Thurstone Preference Model

A Thurstone Preference Model is a preference aggregation model that models pairwise comparison outcomes through latent ability differences assuming normal distributions for preference strength.

• AKA: Thurstone Model, Thurstone Comparative Judgment Model, Thurstone-Mosteller Model, Case V Model.
• Context:
  • It can typically assume Latent Ability Variables follow normal distributions.
  • It can typically model Preference Probability through probit functions.
  • It can often handle Preference Intensity beyond binary outcomes.
  • It can often incorporate Discrimination Parameters for comparison reliability.
  • It can support Maximum Likelihood Estimation for parameter inference.
  • It can enable Ability Score Recovery from incomplete comparisons.
  • It can provide Standard Error Estimates for ability uncertainty.
  • It can complement Bradley-Terry Model with different assumptions.
  • It can range from being a Simple Thurstone Model to being a Extended Thurstone Model, depending on its parameter complexity.
  • It can range from being a Binary Thurstone Model to being a Ordinal Thurstone Model, depending on its response type.
  • It can range from being a Fixed-Variance Thurstone Model to being a Variable-Variance Thurstone Model, depending on its variance assumption.
  • It can range from being a Single-Dimension Thurstone Model to being a Multi-Dimension Thurstone Model, depending on its ability dimensions.
  • ...
• Examples:
  • Classical Thurstone Models, such as:
    • Thurstone Case III Model for unequal variance.
    • Thurstone Case V Model for equal variance.
    • Thurstone Case VI Model for zero correlation.
  • NLG Applications, such as:
    • Translation Quality Thurstone Model for MT ranking.
    • Summary Quality Thurstone Model for summarization assessment.
    • Response Quality Thurstone Model for dialogue evaluation.
  • Extended Thurstone Models, such as:
    • Multi-Attribute Thurstone Model for multiple criterion.
    • Hierarchical Thurstone Model for nested comparisons.
  • ...
• Counter-Examples:
  • Bradley-Terry Model, which uses logistic function.
  • Elo Rating Model, which uses sequential update.
  • Plackett-Luce Model, which handles multiple alternatives.
• See: Preference Aggregation Model, Bradley-Terry Model, Pairwise Comparison Model, Latent Variable Model, Probit Model, Comparative Judgment Theory, Psychometric Model, Ranking Model, Maximum Likelihood Estimation.

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