little_test {MCARtest}

Carry out Little's test of MCAR

Description

Carry out Little's test of MCAR

Usage

little_test(X, alpha, type = "mean&cov")

Arguments

X

The dataset with incomplete data, where all the pairs of variables are observed together.

alpha

The nominal level of the test.

type

Determines the test statistic to use, based on the discussion in Section 5 in Bordino and Berrett (2024). The default option is "mean&cov", and uses the test statistic d^2_{\mathrm{aug}}. When set equal to "cov", implements a test of MCAR based on d^2_{\mathrm{cov}}, while, when set equal to "mean", implements the classical Little's test as defined in Little (1988).

Value

A Boolean, where TRUE stands for reject MCAR. This is computed by comparing the p-value of Little's test, found by comparing the log likelihood ratio statistic to the chi-squared distribution with the appropriate number of degrees of freedom, with the nominal level alpha. Described in Little (1988).

References

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

Little RJ (1988). “A test of Missing Completely at Random for multivariate data with missing values.” J. Amer. Statist. Assoc., 83, 1198–1202.

Examples

library(MASS)
alpha = 0.05
n = 200

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

X1 = mvrnorm(n, c(0,0), SigmaS[[1]])
X2 = mvrnorm(n, c(0,0), SigmaS[[2]])
X3 = mvrnorm(n, c(0,0), SigmaS[[3]])
columns = c("X1","X2","X3")
X = data.frame(matrix(nrow = 3*n, ncol = 3))
X[1:n, c("X1", "X2")] = X1
X[(n+1):(2*n), c("X2", "X3")] = X2
X[(2*n+1):(3*n), c("X1", "X3")] = X3
X = as.matrix(X)

little_test(X, alpha)