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A Psychophysics Paradigm for the Collection and Analysis of Similarity Judgments
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Bayesian Plackett-Luce Mixture Models for Partially Ranked Data.

Cristina Mollica1, Luca Tardella2

  • 1Dipartimento di Scienze Statistiche, Sapienza Università di Roma, Piazzale A. Moro 5, 00185 , Rome, Italy. cristina.mollica@uniroma1.it.

Psychometrika
|October 14, 2016
PubMed
Summary

This study introduces a Bayesian mixture of Plackett-Luce models to analyze preference rankings, effectively handling unobserved sample heterogeneity in partially ranked data for better behavioral insights.

Keywords:
Gibbs samplingMAP estimationPlackett–Luce modeldata augmentationgoodness-of-fitlabel switchingmixture modelsranking data

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Area of Science:

  • Psychology
  • Behavioral Science
  • Statistics

Background:

  • Ordinal judgments on multiple alternatives are crucial in psychological and behavioral experiments.
  • The Plackett-Luce model is a standard for analyzing item rankings.
  • Unobserved sample heterogeneity often complicates the analysis of preference data.

Purpose of the Study:

  • To introduce a Bayesian finite mixture of Plackett-Luce models.
  • To address unobserved sample heterogeneity in partially ranked data.
  • To provide a flexible framework for analyzing preference and choice orientation.

Main Methods:

  • Developed a Bayesian finite mixture of Plackett-Luce models.
  • Incorporated latent group structure using a data augmentation approach.
  • Utilized Expectation-Maximization (EM) and Gibbs sampling for inference.
  • Investigated Bayesian criteria for mixture configuration selection and diagnostic tools.

Main Results:

  • The proposed Bayesian method efficiently accounts for sample heterogeneity.
  • Existing maximum likelihood procedures are shown as special cases.
  • Demonstrated utility with simulated and real preference ranked data.
  • Bayesian criteria and diagnostic tools aid in model selection and assessment.

Conclusions:

  • The novel Bayesian Plackett-Luce mixture effectively characterizes sample heterogeneity in preference data.
  • Accurate diagnostic checks are vital for understanding heterogeneous partial ranking data.
  • The method offers a robust alternative to frequentist and nonparametric approaches.