semTools (version 0.5-6)

mardiaKurtosis: Finding Mardia's multivariate kurtosis

Description

Finding Mardia's multivariate kurtosis of multiple variables

Usage

mardiaKurtosis(dat, use = "everything")

Arguments

dat

The target matrix or data frame with multiple variables

use

Missing data handling method from the cov function.

Value

A value of a Mardia's multivariate kurtosis with a test statistic

Details

The Mardia's multivariate kurtosis formula (Mardia, 1970) is $$ b_{2, d} = \frac{1}{n}\sum^n_{i=1}\left[ \left(\bold{X}_i - \bold{\bar{X}} \right)^{'} \bold{S}^{-1} \left(\bold{X}_i - \bold{\bar{X}} \right) \right]^2, $$ where \(d\) is the number of variables, \(X\) is the target dataset with multiple variables, \(n\) is the sample size, \(\bold{S}\) is the sample covariance matrix of the target dataset, and \(\bold{\bar{X}}\) is the mean vectors of the target dataset binded in \(n\) rows. When the population multivariate kurtosis is normal, the \(b_{2,d}\) is asymptotically distributed as normal distribution with the mean of \(d(d + 2)\) and variance of \(8d(d + 2)/n\).

References

Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519--530. 10.2307/2334770

See Also

• skew Find the univariate skewness of a variable

• kurtosis Find the univariate excessive kurtosis of a variable

• mardiaSkew Find the Mardia's multivariate skewness of a set of variables

Examples

# NOT RUN {
library(lavaan)
mardiaKurtosis(HolzingerSwineford1939[ , paste0("x", 1:9)])

# }