Paired Comparison Data Analysis

Description

Different tools for describing and analysing paired comparison data are presented. Main methods are estimation of products scores according Bradley Terry Luce model. A segmentation of the individual could be conducted on the basis of a mixture distribution approach. The number of classes can be tested by the use of Monte Carlo simulations. This package deals also with multi-criteria paired comparison data.

Details

Function to estimate products configurations (Bradley's scores) and weights of the
classes is EstimBradley().

Function to perform a test concerning the number of classes is ResSimulLvrRatio().

Function to obtain a graphical representation of Bradley's scores is Piplot().

Author(s)

Michel Semenou

Maintainer: <michel.semenou@oniris-nantes.fr>

See Also

EstimBradley, ResSimulLvrRatio, Piplot

Examples

data(Cocktail)
show(Cocktail)
ResCock1<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=0.001,eps1=0.001,TestPi=TRUE)
show(ResCock1)
Res_LvrRatio1<-ResSimulLvrRatio(Cocktail,ResCock1,0,3,level=0.05,eps=0.001,eps1=0.001)
getSimu(Res_LvrRatio1)
getTest(Res_LvrRatio1)

Class "BradleyEstim"

Description

A class for Bradley's scores estimation results

Objects from the Class

Objects can be created by the function EstimBradley().

Slots

Lvriter:

Object of class "matrix" corresponding to the number of iterations of the EM algorithm, LogLikelihoods at the previous step and the current step, and the differences between these 2 LogLikelihoods

Lvr:

Object of class "numeric" final value of the LogLikelihood

Lambda:

Object of class "matrix" weights of the different classes

Pi:

Object of class "list" Bradley's scores for each class and each criteria

Zh:

Object of class "matrix" with the posterior probabilities for each individual to belong to the different classes and the class with the higher probability

Ic:

Object of class "matrix" value of the different Information criterion (AIC, BIC, CAIC)

Restestglob:

Object of class "list" result of testing the whole Bradley's scores equality for each class and each criteria

Restestprod:

Object of class "list" result of multiple comparison tests for Bradley's scores in each class and for each criteria

Varcov:

Object of class "list" of covaraince matrices of Bradley's scores in each class and for each criteria

Methods

getIc

signature(object = "BradleyEstim")

getLambda

signature(object = "BradleyEstim")

getLvr

signature(object = "BradleyEstim")

getLvriter

signature(object = "BradleyEstim")

getPi

signature(object = "BradleyEstim")

getRestestglob

signature(object = "BradleyEstim")

getRestestprod

signature(object = "BradleyEstim")

getVarcov

signature(object = "BradleyEstim")

getZh

signature(object = "BradleyEstim")

show

signature(object = "BradleyEstim")

Examples

data(ResCocktail1)
show(ResCocktail1)

Estimation of Bradley's scores

Description

Returns the Bradley's scores of the different items and the value of the LogLikelihood

Usage

C_piBTL(Matpair, Constraint=0, eps1=1e-04, Pi=NULL, TestPi=FALSE, Zht=NULL)

Arguments

Details

The algorithm is based on a maximum likelihood approach using Dykstra method.

Value

List of following components:

Examples

  data(Cocktail_Cum)
  res<-C_piBTL(Cocktail_Cum,Constraint=0,eps1=1e-04,Pi=NULL,TestPi=TRUE)
  res

Create an object of class DataPairComp

Description

return an object of DataPairComp class

Usage

ClassDataPairComp(Mat, labelprod = NULL, labelcons = NULL, labelcrit = NULL)

Arguments

Value

Object of class DataPairComp with the following elements:

Cons : corresponding to the label of consummers (default : Number of consummers)

Crit : name of the different criteria contained

Prod : names of the different products (default : number of the product)

Paircomp : list of number of criteria elements each corresponding to the results of paired comparisons performed by the consummers.

Classification of paired comparison data

Description

Returns the result of consummers classification

Usage

ClassifPaired(Data,Tcla) 

Arguments

Details

The function performs a hierarchical cluster analysis on a set of dissimilarities based on pairwise comparison matrices, using the functions hclust and cutree of stats package.

Value

vector with group menberships resulting from the classification with Tcla clusters.

See Also

hclust, cutree of stats package

Beverages paired comparison

Description

Paired comparison of 7 beverages by 112 subjects according their preferences

Usage

data(Cocktail)

Format

A DataPairComp class object with the following elements:

Cons : corresponding to the label of consummers (default : Number of consummers)

Crit : name of the different criteria contained

Prod : names of the different products (default : number of the product)

Paircomp : list of number of criteria elements each corresponding to the results of paired comparisons performed by the consummers.

Examples

  data(Cocktail)
  show(Cocktail)

Beverages paired comparison

Description

Paired comparison of 7 beverages by 112 subjects according their preferences

Usage

data(Cocktail)

Format

A matrix resulting of the cumulative paired comparison results of 7 products by 112 consumers. The (i,j) element correponds to the number of time product i was prefered to product j among all comparisons between these two products.

Examples

  data(Cocktail_Cum)
  Cocktail_Cum

Class "DataPairComp"

Description

A class for Paired comparison data

Objects from the Class

Objects can be created by calls of the form new("DataPairComp", ...), or by the function ImportData().

Slots

Cons:

Object of class "character" label for the individuals

Crit:

Object of class "character" label for the criterion

Prod:

Object of class "character" label for the products

Paircomp:

Object of class "list" corresponding to the individual results of paired comparisons for each criteria, when products i and j are presented to individual h, the (i,j) element resulting is coded by 1 if i is choosen against j and 0 otherwise

Methods

getCons

signature(object = "DataPairComp")

getCrit

signature(object = "DataPairComp")

getPaircomp

signature(object = "DataPairComp")

getProd

signature(object = "DataPairComp")

show

signature(object = "DataPairComp")

See Also

ImportData

Examples

data(Cocktail)
show(Cocktail)

Simulation of paired comparison data

Description

Returns paired comparison data according a given configuration

Usage

DataSimulH0(Data, ResH0)

Arguments

Details

The paired comparison data are simulated according the products configuration, the weight of the different classes for the different criteria (stored in the object ResH0 of class BradleyEstim) obtained on the basis of the results of EstimBradley function for the paired comparison data contained in the objet Data of class DataPairComp

Value

Object of class DataPairComp with the following components:

Cons : corresponding to the label of consummers

Crit : names of the different criteria

Prod : names of the different products

Paircomp : list of number of criteria elements each corresponding to the results of simulated paired comparisons performed by the consummers according their belonging to the different classes.

Estimation of Bradley's scores in the different classes of subjects

Description

Estimates Bradley's scores according the desired number of classes.

Usage

EstimBradley(Data, Constraint=0, Tcla=1, eps=1e-04, eps1=1e-04, TestPi=TRUE)

Arguments

Details

The estimation is based on maximum likelihood for mixture distributions with E.M. algorithm.

Value

Object of class BradleyEstim with the following components:

Examples

data(Cocktail)
show(Cocktail)
ResCock1<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=0.001,eps1=0.001,TestPi=TRUE)
show(ResCock1)

Import data file

Description

Import the different paired comparison data files in cvs format and create an object
of class DataPairComp

Usage

ImportData(name,labelprod=FALSE,labelconso=NULL, sep =";",dec=".")

Arguments

Value

Object of class DataPairComp with the following elements:

Cons : corresponding to the label of consummers (default : Number of consummer)

Crit : names of the different criteria contained in the name of the different data files

Prod : names of the different products (default : number of the product)

Paircomp : list of number of criteria elements each corresponding to the results of paired comparisons performed by the consummers.

Class "LvrRatio"

Description

A class for Lilkelihood Ration Test results

Objects from the Class

Objects can be created by ResSimulLvrRatio().

Slots

Simu:

Object of class "matrix" with the number of classes under H0, Loglikelihoods under H0 and H1, difference between these Loglikelihoods.

Test:

Object of class "matrix" with the level and the associated quantile after performing Likelihood Ratio test.

Methods

getSimu

signature(object = "LvrRatio")

getTest

signature(object = "LvrRatio")

Examples

showClass("LvrRatio")

Graphical representation of the Bradley's scores

Description

Gives a graphical representation of the Bradley's scores.

Usage

Piplot(Pi, SigmaPi = NULL, level=0.05, main = NULL, ylab = "Bradley's scores",
xlab = "Item", labelprod = NULL)

Arguments

Details

The representation is based on plot(x) function, with Item on x axis, and Bradley's scores on y axis. If SigmaPi is provided by user, a 1-level (default 95%) confidence interval is drawn for each Item.

Value

A graphical representation of bradley's scores.

Examples

  data(Cocktail_Cum)
  res<-C_piBTL(Cocktail_Cum,Constraint=0,eps1=0.0001,Pi=NULL,TestPi=TRUE)
  Res_Pi<-res$Pi
  Res_Varcov<-res$VarcovPi
  Res_Sigma<-sqrt(diag(Res_Varcov))
  Piplot(Res_Pi, SigmaPi = Res_Sigma, level=0.01, main = NULL, ylab = "Bradley's scores",
  xlab = "Item", labelprod = NULL)
  
  

Result of EstimBradley function for 1 class and data Cocktail

Description

Result of EstimBradley function for 1 class and data Cocktail

Usage

data(ResCocktail1)

Format

A BradleyEstim class object with the following elements:

Examples

data(ResCocktail1)
show(ResCocktail1)

Log Likelihood Ratio Test for Paired comparison data

Description

Returns the result of Log Likelihood Ratio Test of the number of classes for Paired comparison data (T classes versus (T+1) classes)

Usage

ResSimulLvrRatio(Data,ResH0,Constraint,nsimul,level,eps=1e-04,eps1=1e-04)

Arguments

Details

The likelihood ratio test is based on a Monte Carlo procedure. A simulation of nsimul data set is done. We perform estimation of the different parameters for the number of classes defined in the object ResH0 of class BradleyEstim (corresponding to the null hymothesis) and for one more class corresponding to the alternative hypothesis.

We obtain a set of Log Likelihoods under the null and alternative hypothesis on the basis of simulated data and so of the Log Likelihood Ratio Statistic.

We replace the observed value of this statistic for the true data set. And we conclude on the acceptation or not of the null hypothesis (no differences between T and T+1 classes).

Value

Object of class LvrRatio with the following components:

Examples

data(Cocktail)
ResCock1<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
Res_LvrRatio1<-ResSimulLvrRatio(Cocktail,ResCock1,0,3,level=0.05,eps=0.001,eps1=0.001)
getSimu(Res_LvrRatio1)
getTest(Res_LvrRatio1)

Gets the individuals labels.

Description

Gets the individuals labels.

Usage

getCons(object)

Arguments

Value

vector of the individuals labels.

Examples

data(Cocktail)
Cocktail_Cons<-getCons(Cocktail)

Methods for Function getCons

Description

Methods for function getCons

Methods

signature(object = "DataPairComp")

Gets the criteria's labels.

Description

Gets the criteria's labels.

Usage

getCrit(object)

Arguments

Value

vector of the criteria's labels.

Examples

data(Cocktail)
Cocktail_Crit<-getCrit(Cocktail)

Methods for Function getCrit

Description

Methods for function getCrit

Methods

signature(object = "DataPairComp")

Gets the Information criteria's labels.

Description

Gets the Information criteria's labels (AIC, BIC, CAIC).

Usage

getIc(object)

Arguments

Value

vector of Information criteria.

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Ic<-getIc(ResCock)

Methods for Function getIc

Description

Methods for function getIc

Methods

signature(object = "BradleyEstim")

Gets the weight of the different classes.

Description

Gets the weight of the different classes from the function EstimBradley().

Usage

getLambda(object)

Arguments

Value

A vector of the weights of the different classes.

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Lambda<-getLambda(ResCock)

Methods for Function getLambda

Description

Methods for function getLambda

Methods

signature(object = "BradleyEstim")

Gets the final value of loglikelihood.

Description

Gets the final value of loglikelihood from the function EstimBradley().

Usage

getLvr(object)

Arguments

Value

Numeric value of the loglikelihood.

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Lvr<-getLvr(ResCock)

Methods for Function getLvr

Description

Methods for function getLvr

Methods

signature(object = "BradleyEstim")

Gets the iteration done until convergence of the loglikelihood estimation of Bradley's scores.

Description

Gets the iteration done until convergence from the function EstimBradley()

Usage

getLvriter(object)

Arguments

Value

A matrix with numbers of iteration rows and 4 columns giving the iteration, the previous value of loglikelihood, the current value of the loglikelihood, and the difference between these loglikelihoods.

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Lvriter<-getLvriter(ResCock)

Methods for Function getLvriter

Description

Methods for function getLvriter

Methods

signature(object = "BradleyEstim")

Gets the individual paired comparisons.

Description

Gets the individual paired comparisons.

Usage

getPaircomp(object)

Arguments

Value

list of number of criteria elements each corresponding to the results of paired comparisons performed by the consummers.

Examples

data(Cocktail)
Cocktail_Paircomp<-getPaircomp(Cocktail)

Methods for Function getPaircomp

Description

Methods for function getPaircomp

Methods

signature(object = "DataPairComp")

Gets the Bradley's scores.

Description

Gets the Bradley's scores from the function EstimBradley().

Usage

getPi(object)

Arguments

Value

A list of the Bradley's scores for the different criteria .

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Pi<-getPi(ResCock)

Methods for Function getPi

Description

Methods for function getPi

Methods

signature(object = "BradleyEstim")

Gets the products labels.

Description

Gets the products labels.

Usage

getProd(object)

Arguments

Value

vector of the products labels.

Examples

data(Cocktail)
Cocktail_Prod<-getProd(Cocktail)

Methods for Function getProd

Description

Methods for function getProd

Methods

signature(object = "DataPairComp")

Gets the result of the test of Bradley's scores equality.

Description

Gets the result of the test of Bradley's scores equality from the function EstimBradley().

Usage

getRestestglob(object)

Arguments

Value

list of five elements:

lvrH0 matrix of size (Tcla * number of criteria), giving the value of the log likelihood under the hypothesis of equality of Bradley's scores

lvrH1 matrix of size (Tcla * number of criteria), giving the value of the log likelihood under the hypothesis of non equality of Bradley's scores

lRatio matrix of size (Tcla * number of criteria), giving the value of the log likelihood Ratio statistic

Pvalue matrix of size (Tcla * number of criteria), giving the P value of the log likelihood Ratio test

H1 matrix of size (Tcla * number of criteria) giving the result of rejection of equality of Bradley's scores

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Restestglob<-getRestestglob(ResCock)

Methods for Function getRestestglob

Description

Methods for function getRestestglob

Methods

signature(object = "BradleyEstim")

Gets the result of the Bradley's scores multiple comparison tests.

Description

Gets the result of the Bradley's scores multiple comparison tests from the
function EstimBradley().

Usage

getRestestprod(object)

Arguments

Value

list of Tcla elements of type matrix of size (number of paired comparison * 7), each column corresponding to:

class identification,

criterion identification,

product identification i,

product identification j,

value for the statistic corresponding to H0: equality of the Bradley's scores of products i and j,

P value of this test,

Rejection or acceptation of H0 for a level of 5%.

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Restestprod<-getRestestprod(ResCock)

Methods for Function getRestestprod

Description

Methods for function getRestestprod

Methods

signature(object = "BradleyEstim")

Gets the results of Likelihood Ratio Test.

Description

Gets the results of Likelihood Ratio Test obtained by Monte-Carlo simulations.

Usage

getSimu(object)

Arguments

Value

A matrix with the number of classes under H0, the values of Loglikelihood under H0 and H1 and the differences between these Loglikelihoods.

Methods for Function getSimu

Description

Methods for function getSimu

Methods

signature(object = "LvrRatio")

Gets the level and the quantile of Likelihood ratio test.

Description

Gets the level and the quantile of Likelihood ratio test from the function ResSimulLvrRatio()

Usage

getTest(object)

Arguments

Value

Matrix with the level and the associated quantile after performing Likelihood Ratio test.

Methods for Function getTest

Description

Methods for function getTest

Methods

signature(object = "LvrRatio")

Gets the Bradley'scores covariance matrices.

Description

Gets the Bradley'scores covariance matrices from the function EstimBradley().

Usage

getVarcov(object)

Arguments

Value

list of Tcla elements containing Bradley'scores covariance matrices for the different criteria.

Examples

data(Cocktail)
ResCock<-EstimBradley(Cocktail,Constraint=0,Tcla=1,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock_Varcov<-getVarcov(ResCock)

Methods for Function getVarcov

Description

Methods for function getVarcov

Methods

signature(object = "BradleyEstim")

Gets the result of the function EstimBradley()

Description

Gets the posterior probabilities for each individual to belong to the different classes and the class with the higher probability.

Usage

getZh(object)

Arguments

Value

Object of class matrix with the posterior probabilities for each individual to belong to the different classes and the class with the higher probability.

Examples

data(Cocktail)
ResCock2<-EstimBradley(Cocktail,Constraint=0,Tcla=2,eps=1e-04,eps1=1e-04,TestPi=TRUE)
ResCock2_Zh<-getZh(ResCock2)

Methods for Function getZh

Description

Methods for function getZh

Methods

signature(object = "BradleyEstim")

Methods for Function show

Description

Methods for function show

Methods

signature(object = "BradleyEstim")

signature(object = "DataPairComp")