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The **PlackettLuce** package implements a generalization of the model jointly attributed to Plackett (1975) and Luce (1959) 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.
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The **PlackettLuce** package implements a generalization of the model
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jointly attributed to Plackett (1975) and Luce (1959) for modelling
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rankings data. Examples of rankings data might be the finishing order of
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competitors in a race, or the preference of consumers over a set of
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competing products.
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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.
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The output of the model is an estimated **worth** for each item that
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appears in the rankings. The parameters are generally presented on the
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log scale for inference.
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The implementation of the Plackett-Luce model in **PlackettLuce**:
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- Accommodates ties (of any order) in the rankings, e.g. bananas ≻ {apples, oranges} ≻ pears.
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- Accommodates sub-rankings, e.g. pears ≻ apples, when the full set of items is {apples, bananas, oranges, pears}.
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- Handles disconnected or weakly connected networks implied by the rankings, e.g. where one item always loses as in figure below. This is achieved by adding pseudo-rankings with a hypothetical or ghost item.
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- Accommodates ties (of any order) in the rankings, e.g. bananas
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\(\succ\) {apples, oranges} \(\succ\) pears.
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- Accommodates sub-rankings, e.g. pears \(\succ\) apples, when the
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full set of items is {apples, bananas, oranges, pears}.
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- Handles disconnected or weakly connected networks implied by the
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rankings, e.g. where one item always loses as in figure below. This
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is achieved by adding pseudo-rankings with a hypothetical or ghost
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item.
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 </br>
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<!----> </br>
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In addition the package provides methods for
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- Obtaining quasi-standard errors, that don't depend on the constraints applied to the worth parameters for identifiability.
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- Fitting Plackett-Luce trees, i.e. a tree that partitions the rankings by covariate values, such as consumer attributes or racing conditions, identifying subgroups with different sets of worth parameters for the items.
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- Obtaining quasi-standard errors, that don’t depend on the
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constraints applied to the worth parameters for identifiability.
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- Fitting Plackett-Luce trees, i.e. a tree that partitions the
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rankings by covariate values, such as consumer attributes or racing
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conditions, identifying subgroups with different sets of worth
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parameters for the items.
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Installation
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------------
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## Installation
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The package may be installed from GitHub via
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@@ -36,12 +53,19 @@ The package may be installed from GitHub via
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devtools::install_github("hturner/PlackettLuce")
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```
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Usage
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-----
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## Usage
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The [Netflix Prize](http://www.netflixprize.com/) 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](http://www.preflib.org/data/election/netflix/). 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**.
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The [Netflix Prize](http://www.netflixprize.com/) was a competition
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devised by Netflix to improve the accuracy of its recommendation system.
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To facilitate this they released ratings about movies from the users of
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the system that have been transformed to preference data and are
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available from [PrefLib](http://www.preflib.org/data/election/netflix/).
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Each data set comprises rankings of a set of 3 or 4 movies selected at
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random. Here we consider rankings for just one set of movies to
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illustrate the functionality of **PlackettLuce**.
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The data can be read in using the `read.soc` function in **PlackettLuce**
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The data can be read in using the `read.soc` function in
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**PlackettLuce**
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```r
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library(PlackettLuce)
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## 1 68 2 1 4 3
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## 2 53 1 2 4 3
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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.
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Each row corresponds to a unique ordering of the four movies in this
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data set. The number of Netflix users that assigned that ordering is
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given in the first column, followed by the four movies in preference
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order. So for example, 68 users ranked movie 2 first, followed by movie
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1, then movie 4 and finally movie 3.
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`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
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`PlackettLuce`, the model-fitting function in **PlackettLuce** requires
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that the data are provided in the form of *rankings* rather than
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*orderings*, i.e. the rankings are expressed by giving the rank for each
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item, rather than ordering the items. We can create a `"rankings"`
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object from a set of orderings as follows
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```r
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R<- as.rankings(netflix[,-1], input="ordering")
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## 2 1 2 4 3
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## 3 2 1 3 4
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Note that `read.soc` saved the names of the movies in the `"item"` 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.
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Note that `read.soc` saved the names of the movies in the `"item"`
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attribute of `netflix`, so we have used these to label the items.
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Subsetting the rankings object `R` with `as.rankings = FALSE`, returns
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the underlying matrix of rankings corresponding to the subset. So for
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example, in the first ranking the second movie (Beverly Hills Cop) is
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ranked number 1, followed by the first movie (Mean Girls) with rank 2,
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followed by the fourth movie (Mission: Impossible II) and finally the
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third movie (The Mummy Returns), giving the same ordering as in the
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original data.
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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:
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Various methods are provided for `"rankings"` objects, in particular if
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we subset the rankings without `as.rankings = FALSE`, the result is
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again a `"rankings"` object and the corresponding print method is used:
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```r
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R[1:3]
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## 3
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## "Beverly Hills Cop > Mean Girls > The Mummy Returns > Mis ..."
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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.
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The rankings can now be passed to `PlackettLuce` to fit the
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Plackett-Luce model. The counts of each ranking provided in the
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downloaded data are used as weights when fitting the model.
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```r
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mod<- PlackettLuce(R, weights=netflix$n)
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## Mission: Impossible II
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## 0.1498342
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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.
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Calling `coef` with `log = FALSE` gives the worth parameters,
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constrained to sum to one. These parameters represent the probability
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that each movie is ranked first.
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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:
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For inference these parameters are converted to the log scale, by
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default setting the first parameter to zero so that the standard errors
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are estimable:
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```r
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summary(mod)
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## AIC: 3499.5
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## Number of iterations: 5
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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.
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In this way, Mean Girls is treated as the reference movie, the positive
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parameter for Beverly Hills Cop shows this was more popular among the
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users, while the negative parameters for the other two movies show these
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were less popular.
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Comparisons between different pairs of movies can be made visually by plotting the log-worth parameters with comparison intervals based on quasi standard errors.
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Comparisons between different pairs of movies can be made visually by
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plotting the log-worth parameters with comparison intervals based on
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quasi standard errors.
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```r
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qv<- qvcalc(mod)
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plot(qv)
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```
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<!---->
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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.
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If the intervals overlap there is no significant difference. So we can
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see that Beverly Hills Cop is significantly more popular than the other
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three movies, Mean Girls is significant more popular than The Mummy
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Returns or Mission: Impossible II, but there was no significant
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difference in users’ preference for these last two movies.
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Going Further
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-------------
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## Going Further
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The full 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](https://hturner.github.io/PlackettLuce/) or from within R once the package has been installed, e.g. via
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The full functionality of **PlackettLuce** is illustrated in the package
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vignette, along with details of the model used in the package and a
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comparison to other packages. The vignette can be found on the [package
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website](https://hturner.github.io/PlackettLuce/) or from within R once
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the package has been installed, e.g. via
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vignette("Overview", package = "PlackettLuce")
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Code of Conduct
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---------------
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## Code of Conduct
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Please note that this project is released with a [Contributor Code of Conduct](CONDUCT.md). By participating in this project you agree to abide by its terms.
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Please note that this project is released with a [Contributor Code of
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Conduct](CONDUCT.md). By participating in this project you agree to
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abide by its terms.
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References
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----------
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## References
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Luce, R. Duncan. 1959. *Individual Choice Behavior: A Theoretical Analysis*. doi:[10.2307/2282347](https://doi.org/10.2307/2282347).
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<divid="refs"class="references">
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Plackett, Robert L. 1975. “The Analysis of Permutations.” *Appl. Statist* 24 (2): 193–202. doi:[10.2307/2346567](https://doi.org/10.2307/2346567).
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<divid="ref-Luce1959">
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Luce, R. Duncan. 1959. *Individual Choice Behavior: A Theoretical
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Analysis*. New York: Wiley.
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</div>
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<divid="ref-Plackett1975">
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Plackett, Robert L. 1975. “The Analysis of Permutations.” *Appl.
\AppData\Local\Temp\RtmpyQZw3Z\READMEcf025d05abf.html"' had status 99
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* checking CRAN incoming feasibility ...Warning: running command '"pandoc" "C:\Users\hturner\PlackettLuce.Rcheck\00_pkg_src\PlackettLuce\README.md" -s --email-obfuscation=references --self-contained -o "C:\Users\hturner\AppData\Local\Temp\RtmpyQZw3Z\READMEcf025d05abf.html"' had status 99
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The warning seems to be due to pandoc not finding image files in `man/figures`.
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I could successfully run the pandoc command by either changing directory to
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"C:\Users\hturner\PlackettLuce.Rcheck\00_pkg_src\PlackettLuce" and calling
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pandoc on "README.md", or adding `--resource-path
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"C:\Users\hturner\PlackettLuce.Rcheck\00_pkg_src\PlackettLuce` to the call shown
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in the warning.
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The warning seems to be due to pandoc not finding image files in `man/figures`. I could successfully run the pandoc command by either changing directory to "C:\Users\hturner\PlackettLuce.Rcheck\00_pkg_src\PlackettLuce" and calling pandoc on "README.md", or adding `--resource-path "C:\Users\hturner\PlackettLuce.Rcheck\00_pkg_src\PlackettLuce` to the call shown in the warning.
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