Estimating flexible distributions of ideal-points with external analysis of preferences

Ideal-points are widely used to model choices when preferences are single-peaked. Ideal-point choice models have been typically estimated at the individual-level, or have been based on the assumption that ideal-points are normally distributed over the population of choice makers. We propose two probabilistic ideal-point choice models for the external analysis of preferences that allow for more flexible multimodal distributions of ideal-points, thus acknowledging the existence of subpopulations with distinct preferences. The first model extends the ideal-point probit model for heterogeneous preferences to accommodate a mixture of multivariate normal distributions of ideal-points. The second model assumes that ideal-points are uniformly distributed within finite ranges of the attribute space, leading to a more simplistic formulation and a more flexible distribution. The two models are applied to simulated and actual choice data, and compared to the ideal-point probit model.

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

[2]  A. Tversky,et al.  Substitutability and similarity in binary choices , 1969 .

[3]  William L. Hays,et al.  Multidimensional unfolding: Determining configuration from complete rank order preference data , 1961 .

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

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

[6]  Geoffrey J. McLachlan,et al.  Mixture models : inference and applications to clustering , 1989 .

[7]  Allan D. Shocker,et al.  A Consumer-Based Methodology for the Identification of New Product Ideas , 1974 .

[8]  Tsoung-Chao Lee,et al.  The Theory and Practice of Econometrics , 1981 .

[9]  Wagner A. Kamakura,et al.  An Ideal-Point Probabilistic Choice Model for Heterogeneous Preferences , 1986 .

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

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

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

[13]  Richard R. Batsell.  On the use of Hidden Surface Routines in the Analysis of Marketing Data , 1980 .

[14]  Randall G. Chapaaan,et al.  Exploiting Rank Ordered Choice Set Data within the Stochastic Utility Model , 1982 .

[15]  George S. Avrunin,et al.  Single-Peaked Functions and the Theory of Preference. , 1977 .

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

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

[18]  R. Rust,et al.  Incorporating prior theory in covariance structure analysis: A bayesian approach , 1989 .

[19]  Naveen R. Donthu,et al.  Flexible ideal point mapping and product positioning , 1986 .