knitr::opts_chunk$set(fig.path = "man/figures/")
Package website: https://hturner.github.io/PlackettLuce/.
The PlackettLuce package implements a generalization of the model jointly attributed to @Plackett1975 and @Luce1959 for modelling rankings data. Examples of rankings data might be the finishing order of competitors in a race, or the preference of consumers over a set of competing products.
The output of the model is an estimated worth for each item that appears in the rankings. The parameters are generally presented on the log scale for inference.
The implementation of the Plackett-Luce model in PlackettLuce:
library(PlackettLuce) library(igraph) R <- matrix(c(1, 2, 0, 0, 2, 0, 1, 0, 1, 0, 0, 2, 2, 1, 0, 0, 0, 1, 2, 0), byrow = TRUE, ncol = 4, dimnames = list(NULL, LETTERS[1:4])) R <- as.rankings(R) A <- adjacency(R) net <- graph_from_adjacency_matrix(A) plot(net, edge.arrow.size = 0.5, vertex.size = 30)
In addition the package provides methods for
The package may be installed from CRAN via
install.packages("PlackettLuce")
The development version can be installed via
# install.packages("devtools") devtools::install_github("hturner/PlackettLuce")
The Netflix Prize was a competition devised by Netflix to improve the accuracy of its recommendation system. To facilitate this they released ratings about movies from the users of the system that have been transformed to preference data and are available from PrefLib, [@Bennett2007]. Each data set comprises rankings of a set of 3 or 4 movies selected at random. Here we consider rankings for just one set of movies to illustrate the functionality of PlackettLuce.
The data can be read in using the read.soc
function in PlackettLuce
library(PlackettLuce) preflib <- "https://www.preflib.org/static/data/" netflix <- read.soc(file.path(preflib, "netflix/00004-00000138.soc")) head(netflix, 2)
Each row corresponds to a unique ordering of the four movies in this data set. The number of Netflix users that assigned that ordering is given in the first column, followed by the four movies in preference order. So for example, 68 users ranked movie 2 first, followed by movie 1, then movie 4 and finally movie 3.
PlackettLuce
, the model-fitting function in PlackettLuce requires that
the data are provided in the form of rankings rather than orderings, i.e.
the rankings are expressed by giving the rank for each item, rather than
ordering the items. We can create a "rankings"
object from a set of orderings
as follows
R <- as.rankings(netflix[,-1], input = "orderings", items = attr(netflix, "items")) R[1:3, as.rankings = FALSE]
Note that read.soc
saved the names of the movies in the "items"
attribute of
netflix
, so we have used these to label the items. Subsetting the
rankings object R
with as.rankings = FALSE
, returns the underlying matrix of
rankings corresponding to the subset. So for example, in the first ranking the
second movie (Beverly Hills Cop) is ranked number 1, followed by the first movie
(Mean Girls) with rank 2, followed by the fourth movie (Mission: Impossible II)
and finally the third movie (The Mummy Returns), giving the same ordering as in
the original data.
Various methods are provided for "rankings"
objects, in particular if we
subset the rankings without as.rankings = FALSE
, the result is again a
"rankings"
object and the corresponding print method is used:
R[1:3] print(R[1:3], width = 60)
The rankings can now be passed to PlackettLuce
to fit the Plackett-Luce model.
The counts of each ranking provided in the downloaded data are used as weights
when fitting the model.
mod <- PlackettLuce(R, weights = netflix$Freq) coef(mod, log = FALSE)
Calling coef
with log = FALSE
gives the worth parameters, constrained to
sum to one. These parameters represent the probability that each movie is ranked
first.
For inference these parameters are converted to the log scale, by default setting the first parameter to zero so that the standard errors are estimable:
summary(mod)
In this way, Mean Girls is treated as the reference movie, the positive parameter for Beverly Hills Cop shows this was more popular among the users, while the negative parameters for the other two movies show these were less popular.
Comparisons between different pairs of movies can be made visually by plotting the log-worth parameters with comparison intervals based on quasi standard errors.
qv <- qvcalc(mod) plot(qv, ylab = "Worth (log)", main = NULL)
If the intervals overlap there is no significant difference. So we can see that Beverly Hills Cop is significantly more popular than the other three movies, Mean Girls is significant more popular than The Mummy Returns or Mission: Impossible II, but there was no significant difference in users' preference for these last two movies.
The core functionality of PlackettLuce is illustrated in the package vignette, along with details of the model used in the package and a comparison to other packages. The vignette can be found on the package website or from within R once the package has been installed, e.g. via
vignette("Overview", package = "PlackettLuce")
Please note that this project is released with a Contributor Code of Conduct. By participating in this project you agree to abide by its terms.
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