GENFOLD2: A set of models and algorithms for the general UnFOLDing analysis of preference/dominance data

A general set of multidimensional unfolding models and algorithms is presented to analyze preference or dominance data. This class of models termed GENFOLD2 (GENeral UnFOLDing Analysis-Version 2) allows one to perform internal or external analysis, constrained or unconstrained analysis, conditional or unconditional analysis, metric or nonmetric analysis, while providing the flexibility of specifying and/or testing a variety of different types of unfolding-type preference models mentioned in the literature including Caroll's (1972, 1980) simple, weighted, and general unfolding analysis. An alternating weighted least-squares algorithm is utilized and discussed in terms of preventing degenerate solutions in the estimation of the specified parameters. Finally, two applications of this new method are discussed concerning preference data for ten brands of pain relievers and twelve models of residential communication devices.

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

[2]  Forrest W. Young,et al.  Nonmetric individual differences multidimensional scaling: An alternating least squares method with optimal scaling features , 1977 .

[3]  J. Ramsay Some Statistical Approaches to Multidimensional Scaling Data , 1982 .

[4]  Allan D. Shocker,et al.  Linear programming techniques for multidimensional analysis of preferences , 1973 .

[5]  J. Kruskal Nonmetric multidimensional scaling: A numerical method , 1964 .

[6]  J. Davidson A geometrical analysis of the unfolding model: General solutions , 1973 .

[7]  R. J. Dakin,et al.  A tree-search algorithm for mixed integer programming problems , 1965, Comput. J..

[8]  R. Duncan Luce,et al.  Individual Choice Behavior , 1959 .

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

[10]  Brian W. Kernighan,et al.  An Effective Heuristic Algorithm for the Traveling-Salesman Problem , 1973, Oper. Res..

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

[12]  Wayne S. DeSarbo,et al.  Three-Way Metric Unfolding , 1981 .

[13]  Forrest W. Young Computer program abstracts , 1968 .

[14]  P. Schönemann ON METRIC MULTIDIMENSIONAL UNFOLDING , 1970 .

[15]  N. Cliff,et al.  A generalization of the interpoint distance model , 1964 .

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

[17]  Roger Fletcher,et al.  A Rapidly Convergent Descent Method for Minimization , 1963, Comput. J..

[18]  W. DeSarbo Gennclus: New models for general nonhierarchical clustering analysis , 1982 .

[19]  Philip E. Gill,et al.  Practical optimization , 1981 .

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

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

[22]  C. Lawson,et al.  Solving least squares problems , 1976, Classics in applied mathematics.

[23]  Leon Cooper,et al.  Introduction to Methods of Optimization , 1970 .

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

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

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

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

[28]  I. Borg,et al.  A model and algorithm for multidimensional scaling with external constraints on the distances , 1980 .

[29]  A geometrical analysis of the unfolding model: Nondegenerate solutions , 1972 .

[30]  J. Johnston,et al.  Econometric Methods, 2nd Ed. , 1976 .

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

[32]  Louis Guttman,et al.  The Guttman-Lingoes nonmetric program series , 1973 .

[33]  C H COOMBS,et al.  Psychological scaling without a unit of measurement. , 1950, Psychological review.

[34]  W. DeSarbo,et al.  The representation of three-way proximity data by single and multiple tree structure models , 1984 .

[35]  Paul E. Green,et al.  AN ALTERNATING LEAST‐SQUARES PROCEDURE FOR ESTIMATING MISSING PREFERENCE DATA IN PRODUCT‐CONCEPT TESTING* , 1986 .

[36]  J. Kruskal Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis , 1964 .

[37]  Mark L. Davison,et al.  Fitting and testing carroll's weighted unfolding model for preferences , 1976 .

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