Problem
Research questions and friction points this paper is trying to address.
paired comparison
lack of fit
stochastic transitivity
cyclical preferences
model misspecification
Testing for lack of fit in paired comparison data
🤖 AI Summary
This work addresses the limitations of pairwise comparison models that commonly assume linear stochastic transitivity, despite frequent cyclic preferences in real-world data leading to ranking bias. The authors propose a class of goodness-of-fit tests tailored for fixed-size and high-dimensional sparse comparison graphs, which detect model misspecification by identifying cyclic structures within subsets of items and accommodate diverse graph growth mechanisms. Leveraging random graph theory and high-dimensional asymptotic analysis, the proposed test statistic remains powerful near the graph connectivity threshold, significantly improving detection power and characterizing fundamental detectability limits. Empirical evaluations on both synthetic and real datasets demonstrate superior performance over classical Kendall–Smith tests and their cardinal extensions, uncovering previously undetected non-transitivities and structural model mismatches.
📝 Abstract
Linear stochastic transitivity is a central assumption in paired comparison models that is rarely verified in practice. Empirical violations, however, are common and can substantially affect inference and ranking. We develop a class of tests for detecting lack of fit in cardinal paired comparison models, where lack of fit is characterized by the presence of cyclical preferences among subsets of items. We propose a suite of tests adapted to different regimes governing the growth of the comparison graph. For a fixed number of items, the proposed procedures exhibit substantially improved power relative to the classical Kendall--Smith test and its cardinal analogue. We further extend the framework to high--dimensional, sparse comparison graphs near the connectivity threshold in random graph models. The theoretical analysis characterizes the behavior of the tests under both the null and alternative, with particular emphasis on limits of detectability and consistency. Simulation studies corroborate the theoretical findings, and applications to real data uncover substantial and previously unrecognized intransitivity and structural lack of fit.
Innovation
Methods, ideas, or system contributions that make the work stand out.
paired comparison
lack of fit
stochastic transitivity
cyclical preferences
high-dimensional sparse graphs
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