A novel sandwich algorithm for empirical Bayes analysis of rank data

TL;DR

This paper introduces a new sandwich algorithm that significantly improves the efficiency of empirical Bayes analysis for rank data, especially when covariate information influences rankings.

Contribution

The paper proposes a novel, fast-mixing sandwich algorithm for Bayesian analysis of rank data, addressing slow convergence issues of traditional Gibbs sampling methods.

Findings

The sandwich algorithm demonstrates faster convergence than Gibbs sampling.

The method effectively incorporates covariate information into rank data analysis.

Empirical results show improved estimation accuracy and computational efficiency.

Abstract

Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the items are ranked. In this paper we analyze rank data using a purely probabilistic model where the observed ranks are assumed to be perturbed versions of the true rank and each perturbation has a specific probability of occurring. We consider the general case when covariate information is present and has an impact on the rankings. An empirical Bayes approach is taken for estimating the model parameters. The Gibbs sampler is shown to converge very slowly to the target posterior distribution and we show that some of the widely used empirical convergence diagnostic tools may fail to detect this lack of convergence. We propose a novel, fast mixing sandwich algorithm for exploring the posterior distribution. An EM algorithm based on Markov chain Monte Carlo (MCMC) sampling is developed for estimating prior hyperparameters. A real life rank data set is analyzed using the methods developed in the paper. The results obtained indicate the usefulness of these methods in analyzing rank data with covariate information.