Test whether a set of multivariate normal random vectors are independent. The null hypothesis is "H0: The random vectors are independent of each other".
Arguments
- data
The data matrix which is a matrix or data frame. Each column represents a random variable.
- subdim
The dimensions of submatrices. The default is FALSE, which means the independence of all components of the random vector will be tested.
- alpha
The significance level. Default is 0.05.
- verbose
A boolean value. Default is TRUE. If TRUE, the null hypothesis will be displayed. If FALSE, the test will be carried out silently.
Value
An object of class "testResult", which is a list with the following elements:
- Conclusion
The conclusion of the test.
- Stat
A data frame containing the statistics, p value and critical value.
- SampMean
The sample mean.
- SampA
The sample deviation.
- SampAii
The sample deviation of submatrices.
- Df
The degree of freedom.
- b
The Modified factor of the statistic.
References
Huixuan, Gao. Applied Multivariate Statistical Analysis. Peking University Press, 2005: pp.92-94.
Examples
data(iris)
chart <- iris[, 1:4]
# carry out the test
test1 <- indTest.multi(chart)
test2 <- indTest.multi(chart, subdim = c(2, 1, 1))
test3 <- indTest.multi(chart, verbose = FALSE)
#> H0: The random vectors are independent of each other
# get the elements
test1$Stat
#> Value p.value Critical.Value
#> V 8.109611e-03
#> Likelihood Ratio 1.496239e-157
#> Chi2 7.069592e+02 0 12.591587243744
test1$SampMean
#> Sepal.Length Sepal.Width Petal.Length Petal.Width
#> 5.8433 3.0573 3.7580 1.1993
test2$SampAii
#> [[1]]
#> Sepal.Length Sepal.Width
#> Sepal.Length 102.168333 -6.322667
#> Sepal.Width -6.322667 28.306933
#>
#> [[2]]
#> [,1]
#> [1,] 464.3254
#>
#> [[3]]
#> [,1]
#> [1,] 86.56993
#>