Modelling rankings in R: the PlackettLuce package

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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 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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An introduction to recursive partitioning: rationale, application, and characteristics of classification and regression trees, bagging, and random forests.

Carolin Strobl, James Malley, Gerhard Tutz (2009)

Recursive partitioning methods have become popular and widely used tools for nonparametric regression and classification in many scientific fields. Especially random forests, which can deal with large numbers of predictor variables even in the presence of complex interactions, have been applied successfully in genetics, clinical medicine, and bioinformatics within the past few years. High-dimensional problems are common not only in genetics, but also in some areas of psychological research, where only a few subjects can be measured because of time or cost constraints, yet a large amount of data is generated for each subject. Random forests have been shown to achieve a high prediction accuracy in such applications and to provide descriptive variable importance measures reflecting the impact of each variable in both main effects and interactions. The aim of this work is to introduce the principles of the standard recursive partitioning methods as well as recent methodological improvements, to illustrate their usage for low and high-dimensional data exploration, but also to point out limitations of the methods and potential pitfalls in their practical application. Application of the methods is illustrated with freely available implementations in the R system for statistical computing. (c) 2009 APA, all rights reserved.