| mardiaKurtosis {semTools} | R Documentation |
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 |
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.
Value
A value of a Mardia's multivariate kurtosis with a test statistic
Author(s)
Sunthud Pornprasertmanit (psunthud@gmail.com)
References
Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57(3), 519–530. doi:10.2307/2334770
See Also
-
skewFind the univariate skewness of a variable -
kurtosisFind the univariate excessive kurtosis of a variable -
mardiaSkewFind the Mardia's multivariate skewness of a set of variables
Examples
library(lavaan)
mardiaKurtosis(HolzingerSwineford1939[ , paste0("x", 1:9)])