Static and Dynamic BART for Rank-Order Data

TL;DR

This paper introduces novel nonparametric static and dynamic models for rank-order data using Bayesian additive regression trees, effectively capturing nonlinear relationships and temporal dependence, and demonstrating superior performance in various applications.

Contribution

Develops the first nonparametric Bayesian models for static and dynamic rank data using additive regression trees, addressing linearity and temporal dependence limitations.

Findings

Outperforms existing methods in simulations and real data applications.

Effectively models nonlinear covariate effects on ranks.

Provides closed-form filtering and smoothing for dynamic scores.

Abstract

Ranking lists are often provided at regular time intervals in a range of applications, including economics, sports, marketing, and politics. Most popular methods for rank-order data postulate a linear specification for the latent scores, which determine the observed ranks, and ignore the temporal dependence of the ranking lists. To address these issues, novel nonparametric static (ROBART) and autoregressive (ARROBART) models are developed, with latent scores defined as nonlinear Bayesian additive regression tree functions of covariates. To make inferences in the dynamic ARROBART model, closed-form filtering, predictive, and smoothing distributions for the latent time-varying scores are derived. These results are applied in a Gibbs sampler with data augmentation for posterior inference. The proposed methods are shown to outperform existing competitors in simulation studies, static data applications to electoral data, stated preferences for sushi and movies, and dynamic data applications to economic complexity rankings of countries and weekly pollster rankings of NCAA football teams.