| mardiaSkew {semTools} | R Documentation |
Finding Mardia's multivariate skewness of multiple variables
mardiaSkew(dat, use = "everything")
dat |
The target matrix or data frame with multiple variables |
use |
Missing data handling method from the |
The Mardia's multivariate skewness formula (Mardia, 1970) is
b_{1, d} = \frac{1}{n^2}∑^n_{i=1}∑^n_{j=1}≤ft[ ≤ft(\bold{X}_i - \bold{\bar{X}} \right)^{'} \bold{S}^{-1} ≤ft(\bold{X}_j - \bold{\bar{X}} \right) \right]^3,
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 skewness is normal, the \frac{n}{6}b_{1,d} is asymptotically distributed as chi-square distribution with d(d + 1)(d + 2)/6 degrees of freedom.
A value of a Mardia's multivariate skewness with a test statistic
Sunthud Pornprasertmanit (psunthud@gmail.com)
Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519-530.
skew Find the univariate skewness of a variable
kurtosis Find the univariate excessive kurtosis of a variable
mardiaKurtosis Find the Mardia's multivariate kurtosis of a set of variables
library(lavaan)
mardiaSkew(HolzingerSwineford1939[,paste("x", 1:9, sep="")])