PLMIX: anRpackage for modelling and clustering partially ranked data

Abstract

Ranking data represent a peculiar form of multivariate ordinal data taking values in the set of permutations. Despite the numerous methodological contributions to increase the flexibility of ranked data modeling, the application of more sophisticated models is limited by the related computational issues. The PLMIX package offers a comprehensive framework aimed at endowing the R statistical environment with some recent methodological advances in modeling and clustering partially ranked data. The usefulness of the novel PLMIX package can be motivated from several perspectives: (i) it contributes to fill the gap concerning Bayesian estimation of ranking models in R, by focusing on the Plackett-Luce model and its extension within the finite mixture approach as the generative sampling distribution; (ii) it addresses computational complexity by combining the flexibility of R routines and the speed of compiled C++ code, with possible parallel execution; (iii) it covers the fundamental phases of ranking data analysis allowing for a more careful and critical application of ranking models in real experiments; (iv) it provides effective tools for clustering heterogeneous partially ranked data. The functionality of the novel package is illustrated with several applications to simulated and real datasets.

Model-Based Learning from Preference Data

“…Among the Bayesian approaches, Caron & Doucet (2012) proposed an efficient data augmentation scheme, which, combined with the introduction of a conjugate prior specification, allows to perform a Gibbs sampling for the PL parameters. Recently, Mollica & Tardella (2016b) developed the PLMIX R package, which provides basic functions to make Bayesian inference on the PL model parameters. Both Caron & Doucet (2012) and Mollica & Tardella (2016a) specify independent gamma priors for each element of the score parameter vector µ, that is, they assume the prior π…”

“…We used the authors' R package (soon available on CRAN). For the analysis of the PL model, we exploit the PLMIX R package of Mollica & Tardella (2016b), setting the number of mixture components to 1, and with the default choices for the prior hyper-parameters in the gamma priors. The heatplots in Figure 1 represent the marginal posterior distribution of ρ obtained using the BMM.…”

Remarkable properties for diagnostics and inference of ranking data modelling

“…) under the EPL specification By using the rPLMIX function of the PLMIX package in R (Mollica & Tardella, 2020), one can simulate N = 100 orderings of K = 5 items from a genuine EPL model, with a parameter configuration given by ρ ¼ ð1, 5, 2, 4, 3Þ p ¼ ð0:15, 0:4, 0:12, 0:08, 0:25Þ:…”

“…For the second application, we focused on a data set with higher values of both K and N , specifically, the occupation data set available in the PLMIX package (Mollica & Tardella, 2020 ) in R. This came from a survey conducted on graduates from the Technion‐Israel Institute of Technology. A sample of N = 143 graduates were asked to rank K = 10 professions according to their perceived prestige: 1 = faculty member, 2 = owner of a business, 3 = applied scientist, 4 = operations researcher, 5 = industrial engineer, 6 = manager, 7 = mechanical engineer, 8 = supervisor, 9 = technician, 10 = foreman.…”

New algorithms and goodness-of-fit diagnostics from remarkable properties of ranking models

“…Let us write the marginal probability for item 1 to be chosen in the final step K of the ranking process. This can be obtained by marginalizing out the entries of the previous K − 1 Appendix B: an example of matrix T(π) under the EPL specification By using the rPLMIX function of the R package PLMIX (Mollica and Tardella, 2020), one can simulate N = 100 orderings of K = 5 items from a genuine EPL model, with a parameter configuration given by ρ = (1, 5, 2, 4, 3) p = (0.15, 0.4, 0.12, 0.08, 0.25).…”