine multiple sources of data in the estimation of individual choice models and summarize the current state of the art of data combination methods that have been used with market research data. The most successful applications so far have combined revealed and stated preference data. We discuss different types of market and survey data and provide examples of research contexts in which one might wish to combine them. Although these methods show a great deal of promise and have already been used successfully in a number of applications, several important research issues remain. A discussion of these issues and directions for further research conclude the paper.     

Effects of knowledge types on choice quality and perceptions of choice performance

Two types of knowledge used in making choices are examined: knowledge of product-specific information and knowledge of a choice strategy. Product-specific information comprises information about available alternatives, including features and their importance. Strategy information includes knowing an appropriate strategy for integrating and evaluating information about alternatives, as well as knowing how to implement the strategy. The effects of these knowledge types, both singly and jointly, upon choice quality and perceptions of choice quality are examined in two studies. The results of the first study indicate that the knowledge types are differentially beneficial, and that subjects tend to be more overconfident about the perceived quality of their choices when they have product-specific information than when they have choice strategy information. The hypothesis that this difference is due to subjects' greater awareness of produce-specific information, rather than strategy information, is examined and supported in the second study. Implications for marketing and public policy are discussed. © 1996 John Wiley & Sons, Inc.     

Models and optimal designs for conjoint choice experiments including a no-choice option

In a classical conjoint choice experiment, respondents choose one profile from each choice set that has to be evaluated. However, in real life, the respondent does not always make a choice: often he/she does not prefer any of the options offered. Therefore, including a no-choice option in a choice set makes a conjoint choice experiment more realistic. In the literature, three different models are used to analyze the results of a conjoint choice experiment with a no-choice option: the no-choice multinomial logit model, the extended no-choice multinomial logit model, and the nested no-choice multinomial logit model. We develop optimal designs for the two most appealing of these models using the D-optimality criterion and the modified Fedorov algorithm and compare these optimal designs with a reference design, which is constructed while ignoring the no-choice option, in terms of estimation and prediction accuracy. We conclude that taking into account the no-choice option when designing a no-choice experiment only has a marginal effect on the estimation and prediction accuracy as long as the model used for estimation matches the data-generating model.     

Designing Pareto optimal stimuli for multiattribute choice experiments

Full factorial designs have long been used in designing multiattribute stimuli (e.g., hypothetical job applicants) for use in policy capturing and functional measurement models. More recently, marketing researchers have employedfractional factorial designs in multiatribute preference models, such as those used in conjoint analysis.Occasions arise where the researcher also desires the stimulus profiles to be Pareto optimal. This paper addresses some conceptual and methodological issues associated with Pareto optimal choice sets. In particular, we discuss the problem of determining the expected number of dominant-entry pairs. We then consider the task of deriving Pareto optimal choice sets from fractional factorial designs. A heuristic for accomplishing this is described and applied to an illustrative set of main effects and main effects plus interactions designs.     

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 dimensional versus attribute approach for disaggregate choice models

A fundamental issue facing choice modelers is to make a decision on what kind of independent variables to include in a choice model. With survey data, the two immediate options are: actual product attributes or underlying latent dimensions (factor scores). Using behavioral logic we argue that heterogeneity of consumer perceptions of variables and their saliences should be the key items moderating such a decision. We present empirical evidence to support our theory that dimensional (factor score) based models do better in terms of predictions than attribute based models in more heterogeneous populations. Empirical analysis shows that in segments (where consumer heterogeneity is lower) the predictive performance of attribute based models improves relative to the factor score model and may actually have a better predictive fit when the respondents are relatively homogeneous with respect to attribute ratings and saliences.     

The relevance of interaction choice: Customer preferences and willingness to pay

As the number of available channels and ways to use these channels proliferate, current literature and managerial practice assume that broader interaction choice invariably generates value for customers. In light of the costs and complexity of offering these interaction options, the questions become how important having interaction choice is for customers, how much actual willingness to pay exists, and which customer groups particularly value such choice. To investigate this domain, two choice-based conjoint analyses are implemented in the health insurance industry, which provides a unique research opportunity since regulation naturally limits the relevant attributes of offerings. To cope with the substantial heterogeneity in prices for health insurance depending on the insureds' risks, the methodological innovation of quasi-individual pricing is introduced, which leads to highly satisfactory validity of the estimation results. The results indicate that customers have considerable additional willingness to pay for more interaction choice; however, in contrast to the extant literature, this does not hold for all interaction options. Customers' elicited preference structures further show that health insurers can optimize the configuration and pricing of their offerings to improve customers’ experiences and to create value.     

Issues in the estimation and application of latent structure models of choice

Our paper provides a brief review and summary of issues and advances in the use of latent structure and other finite mixture models in the analysis of choice data. Focus is directed to three primary areas: (1) estimation and computational issues, (2) specification and interpretation issues, and (3) future research issues. We comment on what latent structure models have promised, what has been, to date, delivered, and what we should look forward to in the future.     

The no-choice option and dual response choice designs

Choice set designs that include a constant or no-choice option have increased efficiency, better mimic consumer choices, and allow one to model changes in market size. However, when the no-choice option is selected no information is obtained on the relative attractiveness of the available alternatives. One potential solution to this problem is to use a dual response format in which respondents first choose among a set of available alternatives in a forced-choice task and then choose among the available alternatives and a no-choice option. This paper uses a simulation to demonstrate and confirm the possible gains in efficiency of dual response over traditional choice-based conjoint tasks when there are different proportions choosing the no-choice option. Next, two choice-based conjoint analysis studies find little systematic violation of IIA with the addition/deletion of a no-choice option. Further analysis supports the hypothesis that selection of the no-choice option is more closely related to choice set attractiveness than to decision difficulty. Finally, validation evidence is presented. Our findings show that researchers can employ the dual response approach, taking advantages of the increased power of estimation, without concern for systematically biasing the resulting parameter estimates. Hence, we argue this is a valuable approach when there is the possibility of a large number of no-choices and preference heterogeneity.     

On the choice of in-house production versus outsourcing by multinationals

Abstract

The global economy is becoming more integrated with the increase in international fragmentation. This paper examines two forms of global production networks in a general equilibrium framework by building on the ‘knowledge-capital model.’ The focus is the relationship between country characteristics and the multinational firm's choice either to allocate the labor-intensive processing stage in-house to its foreign affiliates or to outsource the activity to outside contractors at arm's-length. Chinese data on the export processing trade are used to test the theory. The findings show that multinational firms with their headquarters in highly skilled-labor-abundant countries of intermediate size have a preference for outsourcing. By contrast, skilled-labor-abundant countries of small size are homes to multinational firms with subsidiary production in the host country where unskilled labor is cheap.     

Exploring the choice between in-store versus online grocery shopping through an application of Semi-Compensatory Independent Availability Logit (SCIAL) model with latent variables

This paper examines individuals' choice of in-store and online grocery shopping channels using stated preference (SP) choice experiments. The study uses 1,391 records from a stated preference choice experiment in the Greater Toronto Area (GTA), Canada. It applies a Semi-Compensatory Independent Availability Logit (SCIAL) Model with latent variables. The methodology accounts for semi-compensatory choice behaviour through probabilistic choice set formation considering effects from socioeconomic and psychological variables. This study demonstrates the advantage of considering probabilistic choice set formation and semi-compensatory behaviour in modelling the adoption of innovative products. Empirical results reveal that shoppers demonstrated similar myopic behaviours once they firmly considered in-store grocery and subscribed free delivery services in their choice sets. They are equally likely to choose both channels without careful comparison to alternative channels once they firmly consider both channels in the choice set. However, considering the latter in choice sets is much costlier than in-store shopping. Therefore, in-store grocery shopping will still dominate the grocery shopping channel unless all home delivery services become free. Moreover, grocery shoppers value same-day delivery service. For typical delivery services charged between $4 and $20 in the GTA, Canada, grocery shoppers are willing to pay between $3.91 and $8.44 for same-day delivery. The latent variable describing shoppers’ perceived pandemic fear significantly contributes to the choice set inclusion probability of in-store grocery pick-up services, but the effect is not significant for other home delivery channels. This highlights heterogeneity in grocery shoppers' choice behaviour within the online channel.     

Behavioral frontiers in choice modeling

We review the discussion at a workshop whose goal was to achieve a better integration among behavioral, economic, and statistical approaches to choice modeling. The workshop explored how current approaches to the specification, estimation, and application of choice models might be improved to better capture the diversity of processes that are postulated to explain how consumers make choices. Some specific challenges include how to capture and parsimoniously describe heterogeneous mixes of heuristic choice rules, methods for building realistic models of choice, and nontraditional methods for estimating models. An agenda for important future work in these areas is also proposed.     

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.     

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.