PLMIX-package {PLMIX}

Bayesian Analysis of Finite Mixtures of Plackett-Luce Models for Partial Rankings/Orderings

Description

The PLMIX package for R provides functions to fit and analyze finite mixtures of Plackett-Luce models for partial top rankings/orderings within the Bayesian framework. It provides MAP point estimates via EM algorithm and posterior MCMC simulations via Gibbs Sampling. It also fits MLE as a special case of the noninformative Bayesian analysis with vague priors.

In addition to inferential techniques, the package assists other fundamental phases of a model-based analysis for partial rankings/orderings, by including functions for data manipulation, simulation, descriptive summary, model selection and goodness-of-fit evaluation.

Specific S3 classes and methods are also supplied to enhance the usability and foster exchange with other packages. Finally, to address the issue of computationally demanding procedures typical in ranking data analysis, PLMIX takes advantage of a hybrid code linking the R environment with the C++ programming language.

Details

The Plackett-Luce model is one of the most popular and frequently applied parametric distributions to analyze partial top rankings/orderings of a finite set of items. The present package allows to account for unobserved sample heterogeneity of partially ranked data with a model-based analysis relying on Bayesian finite mixtures of Plackett-Luce models. The package provides a suite of functions that covers the fundamental phases of a model-based analysis:

Ranking data manipulation

binary_group_ind

Binary group membership matrix from the mixture component labels.

freq_to_unit

From the frequency distribution to the dataset of individual orderings/rankings.

make_complete

Random completion of partial orderings/rankings data.

make_partial

Censoring of complete orderings/rankings data.

rank_ord_switch

From rankings to orderings and vice-versa.

unit_to_freq

From the dataset of individual orderings/rankings to the frequency distribution.

Ranking data simulation

rPLMIX

Random sample from a finite mixture of Plackett-Luce models.

Ranking data description

paired_comparisons

Paired comparison frequencies.

rank_summaries

Summary statistics of partial ranking/ordering data.

Model estimation

gibbsPLMIX

Bayesian analysis with MCMC posterior simulation via Gibbs sampling.

label_switchPLMIX

Label switching adjustment of the Gibbs sampling simulations.

likPLMIX

Likelihood evaluation for a mixture of Plackett-Luce models.

loglikPLMIX

Log-likelihood evaluation for a mixture of Plackett-Luce models.

mapPLMIX

MAP estimation via EM algorithm.

mapPLMIX_multistart

MAP estimation via EM algorithm with multiple starting values.

Class coercion and membership

as.top_ordering

Coercion into top-ordering datasets.

gsPLMIX_to_mcmc

From the Gibbs sampling simulation to an MCMC class object.

is.top_ordering

Test for the consistency of input data with a top-ordering dataset.

S3 class methods

plot.gsPLMIX

Plot of the Gibbs sampling simulations.

plot.mpPLMIX

Plot of the MAP estimates.

print.gsPLMIX

Print of the Gibbs sampling simulations.

print.mpPLMIX

Print of the MAP estimation algorithm.

summary.gsPLMIX

Summary of the Gibbs sampling procedure.

summary.mpPLMIX

Summary of the MAP estimation.

Model selection

bicPLMIX

BIC value for the MLE of a mixture of Plackett-Luce models.

selectPLMIX

Bayesian model selection criteria.

Model assessment

ppcheckPLMIX

Posterior predictive diagnostics.

ppcheckPLMIX_cond

Posterior predictive diagnostics conditionally on the number of ranked items.

Datasets

d_apa

American Psychological Association Data (partial orderings).

d_carconf

Car Configurator Data (partial orderings).

d_dublinwest

Dublin West Data (partial orderings).

d_gaming

Gaming Platforms Data (complete orderings).

d_german

German Sample Data (complete orderings).

d_nascar

NASCAR Data (partial orderings).

d_occup

Occupation Data (complete orderings).

d_rice

Rice Voting Data (partial orderings).

Data have to be supplied as an object of class matrix, where missing positions/items are denoted with zero entries and Rank = 1 indicates the most-liked alternative. For a more efficient implementation of the methods, partial sequences with a single missing entry should be preliminarily filled in, as they correspond to complete rankings/orderings. In the present setting, ties are not allowed. Some quantities frequently recalled in the manual are the following:

N

Sample size.

K

Number of possible items.

G

Number of mixture components.

L

Size of the final posterior MCMC sample (after burn-in phase).

Author(s)

Cristina Mollica and Luca Tardella

Maintainer: Cristina Mollica <[e-mail]>

References

Mollica, C. and Tardella, L. (2017). Bayesian Plackett-Luce mixture models for partially ranked data. Psychometrika, 82(2), pages 442–458, ISSN: 0033-3123, http://dx.doi.org/10.1007/s11336-016-9530-0.

Mollica, C. and Tardella, L. (2014). Epitope profiling via mixture modeling for ranked data. Statistics in Medicine, 33(21), pages 3738–3758, ISSN: 0277-6715, http://onlinelibrary.wiley.com/doi/10.1002/sim.6224/full.