MCARtest (version 1.3)

get_SigmaS: Computes the collection of patterns, means, variances, covariance and correlation matrices for a given dataset with missing values.

Description

Using the same the notation of BB2024;textualMCARtest, computes the collection of patterns \(\mathbb{S}\), means \(\mu_\mathbb{S}\), variances \(\sigma^2_\mathbb{S}\), covariance matrices \(\Omega_\mathbb{S}\) and correlation matrices \(\Sigma_\mathbb{S}\) for a dataset with missing values.

Usage

get_SigmaS(X, min_diff = 0)

Value

patterns The collection of patterns \(\mathbb{S}\).

n_pattern The cardinality of \(\mathbb{S}\).

data_pattern A vector where the data are grouped according to \(\mathbb{S}\).

mu_S The collection of means.

C_S The collection of covariance matrices.

sigma_squared_S The collection of variances.

SigmaS The collection of correlation matrices.

ambient_dimension The dimension \(d\) of the data.

Arguments

X

The dataset with incomplete data.

min_diff

A natural number such that patterns with \(n_S \leq |S| + min_diff\) are discarded. Default to zero.

References

BB2024MCARtest

Examples

library(copula)
library(missMethods)
n = 100

cp = claytonCopula(param = c(1), dim = 5)
P = mvdc(copula = cp, margins = c("exp", "exp", "exp", "exp", "exp"),
         paramMargins = list(list(1), list(1), list(1), list(1), list(1)))
X = rMvdc(n, P)
X = delete_MCAR(X, 0.1, c(1,4,5))

get_SigmaS(X)
get_SigmaS(X, min_diff = 20)