indTest {TestIndVars}

Complete Independent Test

Description

Performs an independent test for a set of variables both for low and high dimensional data.

Usage

indTest(X, covMat = NULL, alpha = 0.05)

Arguments

X

A numeric matrix or data frame containing the measurements on the variables.

covMat

Optional. A numeric matrix representing the population covariance matrix used in the test. If NULL, the sample covariance matrix is used (default is NULL).

alpha

The significance level for the test (default is 0.05).

Value

A data frame containing the observed value of the test statistic, degrees of freedom, alpha value, p-value, and test result. #' @references Marques, F. J., Diogo, J., Norouzirad, M., & Bispo, R. (2023). Testing the independence of variables for specific covariance structures: A simulation study. Mathematical Methods in the Applied Sciences, 46(9), 10421–10434. DOI: 10.1002/mma.9130

Examples

# Example usage:

library(MASS)

n = 50 # Sample Size
p = 5  # number of variables
rho = 0.4
# Building a Covariance structure with Autoregressive structure
cov_mat <- covMatAR(p = p, rho = rho)
# Simulated data
data <- mvrnorm(n = n, mu = rep(0,p), Sigma = cov_mat)
# Performing the test assuming that the population covariance matrix is unknown
indTest(data)
# Performing the test assuming that the population covariance matrix is known
indTest(data, covMat = cov_mat)

# Example for data with missing values
# Generating data with 10% of missing values
missing_rate <- 0.1
missing_index_row <- sample(1:n, size = round(n * missing_rate))
missing_index_col <- sample(1:p, size = 1)
data[missing_index_row, missing_index_col] <- NA # Introducing missing values
# Performing the test assuming that the population covariance matrix is unknown
indTest(data)
# Performing the test assuming that the population covariance matrix is known
indTest(data, covMat = cov_mat)

# Building a Covariance structure with Compound Symmetry structure
cov_mat <- covMatCS(p = p, rho = rho)
# Simulated data
data <- mvrnorm(n = n, mu = rep(0,p), Sigma = cov_mat)
# Performing the test assuming that the population covariance matrix is unknown
indTest(data)
# Performing the test assuming that the population covariance matrix is known
indTest(data, covMat = cov_mat)

# Building a Covariance structure with Circular structure
cov_mat <- covMatC(p = p, rho = rho)
# Simulated data
data <- mvrnorm(n = n, mu = rep(0,p), Sigma = cov_mat)
# Performing the test assuming that the population covariance matrix is unknown
indTest(data)
# Performing the test assuming that the population covariance matrix is known
indTest(data, covMat = cov_mat)