MCARtest (version 1.2.1)

RindexDual: A function computing the incompatibility index and associated closest joint mass function using the dual formulation

Description

A function solving a linear program to compute the incompatibility index \(R()\) defined in BS2022;textualMCARtest, in the case of having discrete random variables. Uses Amatrix to define to constraint matrix and lpSolve to implement the linear optimisation.

Usage

RindexDual(pS, bS, M, lp_solver = "default", simplex_strategy = 4)

Value

The value of \(R()\), in the interval \([0,1]\).

The optimal solution to the linear program

Arguments

pS

A sequence of probability mass functions on the marginal spaces.

bS

A binary matrix specifying the set of observation patterns. Each row encodes a single pattern.

M

A vector of positive integers giving the alphabet sizes of the discrete variables.

lp_solver

An argument passed to HiGHS specifying which solver to use.

simplex_strategy

An argument passed to HiGHS specifying which solver to use.

References

BS2022MCARtest

Examples

bS=matrix(c(1,1,0, 1,0,1, 0,1,1),byrow=TRUE,ncol=3)
M=c(2,2,2)
A=Amatrix(bS,M)

pS=rep(0.25,12)
linprog=RindexDual(pS,bS,M)
rbind(pS,as.vector(A%*%linprog[[2]])/(1-linprog[[1]]))

pS=c(0.125,0.375,0.375,0.125,0.250,0.250,0.250,0.250,0.100,0.400,0.400,0.100)
linprog=RindexDual(pS,bS,M)
rbind(pS,as.vector(A%*%linprog[[2]])/(1-linprog[[1]]))