While multicollinearity may increase the difficulty of interpreting multiple regression (MR) results, it should not cause undue problems for the knowledgeable researcher. In the current paper, we argue that rather than using one technique to investigate regression results, researchers should consider multiple indices to understand the contributions that predictors make not only to a regression model, but to each other as well. Some of the techniques to interpret MR effects include, but are not limited to, correlation coefficients, beta weights, structure coefficients, all possible subsets regression, commonality coefficients, dominance weights, and relative importance weights. This article will review a set of techniques to interpret MR effects, identify the elements of the data on which the methods focus, and identify statistical software to support such analyses.

This is a short overview of the R add-on package BradleyTerry2, which facilitates the specification and fitting of Bradley-Terry logit, probit or cauchit models to paircomparison data. Included are the standard 'unstructured' Bradley-Terry model, structured versions in which the parameters are related through a linear predictor to explanatory variables, and the possibility of an order or 'home advantage' effect or other 'contest-specific' effects. Model fitting is either by maximum likelihood, by penalized quasi-likelihood (for models which involve a random effect), or by bias-reduced maximum likelihood in which the first-order asymptotic bias of parameter estimates is eliminated. Also provided are a simple and efficient approach to handling missing covariate data, and suitably-defined residuals for diagnostic checking of the linear predictor.

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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 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.where A j is the set of alternatives {i j , i j+1 , . . . , i J } from which item i j is chosen. The above model is also derived in Plackett (1975), hence the name Plackett-Luce model.In this paper, we present the R package PlackettLuce . This package implements an extension of the Plackett-Luce model that allows for ties in the rankings. The model can be applied to either complete or partial rankings (complete rankings of subsets of items). PlackettLuce offers a choice of algorithms to fit the model via maximum likelihood. Pseudo-rankings, i.e. pairwise comparisons with a hypothetical item, are used to ensure that the item worths always have finite maximum likelihood estimates (MLEs) with finite standard error. Methods are provided to obtain different parameterizations with corresponding standard errors or quasi-standard errors (that do not change with the identifiability constraint). There is also a method to fit Plackett-Luce trees, which partition the rankings by covariate values to identify subgroups with distinct Plackett-Luce models.In the next section, we review the available software for modelling rankings and make comparisons with Placket-tLuce. Then in Section 3 we describe the Plackett-Luce model with ties and the methods implemented in the package for model-fitting and inference. Plackett-Luce trees are introduced in Section 4, before we conclude the paper with a discussion in Section 5.2 Software for modelling rankings First, in Section 2.1, we consider software to fit the standard Plackett-Luce model. Then in Section 2.2, we review the key packages in terms of their support for features beyond fitting the standard model. Finally in Section 2.3 we review software implementing alternative models for rankings data and discuss how these approaches ...