Design-aware Inference for Ordinal Disparity Indices in Complex Surveys

Thomas M. Menino Convention & Exhibition Center 

Fields like public health and labor economics utilize ordered categorical outcomes (e.g., self-rated health) to monitor group disparities. However, survey methodology often overlooks inference for ordinal disparity measures under complex sampling. Unlike linear statistics such as means and proportions, ordinal indices based on stochastic dominance are nonlinear and biased, even in simple designs. Multistage, unequal-probability sampling further complicates point and variance estimation, especially when using software intended for linear statistics or assuming independent sampling.
We propose the Design-Aware Ordinal Weighted Likelihood Bootstrap (D–OWLB) for model-based inference on these measures. D–OWLB embeds a primary sampling unit-level rescaled bootstrap within a weighted likelihood estimation framework using Gamma-perturbed replicate weights. This approach accounts for stratification, clustering, and unequal selection probabilities to target the sampling distribution of nonlinear disparity functionals and produce population-level inference based on these functionals. While this article focuses primarily on health applications, the framework can be implemented for a broad range of variables where inference needs to be made from ordinal data.
Simulations show that while design-agnostic bootstraps underestimate variance as complexity increases, D–OWLB aligns closely with design-based benchmarks. Applied to 2023 BRFSS data, D–OWLB provides better-calibrated intervals for self-rated health disparities compared to standard weighted likelihood methods.

Ordinal health outcomes

Model-based inference

Complex survey design

Bootstrap

Weighted likelihood

Multilevel models 

Survey Research Methods Section