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Model-based market segmentation analyses often involve an ordinal dependent variable as ordinal responses are frequently collected in marketing research. In the Bayesian segmentation literature, there are models for an interval- or ratio-scaled dependent variable but there is not any general model for an ordinal dependent variable. In this manuscript, the authors propose a new Bayesian procedure to simultaneously perform segmentation and ordinal regression with variable selection within each derived segment. The procedure is robust to outliers and it also provides an option to include concomitant variables that allows the simultaneous profiling of the derived segments. The authors demonstrate that the practice of treating ordinal responses as interval- or ratio-scales to apply existing Bayesian segmentation procedures can lead to very misleading results and conclusions. Through simulation studies, the authors show that the proposed procedure outperforms several benchmark Bayesian segmentation models in parameter recovery, segment retention, and segment membership prediction for such data. Finally, they provide a commercial business customer satisfaction empirical application to illustrate the usefulness of the proposed model.

We propose a new spatial modeling approach to calibrate the potential impact of spatial dependency and heterogeneity on the underlying drivers of customer service and/or satisfaction measurement. The newly proposed procedure derives regionally varying coefficients, provides more flexible fitting, improves calibration fit and predictive validation, and can potentially result in augmented managerial implications compared to existing procedures by utilizing a hierarchical Bayes framework with geographical boundary effects. Using synthetic datasets, we illustrate how the proposed model outperforms four relevant benchmark models including ordinary linear regression, a Spatially Dependent Segmentation model (Govind, Rabikar, and Mittal 2018), classic Geographically Weighted Regression, and Bayesian Geographically Weighted Regression. The improved performance is most prominent when there exist significant differences between geographic boundaries and/or irregular patterns of observation locations. In our automobile customer satisfaction application study, the proposed approach also demonstrates favorable performance compared to these benchmark models. We find a dramatically heterogeneous pattern regarding two covariates in the Mountain U.S. geographic division: dealership service is more important in urban areas (e.g., Phoenix, Salt Lake City and Denver) than in rural areas, but vice-versa concerning vehicle quality.

Assessing market structure by deriving a brand positioning map and segmenting customers is essential for supporting brand-related marketing decisions. We propose adaptive multidimensional scaling (ADMDS) for simultaneously deriving a brand positioning map and market segments using customer data on cognitive decision sets and brand dissimilarities. In ADMDS, the judgment task is adapted to the individual customer where dissimilarity judgments are collected only for those brands within a customers’ awareness set. Thus, respondent fatigue and unfamiliarity with the brands are circumvented thereby improving the validity of the dissimilarity data obtained, as well as the multidimensional spatial structure derived from them. Estimation of the ADMDS model results in a spatial map in which the brands and derived segments of customers are jointly represented as points. The closer a brand is positioned to a segment’s ideal brand, the higher the probability that the brand is considered and chosen. An assumption underlying this model representation is that brands within a customers’ consideration set are relatively similar. In an experiment with 200 respondents and 4 product categories, this assumption is validated. We illustrate adaptive multidimensional scaling model on commercial data for 20 midsize car brands evaluated by 212 members of an on-line consumer panel. Potential applications of the method and future research opportunities are discussed.

The field of marketing has made significant strides over the past 50 years in understanding how methodological choices affect the validity of conclusions drawn from our research. This paper highlights some of these and is organized as follows: We first summarize essential concepts about measurement and the role of cumulating knowledge, then highlight data and analysis methods in terms of their past, present, and future. Lastly, we provide specific examples of the evolution of work on segmentation and brand equity. With relatively well-established methods for measuring constructs, analysis methods have evolved substantially. There have been significant changes in what is seen as the best way to analyze individual studies as well as accumulate knowledge across them via meta-analysis. Collaborations between academia and business can move marketing research forward. These will require the tradeoffs between model prediction and interpretation, and a balance between large-scale use of data and privacy concerns.

Consumer dispersion analysis divides aggregate markets into smaller geographic units that marketers can target with their promotional mix. However, dispersion patterns are not always contiguous. Using survey data from National Football League (NFL) fans, we introduce a new hierarchical expectation-maximization (EM) bi-level clustering model that iteratively classifies both teams and fans (nested within teams) based on the spatial heterogeneity of fans in terms of both distance and direction. The proposed multi-level latent class model with a variable number of classes at the lower level outperforms benchmark models in a Monte Carlo simulation study and points to three non-contiguous team segments with a varying number of fan group vectors in the NFL application. We present these results in two-dimensional consumer dispersion maps and report corresponding differences in consumer behavior.

Graphical models have received an increasing amount of attention in network psychometrics as a promising probabilistic approach to study the conditional relations among variables using graph theory. Despite recent advances, existing methods on graphical models usually assume a homogeneous population and focus on binary or continuous variables. However, ordinal variables are very popular in many areas of psychological science, and the population often consists of several different groups based on the heterogeneity in ordinal data. Driven by these needs, we introduce the finite mixture of ordinal graphical models to effectively study the heterogeneous conditional dependence relationships of ordinal data. We develop a penalized likelihood approach for model estimation, and design a generalized expectation-maximization (EM) algorithm to solve the significant computational challenges. We examine the performance of the proposed method and algorithm in simulation studies. Moreover, we demonstrate the potential usefulness of the proposed method in psychological science through a real application concerning the interests and attitudes related to fan avidity for students in a large public university in the United States.

The hidden Markov model (HMM) provides a framework to model the time-varying effects of marketing mix variables. When employed in a panel data context, it is important to properly account for unobserved heterogeneity across individuals. We propose a new random coefficients mixture HMM (RCMHMM) that allows for flexible patterns of unobserved heterogeneity in both the state-dependent and transition parameters. The RCMHMM nests all HMMs found in the marketing literature. Results of two simulation studies demonstrate that 1) averaging across a large number of different data generating processes, the RCMHMM outperforms all its nested versions using both in-sample and out-of-sample performance and 2) the RCMHMM is more robust than its nested versions when underlying model assumptions are violated. In addition, we apply the RCMHMM to an empirical application where we examine the effectiveness of in-game promotions in increasing the short-term demand for Major League Baseball (MLB) attendance. We find that the effectiveness of four promotional categories varies over the course of the season and across teams and that the RCMHMM performs best.

Consumers’ preferences for various product attributes change over time. Modeling such temporal changes through a single process assumes that all the attributes’ preferences change together with the same dynamics; however, this assumption is not appropriate when there are several processes with distinct characteristics. We propose a new non-homogeneous factorial hidden Markov model (FHMM) for choice models to dynamically segment consumers into distinct states while each preference parameter may follow a distinct Markov process. The transition probabilities are modeled as time-varying at the individual level, affected by covariates of a feedback term of the consumer’s previous purchase decision, specific to each Markov process. We motivate the proposed approach by an application to a scanner panel choice dataset and find two processes with entirely different characteristics governing the shifts in two preference attributes. Model fit and prediction power based on Brier scores show the superiority of the proposed non-homogeneous FHMM in capturing temporal changes in preferences compared to a traditional hidden Markov model as well as a benchmark comparison model.

There is a vast behavioral decision theory literature that suggests different individuals may utilize and/or weigh different attributes of an object to form the basis of their opinions, attitudes, choices, and/or evaluations of such stimuli. This heterogeneity of information utilization and importance can be due to several different factors such as differing goals, level of expertise, contextual factors, knowledge accessibility, time pressure, involvement, mood states, task complexity, communication or influence of relevant others, etc. This phenomenon is particularly pertinent to the evaluation of stimuli involving large numbers of underlying attributes or features. We propose a new hierarchical Bayesian multivariate probit mixture model with variable selection accommodating such forms of choice heterogeneity. Based on a Monte Carlo simulation study, we demonstrate that the proposed model can successfully recover true parameters in a robust manner. Next, we provide a consumer psychology application involving consideration to buy choices for intended consumers of large Sports Utility Vehicles. The application illustrates that the proposed model outperforms several comparison benchmark choice models with respect to face validity and choice predictive validation performance.

While the sport industry is a multibillion dollar industry, there is a paucity of academic marketing research regarding the various aspects of the industry, especially concerning fan avidity—the level of interest, involvement, passion, enthusiasm, and loyalty a fan exhibits to a sport entity. This is somewhat surprising given that avid fans are the lifeblood of any sport organization, spending significantly more money, time, and effort on sport-related products than other consumers. Thus, given its importance to the sport industry, we examine the relationship between fan avidity and its various behavioral manifestations. Recognizing the existence of consumer heterogeneity among fans, we present a new parametric constrained segmentation methodology and corresponding estimation algorithm that incorporates managerial constraints pertinent to the sport industry (or any other industry) while simultaneously segmenting the market and profiling each segment. We conducted a Monte Carlo simulation, which demonstrates the successful performance of the estimation algorithm across various models, data, and error structures. Then, we applied our proposed methodology to college football data for a major US university and found evidence for two distinct market segments. Finally, we performed a series of model comparisons and showed that our parametric constrained segmentation methodology outperforms existing alternatives.

Purpose Joint space multidimensional scaling (MDS) maps are often utilized for positioning analyses and are estimated with survey data of consumer preferences, choices, considerations, intentions, etc. so as to provide a parsimonious spatial depiction of the competitive landscape. However, little attention has been given to the possibility that consumers may display heterogeneity in their information usage (Bettman et al., 1998) and the possible impact this may have on the corresponding estimated joint space maps. This paper aims to address this important issue and proposes a new Bayesian multidimensional unfolding model for the analysis of two or three-way dominance (e.g. preference) data. The authors’ new MDS model explicitly accommodates dimension selection and preference heterogeneity simultaneously in a unified framework. Design/methodology/approach This manuscript introduces a new Bayesian hierarchical spatial MDS model with accompanying Markov chain Monte Carlo algorithm for estimation that explicitly places constraints on a set of scale parameters in such a way as to model a consumer using or not using each latent dimension in forming his/her preferences while at the same time permitting consumers to differentially weigh each utilized latent dimension. In this manner, both preference heterogeneity and dimensionality selection heterogeneity are modeled simultaneously. Findings The superiority of this model over existing spatial models is demonstrated in both the case of simulated data, where the structure of the data is known in advance, as well as in an empirical application/illustration relating to the positioning of digital cameras. In the empirical application/illustration, the policy implications of accounting for the presence of dimensionality selection heterogeneity is shown to be derived from the Bayesian spatial analyses conducted. The results demonstrate that a model that incorporates dimensionality selection heterogeneity outperforms models that cannot recognize that consumers may be selective in the product information that they choose to process. Such results also show that a marketing manager may encounter biased parameter estimates and distorted market structures if he/she ignores such dimensionality selection heterogeneity. Research limitations/implications The proposed Bayesian spatial model provides information regarding how individual consumers utilize each dimension and how the relationship with behavioral variables can help marketers understand the underlying reasons for selective dimensional usage. Further, the proposed approach helps a marketing manager to identify major dimension(s) that could maximize the effect of a change of brand positioning, and thus identify potential opportunities/threats that existing MDS methods cannot provides. Originality/value To date, no existent spatial model utilized for brand positioning can accommodate the various forms of heterogeneity exhibited by real consumers mentioned above. The end result can be very inaccurate and biased portrayals of competitive market structure whose strategy implications may be wrong and non-optimal. Given the role of such spatial models in the classical segmentation-targeting-positioning paradigm which forms the basis of all marketing strategy, the value of such research can be dramatic in many marketing applications, as illustrated in the manuscript via analyses of both synthetic and actual data.

In a sorting task, consumers receive a set of representational items (e.g., products, brands) and sort them into piles such that the items in each pile “go together.” The sorting task is flexible in accommodating different instructions and has been used for decades in exploratory marketing research in brand positioning and categorization. However, no general analytic procedures yet exist for analyzing sorting task data without performing arbitrary transformations to the data that influence the results and insights obtained. This manuscript introduces a flexible framework for analyzing sorting task data, as well as a new optimization approach to identify summary piles, which provide an easy way to explore associations consumers make among a set of items. Using two Monte Carlo simulations and an empirical application of single-serving snacks from a local retailer, the authors demonstrate that the resulting procedure is scalable, can provide additional insights beyond those offered by existing procedures, and requires mere minutes of computational time.

While the smooth transition (ST) model has become popular in business and economics, the treatment of unobserved heterogeneity within these models has received limited attention. We propose a ST finite mixture (STFM) model which simultaneously estimates the presence of time-varying effects and unobserved heterogeneity in a panel data context. Our objective is to accurately recover the heterogeneous effects of our independent variables of interest while simultaneously allowing these effects to vary over time. Accomplishing this objective may provide valuable insights for managers and policy makers. The STFM model nests several well-known ST and threshold models. We develop the specification, estimation, and model selection criteria for the STFM model using Bayesian methods. We also provide a theoretical assessment of the flexibility of the STFM model when the number of regimes grows with the sample size. In an extensive simulation study, we show that ignoring unobserved heterogeneity can lead to distorted parameter estimates, and that the STFM model is fairly robust when underlying model assumptions are violated. Empirically, we estimate the effects of in-game promotions on game attendance in Major League Baseball. Empirical results show that the STFM model outperforms all its nested versions. Supplementary materials for this article are available online.

The Segmentation-Targeting-Positioning (STP) process is the foundation of all marketing strategy. This chapter presents a new constrained clusterwise multidimensional unfolding procedure for performing STP that simultaneously identifies consumer segments, derives a joint space of brand coordinates and segment-level ideal points, and creates a link between specified product attributes and brand locations in the derived joint space. This latter feature permits a variety of policy simulations by brand(s), as well as subsequent positioning optimization and targeting. We first begin with a brief review of the STP framework and optimal product positioning literature. The technical details of the proposed procedure are then presented, as well as a description of the various types of simulations and subsequent optimization that can be performed. An application is provided concerning consumers' intentions to buy various competitive brands of portable telephones. The results of the proposed methodology are then compared to a naive sequential application of multidimensional unfolding, clustering, and correlation/regression analyses with this same communication devices data. Finally, directions for future research are given.

A new Bayesian multinomial probit model is proposed for the analysis of panel choice data. Using a parameter expansion technique, we are able to devise a Markov Chain Monte Carlo algorithm to compute our Bayesian estimates efficiently. We also show that the proposed procedure enables the estimation of individual level coefficients for the single-period multinomial probit model even when the available prior information is vague. We apply our new procedure to consumer purchase data and reanalyze a well-known scanner panel dataset that reveals new substantive insights. In addition, we delineate a number of advantageous features of our proposed procedure over several benchmark models. Finally, through a simulation analysis employing a fractional factorial design, we demonstrate that the results from our proposed model are quite robust with respect to differing factors across various conditions.

This review article provides reflections on the state of the art of research in conjoint analysis—where we came from, where we are, and some directions as to where we might go. We review key articles, mostly contemporary published since 2000, but some classic, drawn from the major marketing as well as various interdisciplinary academic journals to highlight important areas related to conjoint analysis research and identify more recent developments in this area. We develop an organizing framework that attempts to integrate various threads of research in conjoint methods and models. Our goal is to (a) emphasize the major developments in recent years, (b) evaluate these developments, and (c) to identify several potential directions for future research.

Researchers have recently introduced a finite mixture Bayesian regression model to simultaneously identify consumer market segments (heterogeneity) and determine how such segments differ with respect to active regression coefficients (variable selection). This article introduces three extensions of this model to incorporate managerial restrictions (constraints). The authors demonstrate with synthetic data that the new constrained finite mixture Bayesian regression models can be used to identify and represent several constrained heterogeneous response patterns commonly encountered in practice. In addition, they show that the proposed models are more robust against multicollinearity than traditional methods. Finally, to illustrate the proposed models' usefulness, the authors apply the proposed constrained models in the context of a service quality (SERVPERF) survey of National Insurance Company's customers.

Positioning is among a marketer’s preeminent strategic responsibilities. Positioning helps to clarify brand strengths among competitors and identify potential challenges of similar brands and possible substitutability. Assessments of positioning, from initial marketplace efforts to resources directed at modifications and re-positioning, are frequently assisted by the graphical representations of brands in multidimensional space. Such perceptual maps are constructed to reflect the closeness of brands and therefore the extent to which they are seen as interchangeable, versus distances between brands representing their relative positioning distinctiveness. To create perceptual maps, data are frequently obtained that comprise a sample of respondents rating a series of brands with respect to their perceived similarities and differences, as well as the status of each brand along multiple attributes. This research uses the variability inherent in such three-dimensional data to construct confidence regions around point estimates in perceptual maps. Current maps tend to be simply descriptive, with positions reflected by point estimates, but multivariate models including multidimensional scaling and multi-mode factor analysis can be modified to extract the subject heterogeneity and derive inferential perceptual maps. Confidence regions that overlap will indicate more clearly an inference of brand similarity, whereas non-overlapping regions imply statistically differentiated brand perceptions.

The authors propose a new Bayesian latent structure regression model with variable selection to solve various commonly encountered marketing problems related to market segmentation and heterogeneity. The proposed procedure simultaneously performs segmentation and regression analysis within the derived segments, in addition to determining the optimal subset of independent variables per derived segment. The authors present comparative analyses contrasting the performance of the proposed methodology against standard latent class regression and traditional Bayesian finite mixture regression. They demonstrate that their proposed Bayesian model compares favorably with these traditional benchmark models. They then present an actual commercial customer satisfaction study performed for an electric utility company in the southeastern United States, in which they examine the heterogeneous drivers of perceived quality. Finally, they discuss limitations of the research and provide several directions for further research.

The p-median offers an alternative to centroid-based clustering algorithms for identifying unobserved categories. However, existing p-median formulations typically require data aggregation into a single proximity matrix, resulting in masked respondent heterogeneity. A proposed three-way formulation of the p-median problem explicitly considers heterogeneity by identifying groups of individual respondents that perceive similar category structures. Three proposed heuristics for the heterogeneous p-median (HPM) are developed and then illustrated in a consumer psychology context using a sample of undergraduate students who performed a sorting task of major U.S. retailers, as well as a through Monte Carlo analysis.

The sports industry is one of the world's fastest-growing business sectors, and its primary source of revenue is ultimately derived from sports fans. However, little is known about fans' allocations of time, effort, and financial expenditures to the sports they care most about or how they determine their allocations. The objective of our research is to explore the dimensions of sports consumption and fan avidity, and the nature of heterogeneity of such demand aspects vis-à-vis derived market segments. We develop a new constrained latent-structure multidimensional scaling procedure to uncover the underlying dimensions of sports consumption and fan avidity for student college football fans at a large university, and simultaneously derive latent market segments to explore demand heterogeneity. We collected data from a sample of student football fans from a large US public university known for its excellence in college football. We developed 35 expressions of manifestations of fan avidity and investigated how these college fans follow and support their football team. We then extracted four interpretable dimensions and four market segments with the application of this new spatial multidimensional scaling model. This paper discusses the managerial implications of applying this new latent-structure procedure to this college football context.

A variety of joint space multidimensional scaling (MDS) methods have been utilized for the spatial analysis of two- or three-way dominance data involving subjects’ preferences, choices, considerations, intentions, etc. so as to provide a parsimonious spatial depiction of the underlying relevant dimensions, attributes, stimuli, and/or subjects’ utility structures in the same joint space representation. We demonstrate that care must be taken with respect to a key assumption in existent joint space MDS models such that all estimated dimensions are utilized by each and every subject in the sample, as this assumption can lead to serious distortions with respect to the derived joint spaces. We develop a new Bayesian dimension selection methodology for the multidimensional unfolding model which accommodates heterogeneity with respect to such dimensional utilization at the individual subject level for the analysis of two or three-way dominance data. A consumer psychology application regarding the preference for Over-the-Counter (OTC) analgesics is provided. We conclude by discussing the practical implications of the results, as well as directions for future research.

Multiple regression is frequently used across the various social sciences to analyze cross-sectional data. However, it can often times be challenging to justify the assumption of common regression coefficients across all respondents. This manuscript presents a heterogeneous Bayesian regression model that enables the estimation of individual-level-regression coefficients in cross-sectional data involving a single observation per response unit. A Gibbs sampling algorithm is developed to implement the proposed Bayesian methodology. A Monte Carlo simulation study is constructed to assess the performance of the proposed methodology across a number of experimental factors. We then apply the proposed method to analyze data collected from a consumer psychology study that examines the differential importance of price and quality in determining perceived value evaluations.

International audience; Categorization has been extensively studied in both the psychology and marketing literatures. However, very little methodological research has demonstrated the heterogeneity in consumers' unobserved category structures and activations. We propose a new latent structure procedure that simultaneously identifies the unobserved categories that consumers use and represents consumer heterogeneity via different groups of consumers who have activated different unobserved latent categories. The results of an empirical study in Sports Marketing about sports fans' perceptions of various sports illustrates how the proposed methodology can capture heterogeneity at the group level and account for a variety of different category structures.

PurposeThe sports industry is one of the fastest growing business sectors in the world today and its primary source of revenue is derived from fans. Yet, little is known about fans' allocation of time, effort, and/or financial expenditures in regard to the sports they care so desperately about. The purpose of this paper is to explore the multidimensional aspects of such manifestations of fan avidity and examine the nature of heterogeneity of such expressions.Design/methodology/approachData were collected from a student sample of football fans from a well‐known US university.FindingsIn total, 35 different expressions of fan avidity are developed related to how fans follow and support their favorite team. A spatial choice multidimensional scaling model is developed to uncover four latent dimensions of fan avidity expression.Originality/valueThe managerial aspects of these empirical findings are provided, and the authors suggest several directions for future research.

PurposeMultidimensional scaling (MDS) represents a family of various geometric models for the multidimensional representation of the structure in data as well as the corresponding set of methods for fitting such spatial models. Its major uses in business include positioning, market segmentation, new product design, consumer preference analysis, etc. The purpose of this paper is to apply a new stochastic constrained MDS vector model to examine the importance of some 45 different leadership attributes as they impact perceptions of effective leadership practice.Design/methodology/approachThe authors present a new stochastic constrained MDS vector model for the analysis of two‐way dominance data.FindingsThis constrained vector or scalar products model represents the column objects of the input data matrix by points and row objects by vectors in a T‐dimensional derived joint space. Reparameterization options are available for row and/or column representations so as to constrain or reparameterize such objects as functions of designated features or attributes. An iterative maximum likelihood‐based algorithm is devised for efficient parameter estimation.Originality/valueThe authors present an application to a study conducted to examine the importance of leadership attributes as they impact perceptions of effective leadership practice. Implications for future research and limitations are discussed.

PurposeThe paper aims to examine the nature of competition within an industry by proposing and examining three separate sources of competitive heterogeneity: the strategies that industry members use, the performance that they obtain, and how effectively the strategies are utilized to obtain such performance results.Design/methodology/approachTo do so, a restricted latent structure finite mixture model is devised that can quantify the contribution of these three potential sources of heterogeneity in the formulation of latent competitive groups within an industry. The paper illustrate this modeling framework with respect to COMPUSTAT strategy and performance data collected for public banks in the USA.FindingsThe paper shows how traditional conceptualizations via strategic or performance groups are inadequate to fully represent intra‐industry heterogeneity.Originality/valueThis research paper proposes a new class of restricted finite mixture‐based models, which fit a variety of alternative forms/models of heterogeneity. Information heuristics are developed to indicate “best model.”

PurposeCustomer value has recently become a primary focus among many strategy researchers and practitioners as an essential element of a firm's competitive strategy. Many firms are engaged in some form of customer value analysis (CVA), which involves a structural analysis of the antecedent factors of perceived value (i.e. perceived quality and perceived price) to assess their relative importance in the perceptions of their buyers. Previous CVA research has focused upon using aggregate market or market segment level analyses. The purpose of this paper is to expose the limitations of implementing CVA on either an aggregate or market segment level basis, and propose an alternative individual level approach.Design/methodology/approachThe paper develops an extended hierarchical Bayesian approach for cross‐sectional data with one observation per response unit, which allows for estimation at the individual firm level to make CVA more useful. This paper demonstrates the utility of the proposed Bayesian methodology involving a CVA study conducted for a large electric utility company. It also compares the empirical results from aggregate, market segment, and the proposed individual level analyses, and show how traditional approaches mask underlying price and quality importance.FindingsMarketing and management strategy researchers need to exhibit care when conducting such CVA analyses as underlying heterogeneity can be masked when aggregate market or segment level analyses are conducted.Originality/valueThis paper provides a new hierarchical Bayes recursive simultaneous model formulation for CVA analyses to provide individual level insights with cross‐sectional data.

Joint space multidimensional scaling maps are often utilized for positioning analyses and are estimated on survey samples of consumer preferences, choices, considerations, or intentions so as to provide a concise spatial depiction of the competitive landscape including relevant dimensions or attributes, competing brands, and consumers in the same joint space representation. Care has to be given concerning the underlying scale properties of such survey data so as not to distort the resulting joint space positioning map. We present a new joint space multidimensional scaling procedure for positioning analyses for displaying the structure in such survey data when such common ordered successive category measurement scales such as Likert, Edwards, semantic differential, etc., are employed. We present the technical details of this stochastic ordered preference multidimensional scaling vector model as well as the maximum likelihood estimation-based algorithm devised for parameter estimation. Favorable comparisons are made with several existent multidimensional scaling methods in representing the internal structure for such data in marketing positioning studies. An actual commercial positioning application concerning large sports utility vehicles consideration to buy judgments is presented with predictive validation comparisons with other multidimensional scaling joint space procedures.

Multidimensional scaling (MDS) comprises a family of geometric models for the multidimensional representation of data and a corresponding set of methods for fitting such models to actual data. In this paper, we develop a new Bayesian vector MDS model to analyze ordered successive categories preference/dominance data commonly collected in many social science and business studies. A joint spatial representation of the row and column elements of the input data matrix is provided in a reduced dimensionality such that the geometric relationship of the row and column elements renders insight into the utility structure underlying the data. Unlike classical deterministic MDS procedures, the Bayesian method includes a probability based criterion to determine the number of dimensions of the derived joint space map and provides posterior interval as well as point estimates for parameters of interest. Also, our procedure models the raw integer successive categories data which ameliorates the need of any data preproce...

Canonical models of rational choice fail to account for many forms of motivated adaptive behaviors, specifically in domains such as food selections. To describe behavior in such emotion- and reward-laden scenarios, researchers have proposed dual-process models that posit competition between a slower, analytic faculty and a fast, impulsive, emotional faculty. In this paper, we examine the assumptions and limitations of these approaches to modeling motivated choice. We argue that models of this form, though intuitively attractive, are biologically implausible. We describe an approach to motivated choice based on sequential sampling process models that can form a solid theoretical bridge between what is known about brain function and environmental influences upon choice. We further suggest that the complex and dynamic relationships between biology, behavior, and environment affecting choice at the individual level must inform aggregate models of consumer choice. Models using agent-based complex systems may further provide a principled way to relate individual and aggregate consumer choices to the aggregate choices made by businesses and social institutions. We coin the term "brain-to-society systems" choice model for this broad integrative approach.

PurposeThe purpose of this paper is to integrate aspects of the literature on strategic and performance groups and explicitly derive strategic/performance groups which exhibit differences with respect to both strategy and performance, as well as display associations and potential interrelationships between the two sets of variables.Design/methodology/approachA two‐way clusterwise bilinear spatial model was formulated (e.g. a scalar products or vector multidimensional scaling model (MDS)) for the analysis of two‐way strategic and performance data which simultaneously performs MDS and cluster analysis. An efficient alternating least‐squares procedure was devised that estimates conditionally globally optimum estimates of the model parameters within each iterate in analytic, closed‐form expressions.FindingsThis bilinear MDS methodology was deployed in the context of strategic/performance group estimation using archival data for public banks in the NY‐NJ‐PA tri‐state area. For this illustration, four strategic/performance groups and two underlying dimensions were found.Practical implicationsConsideration of both strategy and performance data should be employed in describing the heterogeneity amongst firms competing in the same industry.Originality/valueThe paper provides a new spatial methodology to derive strategic/performance groups in any given industry to more completely summarize intra‐industry heterogeneity.

The segmentation–targeting–positioning conceptual framework has been the traditional foundation and genesis of marketing strategy formulation. The authors propose a general clusterwise bilinear spatial model that simultaneously estimates market segments, their composition, a brand space, and preference/utility vectors per market segment; that is, the model performs segmentation and positioning simultaneously. After a review of related methodological research in the marketing, psychometrics, and classification literature streams, the authors present the technical details of the proposed two-way clusterwise bilinear spatial model. They develop an efficient alternating least squares procedure that estimates conditional globally optimum estimates of the model parameters within each iteration through analytic closed-form expressions. The authors present various model options. They provide a conceptual and empirical comparison with latent-class multidimensional scaling. They use an illustration of the new bilinear multidimensional scaling methodology with an actual commercial study sponsored by a large U.S. automotive manufacturer to examine buying/consideration intentions for small sport-utility vehicles. The authors conclude by summarizing the contributions of this research, discussing the marketing implications for managers, and providing several directions for further research.

Multidimensional scaling (MDS) models for the analysis of dominance data have been developed in the psychometric and classification literature to simultaneously capture subjects’ preference heterogeneity and the underlying dimensional structure for a set of designated stimuli in a parsimonious manner. There are two major types of latent utility models for such MDS models that have been traditionally used to represent subjects’ underlying utility functions: the scalar product or vector model and the ideal point or unfolding model. Although both models have been widely applied in various social science applications, implicit in the assumption of such MDS methods is that all subjects are homogeneous with respect to their underlying utility function; i.e., they all follow a vector model or an ideal point model. We extend these traditional approaches by presenting a Bayesian MDS model that combines both the vector model and the ideal point model in a generalized framework for modeling metric dominance data. This new Bayesian MDS methodology explicitly allows for mixtures of the vector and the ideal point models thereby accounting for both preference heterogeneity and structural heterogeneity. We use a marketing application regarding physicians’ prescription behavior of antidepressant drugs to estimate and compare a variety of spatial models.

The notion of strategic groups has recently emerged as a critical perspective for uncovering firms' strategic postures/recipes and competitive market structures. Firms within strategic groups generally adopt similar strategic recipes and compete more intensely than firms across strategic groups. Building on recent research, the authors develop the concept of hybrid strategic groups, which blend the strategic recipes of more than one group, in contrast to existing conceptualizations of strategic groups, where either firms tightly follow the recipes of a strategic group (i.e., core firms) or firms loosely follow the recipes of a strategic group (i.e., secondary firms). Thus, competition among firms depends not only on the strategic group but also on the overlap of that strategic group with other strategic groups. The authors devise a combinatorial optimization-based classification procedure utilizing a bilinear model that accommodates multiple variable batteries that can estimate hybrid strategic groups. The proposed methodology is illustrated by using archival data on public banks. For this illustration, the hybrid strategic group solution outperforms ordinary cluster analyses and offers critical insights into the nature of competition among firms. Copyright © 2007 John Wiley & Sons, Ltd.

In contrast to Kohlberg's (1969) universal model of moral development, Gilligan's (1982) model posits the existence of separate patterns of moral development for men and women. The pattern for men, termed the "justice ethic," is based on abstract concepts of justice, reciprocity, and individual rights. The pattern for women, termed the "care ethic," is based on responsibility toward others and the preservation of relationships. The purpose of this article is to utilize a recently developed multidimensional scaling methodology to explore the underlying structure of moral reasoning responses to 12 moral dilemmas, developed on the basis of Gilligan's theory, and to relate that structure to individual difference characteristics. Results of findings and implications for future research are discussed.

We introduce a multidimensional scaling procedure that attempts to derive a spatial representation of stimuli unconfounded by the effect of subjects' degrees of familiarity with these stimuli. The proposed model assumes that stimulus unfamiliarity produces a tendency for a subject to anchor his/her dissimilarity judgments towards a reference value on the response scale. The input data needed to perform such analyses are the degree of stimulus familiarity along with the dissimilarity judgments for all pairs of stimuli. In a Monte Carlo study, we investigate the extent to which the procedure recovers known parameters. Furthermore, empirical applications of the model to positioning studies of magazines and banks in the Netherlands are provided.

The growth curve model has been a useful tool for the analysis of repeated measures data. However, it is designed for an aggregate-sample analysis based on the assumption that the entire sample of respondents are from a single homogenous population. Thus, this method may not be suitable when heterogeneous subgroups exist in the population with qualitatively distinct patterns of trajectories. In this paper, the growth curve model is generalized to a fuzzy clustering framework, which explicitly accounts for such group-level heterogeneity in trajectories of change over time. Moreover, the proposed method estimates parameters based on generalized estimating equations thereby relaxing the assumption of correct specification of the population covariance structure among repeated responses. The performance of the proposed method in recovering parameters and the number of clusters is investigated based on two Monte Carlo analyses involving synthetic data. In addition, the empirical usefulness of the proposed method is illustrated by an application concerning the antisocial behavior of a sample of children.

In multidimensional unfolding (MDU), one typically deals with two-way, two-mode dominance data in estimating a joint space representation of row and column objects in a derived Euclidean space. Unfortunately, most unfolding procedures, especially nonmetric ones, are prone to yielding degenerate solutions where the two sets of points (row and column objects) are disjointed or separated in the derived joint space, providing very little insight as to the structure of the input data. We present a new approach to multidimensional unfolding which reduces the occurrence of degenerate solutions. We first describe the technical details of the proposed method. We then conduct a Monte Carlo simulation to demonstrate the superior performance of the proposed model compared to two non-metric procedures, namely, ALSCAL and KYST. Finally, we evaluate the performance of alternative models in two applications. The first application deals with student rank-order preferences (nonmetric data) for attending various graduate business (MBA) programs. Here, we compare the performance of our model with those of KYST and ALSCAL. The second application concerns student preference ratings (metric data) for a number of popular brands of analgesics. Here, we compare the performance of the proposed model with those of two metric procedures, namely, SMACOF-3 and GENFOLD 3. Finally, we provide some directions for future research.

PurposePrincipal components analysis (PCA) is one of the foremost multivariate methods utilized in marketing and business research for data reduction, latent variable modeling, multicollinearity resolution, etc. However, while its optimal properties make PCA solutions unique, interpreting the results of such analyses can be problematic. A plethora of rotation methods are available for such interpretive uses, but there is no theory as to which rotation method should be applied in any given social science problem. In addition, different rotational procedures typically render different interpretive results. The paper aims to introduce restricted PCA (RPCA), which attempts to optimally derive latent components whose coefficients are integer‐constrained (e.g.: {−1,0,1}, {0,1}, etc.).Design/methodology/approachThe paper presents two algorithms for deriving efficient solutions for RPCA: an augmented branch and bound algorithm for sequential extraction, and a combinatorial optimization procedure for simultaneous extraction of these constrained components. The paper then contrasts the traditional PCA‐derived solution with those obtained from both proposed RPCA procedures with respect to a published data set of psychographic variables collected from potential buyers of the Dodge Viper sports car.FindingsThis constraint results in solutions which are easily interpretable with no need for rotation. In addition, the proposed procedure can enhance data reduction efforts since fewer raw variables define each derived component.Originality/valueThe paper provides two algorithms for estimating RPCA solutions from empirical data.

We present a Bayesian change point multiple regression methodology which simultaneously estimates the location of change points/regimes, the corresponding subset of independent variables per regime, as well as the associated regimes’ regression parameters. Unlike existing switching multiple regression models, our method does not require the presence of all independent variables in each regime to detect change points. This allows us to relax the minimum size constraint on each regime as fewer observations are needed to estimate the unknown regression coefficients. Thus our method provides a means to search for small regimes where only a few independent variables are significant. Note that accuracy of change points can drastically affect the identified models within each regime. As the number of change points in the data is typically unknown, we have provided a probability based model selection heuristic to determine its value. Both synthetic and real data sets are utilized to demonstrate that our procedure can yield better fitted models over aggregate OLS regression models and traditional MLE based regime switching models. Furthermore, an actual prescription drug data application involving a promotion response model is used to gainfully illustrate the methodology.