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

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

Arguments

Data

Object of class DataPairComp

ResH0

Object of class BradleyEstim corresponding to the result of BradleyEstim() function for T classes (H0)

Constraint

Kind of constraint on Bradley's scores. If Constraint=0, the sum of Bradley's scores should be equal to 1. For other values for Constraint, the product of Bradley's scores should be equal to 1 (default Constraint=0).

nsimul

number of Monte Carlo simulations

level

level of the Log Likelihood Ratio test defined by the user (default level=0.05).

eps

value of the convergence criteria for the EM algorithm (default eps=1e-04).

eps1

value of the criteria convergence for Dykstra algorithm (default eps1=1e-04).

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:

Simu

Matrix with the number of classes under H0, Loglikelihoods under H0 and H1, difference between these Loglikelihoods.

Test

Matrix with the level of the test and the associated quantile

Examples

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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)

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