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An exploratory factor model for ordinal paired comparison indicators.

Joshua N Pritikin1

  • 1Department of Psychiatry and Virginia Institute for Psychiatric and Behavior Genetics, Virginia Commonwealth University, 800 E. Leigh St., Richmond, VA 23219, USA.

Heliyon
|September 28, 2020
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Summary
This summary is machine-generated.

This study introduces a factor model to estimate latent board game skill across chess, shogi, and Go tournaments. The model helps understand skill variance and provides guidance on sample size for accurate analysis.

Keywords:
Bayesian methodsBradley-Terry modelFactor modelMathematicsOrdinal paired comparisonPsychologyThurstonian model

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Area of Science:

  • Psychometrics
  • Game Theory
  • Statistical Modeling

Background:

  • Estimating player skill in board games like chess, shogi, and Go is complex due to varying tournament structures.
  • Understanding the underlying latent skill that influences performance across different games is a significant challenge.
  • Existing statistical models may not fully capture the nuances of skill measurement in multi-game scenarios.

Purpose of the Study:

  • To introduce a novel factor model for estimating a unified latent skill in board games.
  • To address identification issues within ordinal paired item models for skill assessment.
  • To provide practical guidance on sample size requirements for reliable skill estimation.

Main Methods:

  • Development of a factor model to analyze per-tournament rankings.
  • Discussion and analysis of identification issues in ordinal paired item models.
  • Conducting simulation studies to determine sample size needs.
  • Validation of correlation and factor models using simulation-based calibration.
  • Recommendation of leave-one-out cross-validation for model fit assessment.

Main Results:

  • The proposed factor model effectively estimates latent board game skill.
  • Simulation studies offer crucial insights into optimal sample sizes for robust analysis.
  • Leave-one-out cross-validation is confirmed as a reliable method for assessing model fit.
  • The pcFactorStan R package facilitates the application of these advanced statistical methods.

Conclusions:

  • The factor model provides a robust framework for quantifying latent skill in multi-game environments.
  • The study offers practical tools and guidelines for researchers in psychometrics and game analytics.
  • The open-source R package pcFactorStan democratizes access to these advanced statistical techniques.