Estimating Independent Locally Shifted Random Utility Models for Ranking Data

We consider the estimation of probabilistic ranking models in the context of conjoint experiments. By using approximate rather than exact ranking probabilities, we avoided the computation of high-dimensional integrals. We extended the approximation technique proposed by Henery (1981) in the context of the Thurstone-Mosteller-Daniels model to any independent locally shifted random utility model. In particular, this allowed us to estimate any independent random utility model with common shape (e.g., normal, logistic) and scale. Moreover, our approach also allows for the analysis of any partial ranking. Partial rankings are essential in practical conjoint analysis to collect data efficiently to relieve respondents' task burden. We applied the approach to the reanalysis of the career preference data set described in Maydeu-Olivares and Böckenholt (2005), and to a holiday preferences data set.

[1]  Joseph S. Verducci,et al.  Probability models on rankings. , 1991 .

[2]  Richard M. Johnson.  Trade-Off Analysis of Consumer Values , 1974 .

[3]  Ulf Böckenholt,et al.  Thurstonian-Based Analyses: Past, Present, and Future Utilities , 2006, Psychometrika.

[4]  J. Louviere,et al.  Determining the Appropriate Response to Evidence of Public Concern: The Case of Food Safety , 1992 .

[5]  K. Chrzan,et al.  An Empirical Test of Six Stated Importance Measures , 2006 .

[6]  Moshe Ben-Akiva,et al.  Analysis of the reliability of preference ranking data , 1991 .

[7]  T. Peters,et al.  Best--worst scaling: What it can do for health care research and how to do it. , 2007, Journal of health economics.

[8]  Vithala R. Rao,et al.  Conjoint Measurement- for Quantifying Judgmental Data , 1971 .

[9]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[10]  Alberto Maydeu-Olivares,et al.  Identification and Small Sample Estimation of Thurstone's Unrestricted Model for Paired Comparisons Data , 2007, Multivariate behavioral research.

[11]  Milton Abramowitz,et al.  Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables , 1964 .

[12]  A. Tversky,et al.  Conjoint-measurement analysis of composition rules in psychology. , 1971 .

[13]  R. Plackett.  The Analysis of Permutations , 1975 .

[14]  P. Green,et al.  Conjoint Analysis in Consumer Research: Issues and Outlook , 1978 .

[15]  P. Sen,et al.  Theory of rank tests , 1969 .

[16]  L. Thurstone.  Rank order as a psycho-physical method. , 1931 .

[17]  Ulf Böckenholt,et al.  Structural equation modeling of paired-comparison and ranking data. , 2005, Psychological methods.

[18]  H. Joe.  Multivariate models and dependence concepts , 1998 .

[19]  J. Kruskal.  Analysis of Factorial Experiments by Estimating Monotone Transformations of the Data , 1965 .

[20]  R. J. Henery,et al.  Permutation Probabilities as Models for Horse Races , 1981 .

[21]  J. Marden.  Analyzing and Modeling Rank Data , 1996 .

[22]  L. Thurstone.  A law of comparative judgment. , 1994 .

[23]  H. Harter.  Expected values of normal order statistics , 1961 .

[24]  Harmen Oppewal,et al.  Effects of Package Holiday Information Presentation on Destination Choice , 2008 .

[25]  P. Krishnaiah,et al.  On Covariance Structures. , 1975 .

[26]  F. H. Barron,et al.  AXIOMATIC CONJOINT MEASUREMENT , 1977 .

[27]  R. Luce,et al.  Simultaneous conjoint measurement: A new type of fundamental measurement , 1964 .

[28]  John R. Hauser,et al.  Conjoint Analysis, Related Modeling, and Applications , 2004 .

[29]  J. Louviere,et al.  Some probabilistic models of best, worst, and best–worst choices , 2005 .

[30]  U. Böckenholt,et al.  Modeling Preference Data , 2008 .

[31]  Michael W. Browne,et al.  Topics in Applied Multivariate Analysis: COVARIANCE STRUCTURES , 1982 .

[32]  Eric T. Bradlow.  Current issues and a ‘wish list’ for conjoint analysis , 2005 .

[33]  Albert Maydeu-Olivares,et al.  Thurstonian modeling of ranking data via mean and covariance structure analysis , 1999 .

[34]  J. Yellott.  The relationship between Luce's Choice Axiom, Thurstone's Theory of Comparative Judgment, and the double exponential distribution , 1977 .

[35]  Paul E. Green,et al.  Thirty Years of Conjoint Analysis: Reflections and Prospects , 2001, Interfaces.