little_test {MCARtest} | R Documentation |
Carry out Little's test of MCAR.
Description
Carry out Little's test of MCAR.
Usage
little_test(X, type = "mean&cov")
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 Bordino and Berrett (2025).
The default option is "mean&cov", and uses the test statistic |
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 Little (1988).
References
Bordino A, Berrett TB (2025). “Tests of Missing Completely At Random based on sample covariance matrices.” Ann. Statist., to appear, 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)
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")