Multivariate thurstonian models

The recent development of probabilistic Thurstonian choice models for analyzing preference data has been motivated by the need to describe both inter- and intra-individual difference, the multidimensional nature of choice objects, and the effects of similarity and comparability among choice objects. A common feature of these models is that they focus on asingle preference judgment. It is customary, however, to ask subjects not only for an overall preference judgment but also for additional paired comparison responses regarding specific attributes. This paper proposes a generalization of Thurstonian probabilistic choice models for analyzing both multiple preference responses and their relationships. The approach is illustrated by modeling data from two multivariate preference experiments.

[1]  Yoshio Takane,et al.  MAXIMUM LIKELIHOOD ESTIMATION IN THE GENERALIZED CASE OF THURSTONE'S MODEL OF COMPARATIVE JUDGMENT , 1980 .

[2]  R. A. Bradley,et al.  Rank Analysis of Incomplete Block Designs: I. The Method of Paired Comparisons , 1952 .

[3]  Wolfgang Gaul,et al.  Analysis of choice behaviour via probabilistic ideal point and vector models , 1986 .

[4]  Monica A. Walker,et al.  Studies in Item Analysis and Prediction. , 1962 .

[5]  B. Muthén.  Contributions to factor analysis of dichotomous variables , 1978 .

[6]  B. Muthén.  Latent variable structural equation modeling with categorical data , 1983 .

[7]  Paul W. Holland,et al.  The Dutch Identity: A New Tool for the Study of Item Response Models. , 1990 .

[8]  H. Halff.  Choice theories for differentially comparable alternatives , 1976 .

[9]  R. A. Bradley,et al.  RANK ANALYSIS OF INCOMPLETE BLOCK DESIGNS THE METHOD OF PAIRED COMPARISONS , 1952 .

[10]  Norman L. Johnson,et al.  On some generalized farlie-gumbel-morgenstern distributions , 1975 .

[11]  G. Soete.  On the relation between two generalized cases of Thurstone's law of comparative judgment , 1983 .

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

[13]  Ralph A. Bradley,et al.  14 Paired comparisons: Some basic procedures and examples , 1984, Nonparametric Methods.

[14]  M. Schervish.  Multivariate normal probabilities with error bound , 1984 .

[15]  B. Bloxom.  The simplex in pair comparisons , 1972 .

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

[17]  R. Beaver,et al.  Models for multivariate paired comparison experiments with ties , 1982 .

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

[19]  Anders Christoffersson,et al.  Factor analysis of dichotomized variables , 1975 .

[20]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[21]  N. L. Johnson,et al.  On some generalized farlie-gumbel-morgenstern distributions-II regression, correlation and further generalizations , 1977 .

[22]  Ralph A. Bradley,et al.  Multivariate paired comparisons: The extension of a univariate model and associated estimation and test procedures , 1969 .

[23]  Willem J. Heiser,et al.  Multidimensional mapping of preference data , 1981 .

[24]  M. R. Novick,et al.  Statistical Theories of Mental Test Scores. , 1971 .

[25]  L. A. Goodman.  THE ANALYSIS OF A SET OF MULTIDIMENSIONAL CONTINGENCY TABLES USING LOG-LINEAR MODELS, LATENT-CLASS MODELS, AND CORRELATION MODELS: THE SOLOMON DATA REVISITED , 1987 .

[26]  S. Fienberg,et al.  Log linear representation for paired and multiple comparisons models , 1976 .

[27]  R. Beaver.  Log linear models for multivariate paired comparison experiments with ties , 1983 .

[28]  Yoshio Takane,et al.  Analysis of Covariance Structures and Probabilistic Binary Choice Data , 1989 .

[29]  R. Luce,et al.  The Choice Axiom after Twenty Years , 1977 .

[30]  Ulf Böckenholt,et al.  A logistic representation of multivariate paired-comparison models , 1988 .

[31]  Michael G. Langdon,et al.  Improved Algorithms for Estimating Choice Probabilities in the Multinomial Probit Model , 1984, Transp. Sci..

[32]  Jan de Leeuw,et al.  On the relationship between item response theory and factor analysis of discretized variables , 1987 .