Robust Estimation of Polychoric Correlation for Complex Survey Designs Using Minimum Divergence Methods

2026-06-24

AI Summary

This study addresses the sensitivity of standard maximum likelihood estimation to multivariate correlation structures when survey data are contaminated—such as by response errors, interviewer effects, or careless responding—and its failure to account for varying data quality. The authors propose a novel robust estimation framework for multivariate correlations under complex survey designs by integrating two minimum divergence criteria, namely Hellinger distance and negative exponential disparity, with Horvitz–Thompson sampling weights, and further incorporate Ridge/Lasso regularization to handle redundant parameters. Through influence function analysis and simulations under three contamination scenarios (uniform upper-corner, uniform lower-corner, and heterogeneous mixed-corner), the results demonstrate that penalized Hellinger estimation yields the lowest mean squared error under uniform contamination, whereas negative exponential disparity performs best under heterogeneous or composite misspecification, offering clear guidance for method selection in practice.

Abstract

Standard maximum likelihood estimation of polychoric correlations is highly sensitive to contamination in survey data, including response errors, interviewer effects, and careless responding, yet assigns equal weight to all observations regardless of data quality. We develop robust estimators for polychoric correlation under complex survey designs based on two minimum divergence criteria -- Hellinger distance (HD) and negative exponential disparity (NED) -- incorporating survey weights through Horvitz--Thompson adjusted cell frequencies. For HD, we propose penalized Ridge and Lasso variants that regularize nuisance parameters while leaving the correlation unpenalized, and establish consistency and asymptotic normality with a sandwich covariance reflecting the sampling design. The influence function is finite but not uniformly bounded, reflecting Hellinger's sensitivity to sparse cells. Simulations under Poisson proportional-to-size sampling examine three contamination geometries -- concordant upper, concordant lower, and discordant mixed corner -- crossed with standard and non-standard latent marginals. The two estimator classes offer complementary advantages: penalized HD methods achieve the lowest mean squared error under concordant contamination, while NED performs best under discordant contamination and under compound misspecification--contamination effects. We provide practical guidelines for method selection based on anticipated contamination patterns in survey practice.

Problem

• polychoric correlation
• robust estimation
• survey data contamination
• complex survey designs
• minimum divergence

Innovation

• polychoric correlation
• minimum divergence
• complex survey design
• robust estimation
• Hellinger distance