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  • 1
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; paired comparisons data ; maximum likelihood estimation ; microeconomics ; consumer psychology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; binary data analysis ; maximum likelihood estimation ; stochastic models ; consumer psychology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1860-0980
    Keywords: binary data analysis ; multidimensional scaling ; nonlinear probit model
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract This paper presents a new stochastic multidimensional scaling vector threshold model designed to analyze “pick any/n” choice data (e.g., consumers rendering buy/no buy decisions concerning a number of actual products). A maximum likelihood procedure is formulated to estimate a joint space of both individuals (represented as vectors) and stimuli (represented as points). The relevant psychometric literature concerning the spatial treatment of such binary choice data is reviewed. The nonlinear probit type model is described, as well as the conjugate gradient procedure used to estimate parameters. Results of Monte Carlo analyses investigating the performance of this methodology with synthetic choice data sets are presented. An application concerning consumer choices for eleven competitive brands of soft drinks is discussed. Finally, directions for future research are presented in terms of further applications and generalizing the model to accommodate three-way choice data.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Psychometrika 50 (1985), S. 275-300 
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; unfolding ; preference analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract Three-way unfolding was developed by DeSarbo (1978) and reported in DeSarbo and Carroll (1980, 1981) as a new model to accommodate the analysis of two-mode three-way data (e.g., nonsymmetric proximities for stimulus objects collected over time) and three-mode, three-way data (e.g., subjects rendering preference judgments for various stimuli in different usage occasions or situations). This paper presents a revised objective function and new algorithm which attempt to prevent the common type of degenerate solutions encountered in typical unfolding analysis. We begin with an introduction of the problem and a review of three-way unfolding. The three-way unfolding model, weighted objective function, and new algorithm are presented. Monte Carlo work via a fractional factorial experimental design is described investigating the effect of several data and model factors on overall algorithm performance. Finally, three applications of the methodology are reported illustrating the flexibility and robustness of the procedure.
    Type of Medium: Electronic Resource
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  • 5
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; cluster analysis ; maximum likelihood estimation ; consumer psychology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract 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 andK vectors, one for each cluster or group, in aT-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.
    Type of Medium: Electronic Resource
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  • 6
    ISSN: 1860-0980
    Keywords: multidimensional scaling ; asymmetric proximity data ; Tversky's contrast model ; consumer psychology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract 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 soft-drinks. Finally, other applications and directions for future research are mentioned.
    Type of Medium: Electronic Resource
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  • 7
    ISSN: 1860-0980
    Keywords: consumer psychology ; multidimensional scaling ; maximum likelihood ; consideration sets ; multidimensional unfolding ; successive categories analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Psychology
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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