A compilation of tests for hypotheses regarding covariance and correlation matrices for one or more groups. The hypothesis can be specified through a corresponding hypothesis matrix and a vector or by choosing one of the basic hypotheses, while for the structure test, only the latter works. Thereby Monte-Carlo and Bootstrap-techniques are used, and the respective method must be chosen, and the functions provide p-values and mostly also estimators of calculated covariance matrices of test statistics.
The official version of CovCorTest can be installed using the R Console:
install.packages("CovCorTest")You can install the development version of CovCorTest from GitHub with:
# install.packages("devtools")
devtools::install_github("sjedhoff/CovCorTest")The package is structures in tests regarding the covariance matrix
and the correlation matrix and their structures. A combined test for
both is implemented as well. For each of the matrices, covariance and
correlation, two test functions are defined. The best approach is to
start with the simple functions: test_covariance and
test_correlation respectively allow to test for a selection
of different predefined hypotheses for the corresponding matrices. These
function take the dataset, the group sizes (when testing for multiple
groups) and the hypothesis, which should be tested. Since the hypothesis
can be chosen using a character string like “equal”, no further
knowledge about the matrices used to test the hypotheses is needed. For
more advanced users, alternatively to using the hypothesis
argument, a specific hypothesis matrix C and a
corresponding vector Xi can be passed along to the
function. This can be used to test all forms of hypotheses, but in-depth
knowledge is necessary.
The structures of the covariance and correlation matrices can be
tested using test_covariance_structureand
test_correlation_structure respectively. Instead of a
hypothesis, a structure can be selected using a string, which will then
be tested.
The combined_test functions delivers a possibility to
test for equality of the covariance and correlation matrix of two
groups.
We are using the EEGwide dataset from the
MANOVA.RM package as an example. For this, we are just
focusing on two groups and the numerical variables.
library(CovCorTest)
data("EEGwide", package = "MANOVA.RM")
vars <- colnames(EEGwide)[1:6]
data <- list(t(EEGwide[EEGwide$sex == "M" &
EEGwide$diagnosis == "AD", vars]),
t(EEGwide[EEGwide$sex == "M" &
EEGwide$diagnosis == "MCI", vars]))For the two groups, we can check for equality of the covariance matrices
test_covariance(X = data, nv = c(12,27), hypothesis = "equal")The nv argument is for passing along group sizes. We can also leave it empty and a warning message shows.
We could also test, if the two groups are equal-correlated
test_correlation(X = data, hypothesis = "equal-correlated")With the combined test, we can test for the covariance and the correlation matrices
test_combined(X = data, nv = c(12, 27))The test for the structure of the covariance and correlation matrices are just for one matrix, i.e. just one group. Different structures can be tested:
test_covariance_structure(X = data[[1]], structure = "diag")