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The Interval Consensus Model: Aggregating Continuous Bounded Interval Responses
Matthias Kloft1, Björn S Siepe1, Daniel W Heck1
1Department of Psychology, https://ror.org/01rdrb571Philipps-Universität Marburg, Germany.
Psychometrika
|November 4, 2025
Summary
We introduce a new Interval Consensus Model (ICM) to find shared knowledge for unknown truths, extending Cultural Consensus Theory (CCT) to estimate consensus intervals from continuous bounded interval responses.
Area of Science:
- Social Sciences
- Statistics
- Cognitive Science
Background:
- Cultural Consensus Theory (CCT) aggregates shared knowledge for unknown truths.
- Existing CCT models focus on point truths (dichotomous, polytomous, continuous).
- Domains like risk assessment require consensus on intervals, not just points.
Purpose of the Study:
- Introduce the Interval Consensus Model (ICM) as an extension of CCT.
- Enable estimation of consensus intervals from continuous bounded interval responses.
- Address limitations of existing CCT models for interval-based consensus.
Main Methods:
- Developed a novel Bayesian hierarchical modeling approach.
- Estimated latent consensus intervals from interval responses.
- Utilized a simulation study to evaluate model performance.
Main Results:
- The ICM effectively estimates consensus intervals.
- ICM outperformed simple means and medians in simulation studies.
- Applied the ICM to empirical data on verbal quantifier judgments.
Conclusions:
- The ICM is a valuable extension of CCT for interval-based consensus.
- This model enhances understanding in domains requiring interval judgments.
- The ICM offers a statistically robust method for aggregating interval data.
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