nnig_sim.Rd
Simulates multivariate linearly related non-normally distributed variables
(Foldnes & Olsson, 2016). For marginal distributions, skewness and (excess) kurtosis
values are provided and the values are simulated according to the Fleishman
power transformation (Fleishman, 1978; see fleishman_sim
).
The function nnig_sim
simulates data from a multivariate random variable
\(\bold{Y}\) which is related to a number of independent variables \(\bold{X}\)
(independent generators; Foldnes & Olsson, 2016)
which are Fleishman power normally distributed. In detail, it holds that
\(\bold{Y}=\bold{\mu} + \bold{A} \bold{X}\) where the covariance matrix
\(\bold{\Sigma}\) is decomposed according to a Cholesky decomposition
\(\bold{\Sigma}=\bold{A} \bold{A}^T\).
# determine coefficients nnig_coef(mean=NULL, Sigma, skew, kurt) # simulate values nnig_sim(N, coef)
mean | Vector of means. The default is a vector containing zero means. |
---|---|
Sigma | Covariance matrix |
skew | Vector of skewness values |
kurt | Vector of (excess) kurtosis values |
N | Number of cases |
coef | List of parameters generated by |
A list of parameter values (nnig_coef
) or a data frame with
simulated values (nnig_sim
).
Fleishman, A. I. (1978). A method for simulating non-normal distributions. Psychometrika, 43(4), 521-532. doi: 10.1007/BF02293811
Foldnes, N., & Olsson, U. H. (2016). A simple simulation technique for nonnormal data with prespecified skewness, kurtosis, and covariance matrix. Multivariate Behavioral Research, 51(2-3), 207-219. doi: 10.1080/00273171.2015.1133274
Vale, D. C., & Maurelli, V. A. (1983). Simulating multivariate nonnormal distributions. Psychometrika, 48(3), 465-471. doi: 10.1007/BF02293687
See fungible::monte1
for simulating multivariate linearly related
non-normally distributed variables generated by the method of Vale and Morelli (1983).
See also the MultiVarMI::MVNcorr
function in the MultiVarMI package
and the SimMultiCorrData package.
The MultiVarMI also includes an imputation function MultiVarMI::MI
for non-normally distributed variables.
if (FALSE) { ############################################################################# # EXAMPLE 1: Simulating data with nnig_sim function ############################################################################# #* define input parameters Sigma <- matrix( c(1,.5, .2, .5, 1,.7, .2, .7, 1), 3, 3 ) skew <- c(0,1,1) kurt <- c(1,3,3) #* determine coefficients coeff <- miceadds::nnig_coef( Sigma=Sigma, skew=skew, kurt=kurt ) print(coeff) #* simulate data set.seed(2018) Y <- miceadds::nnig_sim( N=2000, coef=coeff) #* check descriptive statistics apply(Y, 2, TAM::weighted_skewness ) apply(Y, 2, TAM::weighted_kurtosis ) }