# mardiaKurtosis: Finding Mardia's multivariate kurtosis In semTools: Useful Tools for Structural Equation Modeling

## Description

Finding Mardia's multivariate kurtosis of multiple variables

## Usage

 1 mardiaKurtosis(dat, use = "everything") 

## Arguments

 dat The target matrix or data frame with multiple variables use Missing data handling method from the cov function.

## Details

The Mardia's multivariate kurtosis formula (Mardia, 1970) is

b_{2, d} = \frac{1}{n}∑^n_{i=1}≤ft[ ≤ft(\bold{X}_i - \bold{\bar{X}} \right)^{'} \bold{S}^{-1} ≤ft(\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

• 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

 1 2 library(lavaan) mardiaKurtosis(HolzingerSwineford1939[ , paste0("x", 1:9)]) 

semTools documentation built on Jan. 13, 2021, 8:09 p.m.