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% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/dataDiagnosis.R
\name{mardiaSkew}
\alias{mardiaSkew}
\title{Finding Mardia's multivariate skewness}
\usage{
mardiaSkew(dat, use = "everything")
}
\arguments{
\item{dat}{The target matrix or data frame with multiple variables}
\item{use}{Missing data handling method from the \code{\link[stats:cor]{stats::cov()}}
function.}
}
\value{
A value of a Mardia's multivariate skewness with a test statistic
}
\description{
Finding Mardia's multivariate skewness of multiple variables
}
\details{
The Mardia's multivariate skewness formula (Mardia, 1970) is
\deqn{ b_{1, d} = \frac{1}{n^2}\sum^n_{i=1}\sum^n_{j=1}\left[
\left(\bold{X}_i - \bold{\bar{X}} \right)^{'} \bold{S}^{-1}
\left(\bold{X}_j - \bold{\bar{X}} \right) \right]^3, }
where \eqn{d} is the number of variables, \eqn{X} is the target dataset
with multiple variables, \eqn{n} is the sample size, \eqn{\bold{S}} is
the sample covariance matrix of the target dataset, and \eqn{\bold{\bar{X}}}
is the mean vectors of the target dataset binded in \eqn{n} rows.
When the population multivariate skewness is normal, the
\eqn{\frac{n}{6}b_{1,d}} is asymptotically distributed as \eqn{\chi^2}
distribution with \eqn{d(d + 1)(d + 2)/6} degrees of freedom.
}
\examples{
library(lavaan)
mardiaSkew(HolzingerSwineford1939[ , paste0("x", 1:9)])
}
\references{
Mardia, K. V. (1970). Measures of multivariate skewness and
kurtosis with applications. \emph{Biometrika, 57}(3), 519--530.
\doi{10.2307/2334770}
}
\seealso{
\itemize{
\item \code{\link[=skew]{skew()}} Find the univariate skewness of a variable
\item \code{\link[=kurtosis]{kurtosis()}} Find the univariate excessive
kurtosis of a variable
\item \code{\link[=mardiaKurtosis]{mardiaKurtosis()}} Find the Mardia's multivariate
kurtosis of a set of variables
}
}
\author{
Sunthud Pornprasertmanit (\email{psunthud@gmail.com})
}
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