Package 'StatRank'

Title: Statistical Rank Aggregation: Inference, Evaluation, and Visualization
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.
Authors: Hossein Azari Soufiani, William Chen
Maintainer: Hossein Azari Soufiani <[email protected]>
License: GPL (>= 2)
Version: 0.0.6
Built: 2025-01-19 03:30:00 UTC
Source: https://github.com/cran/StatRank

Help Index

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")

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

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 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 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 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)

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)

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

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

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