A New Stochastic Multidimensional Unfolding Model for the Investigation of Paired Comparison Consumer Preference/Choice Data

This paper presents the development of a new stochastic multidimensional (scaling) unfolding (Coombs 1964) methodology which operates on paired comparison consumer preference or choice data and renders a spatial representation of both consumers and the products or brands they choose. Consumers are represented as ideal points and products as points in a T-dimensional space, where the Euclidean distance between the product points and the consumer ideal points provide information as to the utility of such products to these consumers. The econometric and psychometric literature concerning related models which also operate on such paired comparisons data is reviewed, and a technical description of the new methodology is provided. To illustrate the versatility of the model, a small application measuring consumer preference for several actual brands of over-the-counter analgesics, utilizing one of the optional reparametrized models, is described. Finally, future areas of further research are identified.

[1]  Geert De Soete,et al.  The Wandering Ideal Point Model: A Probabilistic Multidimensional Unfolding Model for Paired Comparisons Data , 1986 .

[2]  Wayne S. DeSarbo,et al.  A Probabilistic Multidimensional Scaling Vector Model , 1986 .

[3]  Bruce Bloxom,et al.  Constrained multidimensional scaling inN spaces , 1978 .

[4]  Lyle V. Jones,et al.  The Measurement and Prediction of Judgement and Choice , 1971 .

[5]  Geert De Soete,et al.  A maximum likelihood method for fitting the wandering vector model , 1983 .

[6]  Peter Schmidt,et al.  The Theory and Practice of Econometrics , 1985 .

[7]  Lee G. Cooper,et al.  Two logit models for external analysis of preferences , 1983 .

[8]  G. Judge,et al.  The Theory and Practice of Econometrics , 1981 .

[9]  C. Coombs.  A theory of data. , 1965, Psychology Review.

[10]  Wayne S. DeSarbo,et al.  Two-Way Spatial Methods For Modeling Individual Differences in Preference , 1985 .

[11]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[12]  Elliot Noma,et al.  Constraining Nonmetric Multidimensional Scaling Configurations. , 1977 .

[13]  F. Sixtl.  Probabilistic unfolding , 1973 .

[14]  D. McFadden.  Quantal Choice Analysis: A Survey , 1976 .

[15]  Joseph L. Zinnes,et al.  A double law of comparative judgment for the analysis of preferential choice and similarities data , 1961 .

[16]  J. Kruskal,et al.  Candelinc: A general approach to multidimensional analysis of many-way arrays with linear constraints on parameters , 1980 .

[17]  W. DeSarbo,et al.  Three-way metric unfolding via alternating weighted least squares , 1985 .

[18]  Gordon G. Bechtel,et al.  A scalar product model for the multidimensional scaling of choice , 1971 .

[19]  P. Schönemann,et al.  A Conjugate Gradient Algorithm for the Multidimensional Analysis of Preference Data. , 1975, Multivariate behavioral research.

[20]  Joseph L. Zinnes,et al.  Probabilistic multidimensional scaling: Complete and incomplete data , 1983 .

[21]  L. V. Jones,et al.  The measurement and prediction of judgment and choice. , 1970 .

[22]  Erling B. Andersen,et al.  Discrete Statistical Models with Social Science Applications. , 1980 .

[23]  Gordon G. Bechtel,et al.  Multidimensional preference scaling , 1976 .

[24]  Eugene Galanter,et al.  Handbook of mathematical psychology: I. , 1963 .

[25]  Patrick Slater,et al.  THE ANALYSIS OF PERSONAL PREFERENCES , 1960 .

[26]  Wayne S. DeSarbo,et al.  Three-Way Multivariate Conjoint Analysis , 1982 .

[27]  C. M. Reeves,et al.  Function minimization by conjugate gradients , 1964, Comput. J..

[28]  Joseph L. Zinnes,et al.  Theory and Methods of Scaling. , 1958 .

[29]  Singiresu S. Rao,et al.  Optimization Theory and Applications , 1980, IEEE Transactions on Systems, Man, and Cybernetics.

[30]  A. Mclntosh.  The Conjugate Gradient Algorithm , 1982 .

[31]  V. Rao,et al.  GENFOLD2: A set of models and algorithms for the general UnFOLDing analysis of preference/dominance data , 1984 .

[32]  D. G. Weeks,et al.  Restricted multidimensional scaling models , 1978 .

[33]  Joseph L. Zinnes,et al.  Probabilistic, multidimensional unfolding analysis , 1974 .

[34]  W. Hays,et al.  Multidimensional unfolding: Determining the dimensionality of ranked preference data , 1960 .

[35]  Willem J. Heiser,et al.  Constrained Multidimensional Scaling, Including Confirmation , 1983 .

[36]  M. J. D. Powell,et al.  Restart procedures for the conjugate gradient method , 1977, Math. Program..

[37]  R. Courant.  Differential and Integral Calculus , 1935 .

[38]  Wayne S. DeSarbo,et al.  A Constrained Unfolding Methodology for Product Positioning , 1986 .

[39]  Ming-Mei Wang,et al.  An individual difference model for the multidimensional analysis of preference data , 1972 .

[40]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[41]  H. A. David,et al.  The method of paired comparisons , 1966 .

[42]  David Mautner Himmelblau,et al.  Applied Nonlinear Programming , 1972 .

[43]  Joseph L. Zinnes,et al.  Single and multidimensional same-different judgments , 1977 .

[44]  Gordon G. Bechtel,et al.  Folded and unfolded scaling from preferential paired comparisons , 1968 .

[45]  R. Goodstein,et al.  Differential and Integral Calculus , 1947 .

[46]  Arnold Zellner,et al.  JOINT ESTIMATION OF RELATIONSHIPS INVOLVING DISCRETE RANDOM VARIABLES , 1965 .