| Type: | Package |
| Title: | Statistical Rank Aggregation: Inference, Evaluation, and Visualization |
| Version: | 0.0.6 |
| Date: | 2015-08-20 |
| Author: | Hossein Azari Soufiani, William Chen |
| Maintainer: | Hossein Azari Soufiani <azari.hossein@gmail.com> |
| Description: | A set of methods to implement Generalized Method of Moments and Maximal Likelihood methods for Random Utility Models. These methods are meant to provide inference on rank comparison data. These methods accept full, partial, and pairwise rankings, and provides methods to break down full or partial rankings into their pairwise components. Please see Generalized Method-of-Moments for Rank Aggregation from NIPS 2013 for a description of some of our methods. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Imports: | truncdist, plyr, ggplot2 |
| Suggests: | gridExtra, grid, testthat, lattice |
| NeedsCompilation: | no |
| Packaged: | 2015-09-07 19:53:49 UTC; william |
| Repository: | CRAN |
| Date/Publication: | 2015-09-09 09:34:43 |
Breaks full or partial orderings into pairwise comparisons
Description
Given full or partial orderings, this function will generate pairwise comparison Options 1. full - All available pairwise comparisons. This is used for partial rank data where the ranked objects are a random subset of all objects 2. adjacent - Only adjacent pairwise breakings 3. top - also takes in k, will break within top k and will also generate pairwise comparisons comparing the top k with the rest of the data 4. top.partial - This is used for partial rank data where the ranked alternatives are preferred over the non-ranked alternatives
Usage
Breaking(Data, method, k = NULL)
Arguments
Data |
data in either full or partial ranking format |
method |
- can be full, adjacent, top or top.partial |
k |
This applies to the top method, choose which top k to focus on |
Value
Pairwise breakings, where the three columns are winner, loser and rank distance (latter used for Zemel)
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
A1 Election Data
Description
This is a public election dataset collected by Nicolaus Tideman where the voters provided partial orders on candidates. A partial order includes comparisons among a subset of alternative, and the non-mentioned alternatives in the partial order are considered to be ranked lower than the lowest ranked alternative among mentioned alternatives.
Usage
data(Data.Election1)
Author(s)
Nicolaus Tideman
A6 Election Data
Description
This is a public election dataset collected by Nicolaus Tideman where the voters provided partial orders on candidates. A partial order includes comparisons among a subset of alternative, and the non-mentioned alternatives in the partial order are considered to be ranked lower than the lowest ranked alternative among mentioned alternatives.
Usage
data(Data.Election6)
Author(s)
Nicolaus Tideman
A9 Election Data
Description
This is a public election dataset collected by Nicolaus Tideman where the voters provided partial orders on candidates. A partial order includes comparisons among a subset of alternative, and the non-mentioned alternatives in the partial order are considered to be ranked lower than the lowest ranked alternative among mentioned alternatives.
Usage
data(Data.Election9)
Author(s)
Nicolaus Tideman
Nascar Data
Description
Nascar Data
Usage
data(Data.Nascar)
Trimmed Nascar Data
Description
Nascar data that only keeps racers that are represented in between 20 - 30 of total races
Usage
data(Data.NascarTrimmed)
Tiny test dataset
Description
This is a randomly generated tiny ranks file that we can use to test our methods
Usage
data(Data.Test)
Performs parameter estimation for a Generalized Random Utility Model with user and alternative characteristics
Description
This function supports RUMs 1) Normal with fixed variance (fixed at 1)
Usage
Estimation.GRUM.MLE(Data, X, Z, iter, dist, din, Bin)
Arguments
Data |
data in either partial or full rankings |
X |
user characteristics |
Z |
alternative characteristics |
iter |
number of iterations to run algorithm |
dist |
choice of distribution |
din |
initialization of delta vector |
Bin |
intialization of B matrix |
Value
results from the inference
Examples
#data(Data.Test)
#Data.X= matrix( runif(15),5,3)
#Data.Z= matrix(runif(10),2,5)
#Estimation.GRUM.MLE(Data.Test, Data.X, Data.Z, iter = 3, dist = "norm",
#din=runif(5), Bin=matrix(runif(6),3,2))
GMM Method for Estimating Random Utility Model wih Normal dsitributions
Description
GMM Method for Estimating Random Utility Model wih Normal dsitributions
Usage
Estimation.Normal.GMM(Data.pairs, m, iter = 1000, Var = FALSE, prior = 0)
Arguments
Data.pairs |
data broken up into pairs |
m |
number of alternatives |
iter |
number of iterations to run |
Var |
indicator for difference variance (default is FALSE) |
prior |
magnitude of fake observations input into the model |
Value
Estimated mean parameters for distribution of underlying normal (variance is fixed at 1)
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
Estimation.Normal.GMM(Data.Test.pairs, 5)
GMM Method for estimating Plackett-Luce model parameters
Description
GMM Method for estimating Plackett-Luce model parameters
Usage
Estimation.PL.GMM(Data.pairs, m, prior = 0, weighted = FALSE)
Arguments
Data.pairs |
data broken up into pairs |
m |
number of alternatives |
prior |
magnitude of fake observations input into the model |
weighted |
if this is true, then the third column of Data.pairs is used as a weight for that data point |
Value
Estimated mean parameters for distribution of underlying exponential
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
Estimation.PL.GMM(Data.Test.pairs, 5)
Performs parameter estimation for the Plackett-Luce model using an Minorize Maximize algorithm
Description
Performs parameter estimation for the Plackett-Luce model using an Minorize Maximize algorithm
Usage
Estimation.PL.MLE(Data, iter = 10)
Arguments
Data |
data in either partial or full rankings (Partial rank case works for settings like car racing) |
iter |
number of MM iterations to run |
Value
list of estimated means (Gamma) and the log likelihoods
Examples
data(Data.Test)
Estimation.PL.MLE(Data.Test)
Performs parameter estimation for a Random Utility Model with different noise distributions
Description
This function supports RUMs 1) Normal 2) Normal with fixed variance (fixed at 1) 3) Exponential (top k setting like Election)
Usage
Estimation.RUM.MLE(Data, iter = 10, dist, race = FALSE)
Arguments
Data |
data in either partial or full rankings |
iter |
number of EM iterations to run |
dist |
underlying distribution. Can be "norm", "norm.fixedvariance", "exp" |
race |
indicator that each agent chose a random subset of alternatives to compare |
Value
parameters of the latent RUM distributions
Examples
Data.Tiny <- matrix(c(1, 2, 3, 3, 2, 1, 1, 2, 3), ncol = 3, byrow = TRUE)
Estimation.RUM.MLE(Data.Tiny, iter = 2, dist="norm")
Performs parameter estimation for a Multitype Random Utility Model
Description
This function supports RUMs 1) Normal 2) Normal with fixed variance (fixed at 1) 3) Exponential
Usage
Estimation.RUM.MultiType.MLE(Data, K = 2, iter = 10, dist, ratio = 0.2,
race = FALSE)
Arguments
Data |
data in either partial or full rankings |
K |
number of components in mixture distribution |
iter |
number of EM iterations to run |
dist |
underlying distribution. Can be "norm", "norm.fixedvariance", "exp" |
ratio |
parameter in the algorithm that controls the difference of the starting points, the bigger the ratio the more the distance |
race |
TRUE if data is sub partial, FALSE (default) if not |
Value
results from the inference
Examples
Data.Tiny <- matrix(c(1, 2, 3, 3, 2, 1, 1, 2, 3), ncol = 3, byrow = TRUE)
Estimation.RUM.MultiType.MLE(Data.Tiny, K=2, iter = 3, dist= "norm.fixedvariance")
Nonparametric RUM Estimator
Description
Given rank data (full, top partial, or sub partial), this function returns an inference object that fits nonparametric latent utilties on the rank data.
Usage
Estimation.RUM.Nonparametric(Data, m, iter = 10, bw = 0.025,
utilities.per.agent = 20, race = FALSE)
Arguments
Data |
full, top partial, or sub partial rank data |
m |
number of alternatives |
iter |
number of EM iterations to run |
bw |
bandwidth, or smoothing parameter for KDE |
utilities.per.agent |
Number of utility vector samples that we get per agent. More generally gives a more accurate estimate |
race |
TRUE if data is sub partial, FALSE (default) if not |
Examples
data(Data.Test)
Estimation.RUM.Nonparametric(Data.Test, m = 5, iter = 3)
Estimates Zemel Parameters via Gradient Descent
Description
This function takes in data broken into pairs, and estimates the parameters of the Zemel mode via Gradient Descent
Usage
Estimation.Zemel.MLE(Data.pairs, m, threshold = 1e-04,
learning.rate = 1/30000)
Arguments
Data.pairs |
data broken up into pairwise comparisons |
m |
how many alternatives |
threshold |
turning parameter for gradient descent |
learning.rate |
turning parameter for gradient descent |
Value
a set of scores for the alternatives, normalized such that the sum of the log scores is 0 scores <- Generate.Zemel.Parameters(10)$Score pairs <- Generate.Zemel.Ranks.Pairs(scores, 10, 10) Estimation.Zemel.MLE(pairs, 10, threshold = .1)
Calculates the Average Precision
Description
Calculates the Average Precision
Usage
Evaluation.AveragePrecision(EstimatedRank, RelevanceLevel)
Arguments
EstimatedRank |
estimated ranking |
RelevanceLevel |
score for the document |
Value
The AP for this estimation and relevance level
Examples
EstimatedRank <- scramble(1:10)
RelevanceLevel <- runif(10)
Evaluation.AveragePrecision(EstimatedRank, RelevanceLevel)
Calculates KL divergence between empirical pairwise preferences and modeled pairwise preferences
Description
Calculates KL divergence between empirical pairwise preferences and modeled pairwise preferences
Usage
Evaluation.KL(Data.pairs, m, Estimate, pairwise.prob = NA, prior = 0,
nonparametric = FALSE, ...)
Arguments
Data.pairs |
data broken up into pairs using Breaking function |
m |
number of alternatives |
Estimate |
estimation object from an Estimate function |
pairwise.prob |
Function that given two alternatives from the the Parameters argument, returns back a model probability that one is larger than the other |
prior |
prior weight to put in pairwise frequency matrix |
nonparametric |
indicator that model is nonparametric (default FALSE) |
... |
additional arguments passed to generateC.model |
Value
the KL divergence between modeled and empirical pairwise preferences, thinking of the probabilities as a probability distribution over the (n choose 2) pairs
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
m <- 5
Estimate <- Estimation.PL.GMM(Data.Test.pairs, m)
Evaluation.KL(Data.Test.pairs, m, Estimate, PL.Pairwise.Prob)
Calculates the Kendall Tau correlation between two ranks
Description
Calculates the Kendall Tau correlation between two ranks
Usage
Evaluation.KendallTau(rank1, rank2)
Arguments
rank1 |
two rankings. Order does not matter |
rank2 |
two rankings. Order does not matter |
Value
The Kendall Tau correlation
Examples
rank1 <- scramble(1:10)
rank2 <- scramble(1:10)
Evaluation.KendallTau(rank1, rank2)
Calculates the location of the True winner in the estimated ranking
Description
Calculates the location of the True winner in the estimated ranking
Usage
Evaluation.LocationofWinner(EstimatedRank, TrueRank)
Arguments
EstimatedRank |
estimated ranking |
TrueRank |
true ranking |
Value
The location of the true best in the estimated rank
Examples
rank1 <- scramble(1:10)
rank2 <- scramble(1:10)
Evaluation.LocationofWinner(rank1, rank2)
Calculates MSE between empirical pairwise preferences and modeled pairwise preferences
Description
Calculates MSE between empirical pairwise preferences and modeled pairwise preferences
Usage
Evaluation.MSE(Data.pairs, m, Estimate, pairwise.prob = NA, prior = 0,
nonparametric = FALSE, ...)
Arguments
Data.pairs |
data broken up into pairs using Breaking function |
m |
number of alternatives |
Estimate |
estimation object from an Estimate function |
pairwise.prob |
Function that given two alternatives from |
prior |
prior weight to put in pairwise frequency matrix |
nonparametric |
indicator that model is nonparametric (default FALSE) the the Parameters argument, returns back a model probability that one is larger than the other |
... |
additioanal parameters passed into generateC.model |
Value
the KL divergence between modeled and empirical pairwise preferences, thinking of the probabilities as a probability distribution over the (n choose 2) pairs
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
m <- 5
Estimate <- Estimation.PL.GMM(Data.Test.pairs, m)
Evaluation.MSE(Data.Test.pairs, m, Estimate, PL.Pairwise.Prob)
Calculates the Normalized Discounted Cumluative Gain
Description
Calculates the Normalized Discounted Cumluative Gain
Usage
Evaluation.NDCG(EstimatedRank, RelevanceLevel)
Arguments
EstimatedRank |
estimated ranking |
RelevanceLevel |
score for the document |
Value
The NDCG for this estimation and relevance level
Examples
EstimatedRank <- scramble(1:10)
RelevanceLevel <- runif(10)
Evaluation.NDCG(EstimatedRank, RelevanceLevel)
Calculates the Average Precision at k
Description
Calculates the Average Precision at k
Usage
Evaluation.Precision.at.k(EstimatedRank, RelevanceLevel, k)
Arguments
EstimatedRank |
estimated ranking |
RelevanceLevel |
score for the document |
k |
positive that we want to run this algorithm for |
Value
The AP at k for this estimation and relevance level
Examples
EstimatedRank <- scramble(1:10)
RelevanceLevel <- runif(10)
Evaluation.Precision.at.k(EstimatedRank, RelevanceLevel, 5)
Calculates TVD between empirical pairwise preferences and modeled pairwise preferences
Description
Calculates TVD between empirical pairwise preferences and modeled pairwise preferences
Usage
Evaluation.TVD(Data.pairs, m, Estimate, pairwise.prob = NA, prior = 0,
nonparametric = FALSE, ...)
Arguments
Data.pairs |
data broken up into pairs using Breaking function |
m |
number of alternatives |
Estimate |
estimation object from an Estimate function |
pairwise.prob |
Function that given two alternatives from |
prior |
prior weight to put in pairwise frequency matrix |
nonparametric |
indicator that model is nonparametric (default FALSE) the the Parameters argument, returns back a model probability that one is larger than the other |
... |
additional arguments passed to generateC.model |
Value
the TVD between modeled and empirical pairwise preferences, thinking of the probabilities as a probability distribution over the (n choose 2) pairs
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
m <- 5
Estimate <- Estimation.PL.GMM(Data.Test.pairs, m)
Evaluation.TVD(Data.Test.pairs, m, Estimate, PL.Pairwise.Prob)
Pairwise Probability for PL Multitype Model
Description
Given alternatives a and b (both items from the inference object) what is the probability that a beats b?
Usage
Expo.MultiType.Pairwise.Prob(a, b)
Arguments
a |
list containing parameters for a |
b |
list containing parameters for b |
Value
probability that a beats b
Generate data from an NPRUM model
Description
This is useful for performing inference tasks for NPRUM
Usage
Generate.NPRUM.Data(Estimate, n, bw = 0.1)
Arguments
Estimate |
fitted NPRUM object |
n |
number of agents that we want in our sample |
bw |
smoothing parameter to use when sampling data |
Examples
Data.Tiny <- matrix(c(1, 2, 3, 3, 2, 1, 1, 2, 3), ncol = 3, byrow = TRUE)
Estimate <- Estimation.RUM.Nonparametric(Data.Tiny, m = 3, iter = 3)
Generate.NPRUM.Data(Estimate, 3, bw = 0.1)
Generate observation of ranks given parameters
Description
Given a list of parameters (generated via the Generate RUM Parameters function), generate random utilities from these models and then return their ranks
Usage
Generate.RUM.Data(Params, m, n, distribution)
Arguments
Params |
inference object from an Estimation function, or parameters object from a generate function |
m |
number of alternatives |
n |
number of agents |
distribution |
can be either 'normal' or 'exponential' |
Value
a matrix of observed rankings
Examples
Params = Generate.RUM.Parameters(10, "normal")
Generate.RUM.Data(Params,m=10,n=5,"normal")
Params = Generate.RUM.Parameters(10, "exponential")
Generate.RUM.Data(Params,m=10,n=5,"exponential")
Parameter Generation for a RUM model
Description
Exponential models mean parameters are drawn from a uniform distribution Normal models, mean and standard devaition parameters are drawn from a standard unifrom
Usage
Generate.RUM.Parameters(m, distribution)
Arguments
m |
number of sets of parameters to be drawn |
distribution |
either 'normal' or 'exponential' |
Value
a list of RUM parameters
Examples
Generate.RUM.Parameters(10, "normal")
Generate.RUM.Parameters(10, "exponential")
Generates possible scores for a Zemel model
Description
Generates possible scores for a Zemel model
Usage
Generate.Zemel.Parameters(m)
Arguments
m |
Number of alternatives |
Value
a set of scores, all whose logs sum to 1
Examples
Generate.Zemel.Parameters(10)
Generates pairwise ranks from a Zemel model given a set of scores
Description
Generates pairwise ranks from a Zemel model given a set of scores
Usage
Generate.Zemel.Ranks.Pairs(scores, m, n)
Arguments
scores |
a vector of scores |
m |
Number of alternatives |
n |
Number of pairwise alternatives to generate |
Value
simulated pairwise comparison data
Examples
scores <- Generate.Zemel.Parameters(10)$Score
Generate.Zemel.Ranks.Pairs(scores, 10, 10)
Calculates KL Divergence between non-diagonal entries of two matrices
Description
Calculates KL Divergence between non-diagonal entries of two matrices
Usage
KL(A, B)
Arguments
A |
first matrix, this is the "true" distribution |
B |
second matrix, this is the "estimated" distribution |
Value
KL divergence
Examples
KL(matrix(runif(25), nrow=5), matrix(runif(25), nrow=5))
Calculate Likelihood for the nonparametric model
Description
Computes likelihood in the case that we assume no correlation structure
Usage
Likelihood.Nonparametric(Data, Estimate, race = FALSE)
Arguments
Data |
full, top partial, or subpartial data |
Estimate |
fitted NPRUM object |
race |
indicator that the data is from subpartial data |
Examples
data(Data.Test)
Estimate <- Estimation.RUM.Nonparametric(Data.Test, m = 5, iter = 3)
Likelihood.Nonparametric(Data.Test, Estimate)
A faster Likelihood for Plackett-Luce Model
Description
A faster Likelihood for Plackett-Luce Model
Usage
Likelihood.PL(Data, parameter)
Arguments
Data |
ranking data |
parameter |
Mean of Exponential Distribution |
Value
log likelihood
Examples
data(Data.Test)
parameter = Generate.RUM.Parameters(5, "exponential")
Likelihood.PL(Data.Test, parameter)
Likelihood for general Random Utility Models
Description
Likelihood for general Random Utility Models
Usage
Likelihood.RUM(Data, parameter, dist = "exp", range = NA, res = NA,
race = FALSE)
Arguments
Data |
ranking data |
parameter |
Mean of Exponential Distribution |
dist |
exp or norm |
range |
range |
res |
res |
race |
TRUE if data is sub partial, FALSE (default) if not |
Value
log likelihood
Examples
data(Data.Test)
parameter = Generate.RUM.Parameters(5, "normal")
Likelihood.RUM(Data.Test,parameter, "norm")
Likelihood for Multitype Random Utility Models
Description
Likelihood for Multitype Random Utility Models
Usage
Likelihood.RUM.Multitype(Data, Estimate, dist, race = FALSE)
Arguments
Data |
n by m table of rankings |
Estimate |
Inference object from Estimation function |
dist |
Distribution of noise (exp or norm) |
race |
TRUE if data is sub partial, FALSE (default) if not |
Value
log likelihood
Examples
Data.Tiny <- matrix(c(1, 2, 3, 3, 2, 1, 1, 2, 3), ncol = 3, byrow = TRUE)
Estimate <- Estimation.RUM.MultiType.MLE(Data.Tiny, K=2, iter = 1, dist= "norm")
Likelihood.RUM.Multitype(Data.Tiny, Estimate, dist = "norm")
Gives Zemel pairwise Log-likelihood with data and scores
Description
Calculates the log-likelihood in the pairwise Zemel model
Usage
Likelihood.Zemel(Data.pairs, Estimate)
Arguments
Data.pairs |
data broken up into pairwise comparisons |
Estimate |
Inference object from Estimate function |
Value
a log-likelihood of the data under the Zemel model
Examples
Estimate <- Generate.Zemel.Parameters(10)
pairs <- Generate.Zemel.Ranks.Pairs(Estimate$Score, 10, 10)
Likelihood.Zemel(pairs, Estimate)
Calculates MSE between non-diagonal entries of two matrices if the diagonal elements are 0s
Description
Calculates MSE between non-diagonal entries of two matrices if the diagonal elements are 0s
Usage
MSE(A, B)
Arguments
A |
first matrix |
B |
second matrix |
Value
MSE divergence
Examples
MSE(matrix(runif(25), nrow=5), matrix(runif(25), nrow=5))
Pairwise Probability for Normal Multitype Model
Description
Given alternatives a and b (both items from the inference object) what is the probability that a beats b?
Usage
Normal.MultiType.Pairwise.Prob(a, b)
Arguments
a |
list containing parameters for a |
b |
list containing parameters for b |
Value
probability that a beats b
Pairwise Probability for Normal Model
Description
Given alternatives a and b (both items from the inference object) what is the probability that a beats b?
Usage
Normal.Pairwise.Prob(a, b)
Arguments
a |
list containing parameters for a |
b |
list containing parameters for b |
Value
probability that a beats b
Pairwise Probability for PL Model
Description
Given alternatives a and b (both items from the inference object) what is the probability that a beats b?
Usage
PL.Pairwise.Prob(a, b)
Arguments
a |
list containing parameters for a |
b |
list containing parameters for b |
Value
probability that a beats b
Calculates TVD between two matrices
Description
Calculates TVD between two matrices
Usage
TVD(A, B)
Arguments
A |
first matrix |
B |
second matrix |
Value
Total variation distance
Examples
TVD(matrix(runif(25), nrow=5), matrix(runif(25), nrow=5))
RPD Visualization
Description
Creates histograms of the empriical rank position distribution for each alternative in rank data
Usage
Visualization.Empirical(Data, ymax, ncol = 5, names = NA)
Arguments
Data |
full, top partial, or sub partial data |
ymax |
maximum value of density to show on graph |
ncol |
number of columns visualization is displayed in |
names |
names of alternatives |
Examples
library(ggplot2)
library(gridExtra)
data(Data.Test)
Visualization.Empirical(Data.Test, 0.5)
Multitype Random Utility visualizer
Description
Multitype Random Utility visualizer
Usage
Visualization.MultiType(multitype.output, min, max, names, ncol)
Arguments
multitype.output |
output from a multitype fitter |
min |
left boundary of graphed x-axis |
max |
right boundary of graphed x-axis |
names |
names of alternatives |
ncol |
number of columns in final output |
Value
none
Examples
library(ggplot2)
library(gridExtra)
Data.Tiny <- matrix(c(1, 2, 3, 3, 2, 1, 1, 2, 3), ncol = 3, byrow = TRUE)
multitype.output <- Estimation.RUM.MultiType.MLE(Data.Tiny, iter = 1, dist = "norm", ratio = .5)
names <- 1:3
#run the following code to make plots
#plots <- Visualization.MultiType(multitype.output, -2, 2, names, 3)
Creates pairwise matrices to compare inference results with the empirical pairwise probabilities
Description
Creates pairwise matrices to compare inference results with the empirical pairwise probabilities
Usage
Visualization.Pairwise.Probabilities(Data.pairs, Parameters, get.pairwise.prob,
name.of.method)
Arguments
Data.pairs |
datas broken into pairs |
Parameters |
The Parameter element of a result from an Estimation function |
get.pairwise.prob |
function that we use to generate the pairwise probability of beating |
name.of.method |
names of the alternatives |
Value
none
Examples
library(ggplot2)
library(gridExtra)
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
Parameters <- Estimation.PL.GMM(Data.Test.pairs, 5)$Parameters
PL.Pairwise.Prob <- function(a, b) a$Mean / (a$Mean + b$Mean)
Visualization.Pairwise.Probabilities(Data.Test.pairs, Parameters, PL.Pairwise.Prob, "PL")
RUMplot visualization
Description
Creates marginal random utility density plots for each alternatives given an Estimation object for a PL or Nonparameteric model
Usage
Visualization.RUMplots(RUM = "Exponential", Estimate = NA, min = -5,
max = 5, ncol = 5, names = NA)
Arguments
RUM |
choice of Exponential, Gumbel, or Nonparametric |
Estimate |
fitted RUM object |
min |
minimum x value to display |
max |
maximum x value to display |
ncol |
number of columns in the visualization |
names |
names of alternatives |
Examples
library(ggplot2)
library(gridExtra)
Data.Tiny <- matrix(c(1, 2, 3, 3, 2, 1, 1, 2, 3), ncol = 3, byrow = TRUE)
Estimate <- Estimation.PL.GMM(Breaking(Data.Tiny, method = "full"), m = 3)
Visualization.RUMplots("Exponential", Estimate, names = 1:3)
Pairwise Probability for Zemel
Description
Given alternatives a and b (both items from the inference object) what is the probability that a beats b?
Usage
Zemel.Pairwise.Prob(a, b)
Arguments
a |
list containing parameters for a |
b |
list containing parameters for b |
Value
probability that a beats b
Helper function for the graphing interface
Description
As named, this function takes a vector where each element is a mean, then returns back a list, with each list item having the mean
Usage
convert.vector.to.list(Parameters, name = "Mean")
Arguments
Parameters |
a vector of parameters |
name |
Name of the parameter |
Value
a list, where each element represents an alternative and has a Mean value
Generate a matrix of pairwise wins
Description
This function takes in data that has been broken up into pair format. The user is given a matrix C, where element C[i, j] represents (if normalized is FALSE) exactly how many times alternative i has beaten alternative j (if normalized is TRUE) the observed probability that alternative i beats j
Usage
generateC(Data.pairs, m, weighted = FALSE, prior = 0, normalized = TRUE)
Arguments
Data.pairs |
the data broken up into pairs |
m |
the tot al number of alternatives |
weighted |
whether or not this generateC should use the third column of Data.pairs as the weights |
prior |
the initial "fake data" that you want to include in C. A prior of 1 would mean that you initially "observe" that all alternatives beat all other alternatives exactly once. |
normalized |
if TRUE, then normalizes entries to probabilities |
Value
a Count matrix of how many times alternative i has beat alternative j
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
generateC(Data.Test.pairs, 5)
Turns inference object into modeled C matrix.
Description
For parametric models, plug in a pairwise function for get.pairwise.prob. For nonparametric models, set nonparametric = TRUE
Usage
generateC.model(Estimate, get.pairwise.prob = NA, nonparametric = FALSE,
...)
Arguments
Estimate |
inference object with a Parameter element, with a list of parameters for each alternative |
get.pairwise.prob |
(use this if its a parametric model) function that takes in two lists of parameters and computes the probability that the first is ranked higher than the second |
nonparametric |
set this flag to TRUE if this is a non-parametric model |
... |
additional arguments passed to generateC.model.Nonparametric (bandwidth) |
Examples
data(Data.Test)
Data.Test.pairs <- Breaking(Data.Test, "full")
Estimate <- Estimation.Normal.GMM(Data.Test.pairs, 5)
generateC.model(Estimate, Normal.Pairwise.Prob)
Generate pairwise matrix for an NPRUM model
Description
Generates a matrix where entry i, j is the estimated probabiltiy that alternative i beats alternative j
Usage
generateC.model.Nonparametric(Estimate, bw = 0.1)
Arguments
Estimate |
fitted NPRUM object |
bw |
bandwidth used for generating the pairwise probabilites |
Examples
data(Data.Test)
Estimate <- Estimation.RUM.Nonparametric(Data.Test, m = 5, iter = 3)
generateC.model.Nonparametric(Estimate)
Converts scores to a ranking
Description
takes in vector of scores (with the largest score being the one most preferred) and returns back a vector of WINNER, SECOND PLACE, ... LAST PLACE
Usage
scores.to.order(scores)
Arguments
scores |
the scores (e.g. means) of a set of alternatives |
Value
an ordering of the index of the winner, second place, etc.
Examples
scores <- Generate.RUM.Parameters(10, "exponential")$Mean
scores.to.order(scores)
Scramble a vector
Description
This function takes a vector and returns it in a random order
Usage
scramble(x)
Arguments
x |
a vector |
Value
a vector, now in random order
Examples
scramble(1:10)
Converts a matrix into a table
Description
takes a matrix and returns a data frame with the columns being row, column, entry
Usage
turn_matrix_into_table(A, uppertriangle = FALSE)
Arguments
A |
matrix to be converted |
uppertriangle |
if true, then will only convert the upper right triangle of matrix |
Value
a table with the entries being the row, column, and matrix entry