Modelling Time-Varying Rankings with Autoregressive and Score-Driven Dynamics

TL;DR

This paper introduces a novel statistical model for analyzing time-varying ranking data, incorporating exogenous covariates and partial rankings, estimated via maximum likelihood, and demonstrated through simulations and an empirical case study.

Contribution

It presents a new dynamic ranking model using Plackett-Luce distribution with score-driven parameters, accommodating large datasets and partial rankings, with straightforward estimation.

Findings

Maximum likelihood estimator properties improve with longer time series.

Standard errors are reliable even for medium-sized samples.

Empirical application to Ice Hockey World Championships demonstrates model effectiveness.

Abstract

We develop a new statistical model to analyse time-varying ranking data. The model can be used with a large number of ranked items, accommodates exogenous time-varying covariates and partial rankings, and is estimated via the maximum likelihood in a straightforward manner. Rankings are modelled using the Plackett-Luce distribution with time-varying worth parameters that follow a mean-reverting time series process. To capture the dependence of the worth parameters on past rankings, we utilise the conditional score in the fashion of the generalised autoregressive score (GAS) models. Simulation experiments show that the small-sample properties of the maximum-likelihood estimator improve rapidly with the length of the time series and suggest that statistical inference relying on conventional Hessian-based standard errors is usable even for medium-sized samples. In an empirical study, we apply the model to the results of the Ice Hockey World Championships. We also discuss applications to rankings based on underlying indices, repeated surveys, and non-parametric efficiency analysis.