This manuscript introduces a new Bayesian finite mixture methodology for the joint clustering of row and column stimuli/objects associated with two-mode asymmetric proximity, dominance, or profile data. That is, common clusters are derived which partition both the row and column stimuli/objects simultaneously into the same derived set of clusters. In this manner, interrelationships between both sets of entities (rows and columns) are easily ascertained. We describe the technical details of the proposed two-mode clustering methodology including its Bayesian mixture formulation and a Bayes factor heuristic for model selection. We present a modest Monte Carlo analysis to investigate the performance of the proposed Bayesian two-mode clustering procedure with respect to synthetically created data whose structure and parameters are known. Next, a consumer psychology application is provided examining physician pharmaceutical prescription behavior for various brands of prescription drugs in the neuroscience health market. We conclude by discussing several fertile areas for future research.

In many regression applications, users are often faced with difficulties due to nonlinear relationships, heterogeneous subjects, or time series which are best represented by splines. In such applications, two or more regression functions are often necessary to best summarize the underlying structure of the data. Unfortunately, in most cases, it is not known a priori which subset of observations should be approximated with which specific regression function. This paper presents a methodology which simultaneously clusters observations into a preset number of groups and estimates the corresponding regression functions' coefficients, all to optimize a common objective function. We describe the problem and discuss related procedures. A new simulated annealing-based methodology is described as well as program options to accommodate overlapping or nonoverlapping clustering, replications per subject, univariate or multivariate dependent variables, and constraints imposed on cluster membership. Extensive Monte Carlo analyses are reported which investigate the overall performance of the methodology. A consumer psychology application is provided concerning a conjoint analysis investigation of consumer satisfaction determinants. Finally, other applications and extensions of the methodology are discussed.

The standard tobit or censored regression model is typically utilized for regression analysis when the dependent variable is censored. This model is generalized by developing a conditional mixture, maximum likelihood method for latent class censored regression. The proposed method simultaneously estimates separate regression functions and subject membership in K latent classes or groups given a censored dependent variable for a cross-section of subjects. Maximum likelihood estimates are obtained using an EM algorithm. The proposed method is illustrated via a consumer psychology application.

This paper presents a new stochastic multidimensional scaling procedure for the analysis of three-mode, three-way pick any/J data. The method provides either a vector or ideal-point model to represent the structure in such data, as well as “floating” model specifications (e.g., different vectors or ideal points for different choice settings), and various reparameterization options that allow the coordinates of ideal points, vectors, or stimuli to be functions of specified background variables. A maximum likelihood procedure is utilized to estimate a joint space of row and column objects, as well as a set of weights depicting the third mode of the data. An algorithm using a conjugate gradient method with automatic restarts is developed to estimate the parameters of the models. A series of Monte Carlo analyses are carried out to investigate the performance of the algorithm under diverse data and model specification conditions, examine the statistical properties of the associated test statistic, and test the robustness of the procedure to departures from the independence assumptions. Finally, a consumer psychology application assessing the impact of situational influences on consumers' choice behavior is discussed.

We devise a new statistical methodology called constrained stochastic extended redundancy analysis (CSERA) to examine the comparative impact of various conceptual factors, or drivers, as well as the specific predictor variables that contribute to each driver on designated dependent variable(s). The technical details of the proposed methodology, the maximum likelihood estimation algorithm, and model selection heuristics are discussed. A sports marketing consumer psychology application is provided in a Major League Baseball (MLB) context where the effects of six conceptual drivers of game attendance and their defining predictor variables are estimated. Results compare favorably to those obtained using traditional extended redundancy analysis (ERA).

The psychometric and classification literatures have illustrated the fact that a wide class of discrete or network models (e.g., hierarchical or ultrametric trees) for the analysis of ordinal proximity data are plagued by potential degenerate solutions if estimated using traditional nonmetric procedures (i.e., procedures which optimize a STRESS-based criteria of fit and whose solutions are invariant under a monotone transformation of the input data). This paper proposes a new parametric, maximum likelihood based procedure for estimating ultrametric trees for the analysis of conditional rank order proximity data. We present the technical aspects of the model and the estimation algorithm. Some preliminary Monte Carlo results are discussed. A consumer psychology application is provided examining the similarity of fifteen types of snack/breakfast items. Finally, some directions for future research are provided.

The vast majority of existing multidimensional scaling (MDS) procedures devised for the analysis of paired comparison preference/choice judgments are typically based on either scalar product (i.e., vector) or unfolding (i.e., ideal-point) models. Such methods tend to ignore many of the essential components of microeconomic theory including convex indifference curves, constrained utility maximization, demand functions, et cetera. This paper presents a new stochastic MDS procedure called MICROSCALE that attempts to operationalize many of these traditional microeconomic concepts. First, we briefly review several existing MDS models that operate on paired comparisons data, noting the particular nature of the utility functions implied by each class of models. These utility assumptions are then directly contrasted to those of microeconomic theory. The new maximum likelihood based procedure, MICROSCALE, is presented, as well as the technical details of the estimation procedure. The results of a Monte Carlo analysis investigating the performance of the algorithm as a number of model, data, and error factors are experimentally manipulated are provided. Finally, an illustration in consumer psychology concerning a convenience sample of thirty consumers providing paired comparisons judgments for some fourteen brands of over-the-counter analgesics is discussed.

This paper develops a maximum likelihood based method for simultaneously performing multidimensional scaling and cluster analysis on two-way dominance or profile data. This MULTICLUS procedure utilizes mixtures of multivariate conditional normal distributions to estimate a joint space of stimulus coordinates and K vectors, one for each cluster or group, in a T-dimensional space. The conditional mixture, maximum likelihood method is introduced together with an E-M algorithm for parameter estimation. A Monte Carlo analysis is presented to investigate the performance of the algorithm as a number of data, parameter, and error factors are experimentally manipulated. Finally, a consumer psychology application is discussed involving consumer expertise/experience with microcomputers.

This paper presents a new procedure called TREEFAM for estimating ultrametric tree structures from proximity data confounded by differential stimulus familiarity. The objective of the proposed TREEFAM procedure is to quantitatively “filter out” the effects of stimulus unfamiliarity in the estimation of an ultrametric tree. A conditional, alternating maximum likelihood procedure is formulated to simultaneously estimate an ultrametric tree, under the unobserved condition of complete stimulus familiarity, and subject-specific parameters capturing the adjustments due to differential unfamiliarity. We demonstrate the performance of the TREEFAM procedure under a variety of alternative conditions via a modest Monte Carlo experimental study. An empirical application provides evidence that the TREEFAM outperforms traditional models that ignore the effects of unfamiliarity in terms of superior tree recovery and overall goodness-of-fit.

We propose a two-way Bayesian vector spatial procedure incorporating dimension reparameterization with a variable selection option to determine the dimensionality and simultaneously identify the significant covariates that help interpret the derived dimensions in the joint space map. We discuss how we solve identifiability problems in a Bayesian context that are associated with the two-way vector spatial model, and demonstrate through a simulation study how our proposed model outperforms a popular benchmark model. In addition, an empirical application dealing with consumers’ ratings of large sport utility vehicles is presented to illustrate the proposed methodology. We are able to obtain interpretable and managerially insightful results from our proposed model with variable selection in comparison with the benchmark model.

We introduce a new statistical procedure for the identification of unobserved categories that vary between individuals and in which objects may span multiple categories. This procedure can be used to analyze data from a proposed sorting task in which individuals may simultaneously assign objects to multiple piles. The results of a synthetic example and a consumer psychology study involving categories of restaurant brands illustrate how the application of the proposed methodology to the new sorting task can account for a variety of categorization phenomena including multiple category memberships and for heterogeneity through individual differences in the saliency of latent category structures.

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.

A cyclical conditional maximum likelihood estimation procedure is developed for the multidimensional unfolding of two- or three-way dominance data (e.g., preference, choice, consideration) measured on ordered successive category rating scales. The technical description of the proposed model and estimation procedure are discussed, as well as the rather unique joint spaces derived. We then conduct a modest Monte Carlo simulation to demonstrate the parameter recovery of the proposed methodology, as well as investigate the performance of various information heuristics for dimension selection. A consumer psychology application is provided where the spatial results of the proposed model are compared to solutions derived from various traditional multidimensional unfolding procedures. This application deals with consumers intending to buy new luxury sport-utility vehicles (SUVs). Finally, directions for future research are discussed.

This paper presents a stochastic multidimensional unfolding (MDU) procedure to spatially represent individual differences in phased or sequential decision processes. The specific application or scenario to be discussed involves the area of consumer psychology where consumers form judgments sequentially in their awareness, consideration, and choice set compositions in a phased or sequential manner as more information about the alternative brands in a designated product/service class are collected. A brief review of the consumer psychology literature on these nested congnitive sets as stages in phased decision making is provided. The technical details of the proposed model, maximum likelihood estimation framework, and algorithm are then discussed. A small scale Monte Carlo analysis is presented to demonstrate estimation proficiency and the appropriateness of the proposed model selection heuristic. An application of the methodology to capture awareness, consideration, and choice sets in graduate school applicants is presented. Finally, directions for future research and other potential applications are given.

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.

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.

Tversky's contrast model of proximity was initially formulated to account for the observed violations of the metric axioms often found in empirical proximity data. This set-theoretic approach models the similarity/dissimilarity between any two stimuli as a linear (or ratio) combination of measures of the common and distinctive features of the two stimuli. This paper proposes a new spatial multidimensional scaling (MDS) procedure called TSCALE based on Tversky's linear contrast model for the analysis of generally asymmetric three-way, two-mode proximity data. We first review the basic structure of Tversky's conceptual contrast model. A brief discussion of alternative MDS procedures to accommodate asymmetric proximity data is also provided. The technical details of the TSCALE procedure are given, as well as the program options that allow for the estimation of a number of different model specifications. The nonlinear estimation framework is discussed, as are the results of a modest Monte Carlo analysis. Two consumer psychology applications are provided: one involving perceptions of fast-food restaurants and the other regarding perceptions of various competitive brands of cola softdrinks. Finally, other applications and directions for future research are mentioned.

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.