V {MCARtest}

Computes an inconsistency index for sequences of variances.

Description

A function that computes the inconsistency index V(\sigma^2_\mathbb{S}) for a sequence of variances as defined in Section 2 in Bordino and Berrett (2024), given the fact that \bar{\operatorname{av}}(\sigma^2_{\mathbb{S}_j}) = 1.

Usage

V(sigma_squared_S, patterns)

Arguments

sigma_squared_S

The sequence of variances \sigma_\mathbb{S}^2.

patterns

A vector with all the patterns in \mathbb{S}.

Value

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

References

Bordino A, Berrett TB (2024). “Tests of Missing Completely At Random based on sample covariance matrices.” arXiv preprint arXiv:2401.05256.

Examples

library(MASS)

d = 3
n = 200
SigmaS=list() #Random 2x2 correlation matrices (necessarily consistent)
for(j in 1:d){
x=runif(2,min=-1,max=1); y=runif(2,min=-1,max=1); SigmaS[[j]]=cov2cor(x%*%t(x) + y%*%t(y))
}

X = data.frame(matrix(nrow = 3*n, ncol = 3))
X[1:n, c(1,2)] = mvrnorm(n, c(0,0), SigmaS[[1]])
X[(n+1):(2*n), c(2, 3)] = mvrnorm(n, c(0,0), SigmaS[[2]])
X[(2*n+1):(3*n), c(1, 3)] = mvrnorm(n, c(0,0), SigmaS[[3]])
X = as.matrix(X)

xxx = get_SigmaS(X)$patterns
av_sigma = compute_av("var", X)
X_new = X
for (j in 1:3){
  X_new[,j] = X[,j]/sqrt(av_sigma[j])
  }

V(get_SigmaS(X_new)$sigma_squared_S, xxx)