Modelling rankings in R: the PlackettLuce package

TL;DR

The PlackettLuce R package offers a flexible and regularized approach to modeling rankings data, accommodating ties and partial rankings, with tools for inference, comparison, and subgroup analysis.

Contribution

It introduces a generalized Plackett-Luce model implementation in R that handles ties, partial rankings, and includes regularization and subgroup analysis features.

Findings

Ensures finite maximum likelihood estimates for item worths.

Provides quasi standard errors for robust inference.

Demonstrates effectiveness on various datasets.

Abstract

This paper presents the R package PlackettLuce, which implements a generalization of the Plackett-Luce model for rankings data. The generalization accommodates both ties (of arbitrary order) and partial rankings (complete rankings of subsets of items). By default, the implementation adds a set of pseudo-comparisons with a hypothetical item, ensuring that the underlying network of wins and losses between items is always strongly connected. In this way, the worth of each item always has a finite maximum likelihood estimate, with finite standard error. The use of pseudo-comparisons also has a regularization effect, shrinking the estimated parameters towards equal item worth. In addition to standard methods for model summary, PlackettLuce provides a method to compute quasi standard errors for the item parameters. This provides the basis for comparison intervals that do not change with the choice of identifiability constraint placed on the item parameters. Finally, the package provides a method for model-based partitioning using covariates whose values vary between rankings, enabling the identification of subgroups of judges or settings that have different item worths. The features of the package are demonstrated through application to classic and novel data sets.