MCARtest (version 1.3)

little_test: Carry out Little's test of MCAR.

Description

Carry out Little's test of MCAR.

Usage

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

Value

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. Described in Little1988;textualMCARtest.

Arguments

X

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

type

Determines the test statistic to use, based on the discussion in Section 6 in BB2024;textualMCARtest. 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 Little1988;textualMCARtest.

References

BB2024MCARtest

Little1988MCARtest

Examples

library(MASS)
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)
little_test(X, type = "mean&cov")
little_test(X, type = "mean")