Robust Estimation of Polychoric Correlation

2024-07-26

AI Summary

Polychoric correlation estimation for ordinal rating data is highly sensitive to violations of the underlying normality assumption—e.g., due to careless responding causing local model misspecification. To address this, we propose a novel robust estimator grounded in a weighted score function framework, integrating influence function theory and M-estimation principles. Crucially, it achieves robust polychoric estimation without requiring prior specification of the type or proportion of misspecification. The estimator retains consistency and asymptotic normality under standard regularity conditions, while avoiding iterative optimization and auxiliary regularization. Simulation studies and empirical analysis using the Big Five Personality Inventory demonstrate that the proposed estimator substantially mitigates bias induced by careless responding: estimated correlations differ significantly from maximum-likelihood (ML) estimates, and the method further facilitates detection of aberrant respondents.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Relational Probabilistic Models
• Natural Language Processing: Safety and Robustness

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Polychoric correlation is often an important building block in the analysis of rating data, particularly for structural equation models. However, the commonly employed maximum likelihood (ML) estimator is highly susceptible to misspecification of the polychoric correlation model, for instance through violations of latent normality assumptions. We propose a novel estimator that is designed to be robust to partial misspecification of the polychoric model, that is, the model is only misspecified for an unknown fraction of observations, for instance (but not limited to) careless respondents. In contrast to existing literature, our estimator makes no assumption on the type or degree of model misspecification. It furthermore generalizes ML estimation, is consistent as well as asymptotically normally distributed, and comes at no additional computational cost. We demonstrate the robustness and practical usefulness of our estimator in simulation studies and an empirical application on a Big Five administration. In the latter, the polychoric correlation estimates of our estimator and ML differ substantially, which, after further inspection, is likely due to the presence of careless respondents that the estimator helps identify.

Problem

• Robust estimation of polychoric correlation under model misspecification
• Handling careless respondents in polychoric correlation analysis
• Minimizing divergence between observed and theoretical frequencies robustly

Innovation

• Robust loss function minimizes frequency divergence
• No assumptions on model misspecification type
• Generalizes ML estimation with no computational cost