Modelling rankings in R: the PlackettLuce package
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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 any order) and partial rankings (rankings of only some items). By default, the implementation adds a set of pseudo-comparisons with a hypothetical item, ensuring that the network of wins and losses is always strongly connected, i.e. all items are connected to every other item by both a path of wins and a path of losses. This means that the worth of each item can always be estimated by maximum likelihood, with finite standard error. It 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, so that comparison intervals can be derived even when a reference item is set. Finally the package provides a method for model-based partitioning using ranking-specific covariates, enabling the identification of subgroups where items have been ranked differently. These features are demonstrated through application to classic and novel data sets.
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