Package 'covsim'

Simulation of non-normal data

Description

Using the IG method to simulate non-normal data

Usage

rIG(N, sigma.target, skewness, excesskurtosis, reps = 1, typeA = "triang")

Arguments

N	Number of observations to simulate.
sigma.target	Target population covariance matrix
skewness	Target skewness
excesskurtosis	Target excess kurtosis
reps	Number of simulated samples
typeA	Symmetrical or triangular (default) A matrix

Value

A list of simulated samples

Author(s)

Njål Foldnes ([email protected])

References

Foldnes, N. and Olson, 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

Examples

set.seed(1234)
model <- '
 # measurement model
   ind60 =~ x1 + x2 + x3
   dem60 =~ y1 + y2 + y3 + y4
   dem65 =~ y5 + y6 + y7 + y8
 # regressions
   dem60 ~ ind60
   dem65 ~ ind60 + dem60
 # residual correlations
   y1 ~~ y5
   y2 ~~ y4 + y6
   y3 ~~ y7
   y4 ~~ y8
   y6 ~~ y8'
fit  <- lavaan::sem(model, data=lavaan::PoliticalDemocracy)
population.sigma <- lavaan::lavInspect(fit, "sigma.hat")
population.skew  <- c(0, 0, 0, 0, 1, 1, 1, 1, 2,2,2 )
population.excesskurt <- c( 1 , 1, 1, 1, 3, 3, 3, 3, 15, 15, 15)
my.samples <- rIG(N=10^3, sigma=population.sigma,
        skewness=population.skew,
        excesskurt=population.excesskurt,
        reps=5)

---

Simulation of non-normal data

Description

Using the piecewise linear PLSIM method to simulate non-normal data

Usage

rPLSIM(
  N,
  sigma.target,
  skewness,
  excesskurtosis,
  reps = 1,
  numsegments = 4,
  gammalist = NULL,
  monot = FALSE,
  verbose = TRUE
)

Arguments

N	Number of observations to simulate.
sigma.target	Target population covariance matrix
skewness	Target skewness
excesskurtosis	Target excess kurtosis
reps	Number of simulated samples
numsegments	The number of line segments in each marginal
gammalist	A list of breakpoints in each margin
monot	True if piecewise linear functions are forced to be monotonous. The copula will then be normal.
verbose	If true, progress details of the procedure are printed

Value

A list with two elements. First element: the list of simulated samples. Second element: The fitted piecewise linear functions and the intermediate correlations matrix.

Author(s)

Njål Foldnes ([email protected])

References

Foldnes, N. and Grønneberg S. (2021). Non-normal data simulation using piecewise linear transforms.Under review.

Examples

set.seed(1)
sigma.target  <- cov(MASS::mvrnorm(5, rep(0,3), diag(3)))
res  <- covsim::rPLSIM(10^5, sigma.target, skewness=rep(1,3), excesskurtosis=rep(4,3))
my.sample  <- res[[1]][[1]]

---

Calibrate a regular vine

Description

vita implements the VITA (VIne-To-Anything) algorithm. Covariance matrix and margins are specified, and vita calibrates the pair-copulas in each node of the tree to match the target covariance.

Usage

vita(
  margins,
  sigma.target,
  vc = NULL,
  family_set = c("clayton", "gauss", "joe", "gumbel", "frank"),
  Nmax = 10^6,
  numrootpoints = 10,
  conflevel = 0.995,
  numpoints = 4,
  verbose = TRUE,
  cores = parallel::detectCores()
)

Arguments

margins	A list where each element corresponds to a margin. Each margin element is a list containing the distribution family ("distr") and additional parameters. Must be a distribution available in the stats package.
sigma.target	The target covariance matrix that is to be matched. The diagonal elements must contain the variances of marginal distributions.
vc	A vine dist object as specified by the rvinecopulib package. This object specifies the vine that is to be calibrated. If not provided, a D-vine is assumed.
family_set	A vector of one-parameter pair-copula families that is to be calibrated at each node in the vine. Possible entries are "gauss", "clayton", "joe", "gumbel" and "frank". Calibration of pair-copula families is attempted in the order provided.
Nmax	The sample size used for calibration. Reduce for faster calibration, at the cost of precision.
numrootpoints	The number of estimated roots at the initial calibration stage, which determines a search interval where Nmax samples are drawn
conflevel	Confidence level for determining search interval
numpoints	The number of samples drawn with size Nmax, to determine the root within search interval To increase precision increase this number. To calibrate faster (but less precisely), may be reduced to a number no lower than 2
verbose	If TRUE, outputs details of calibration of each bicopula
cores	Number of cores to use. If larger than 1, computations are done in parallel. May be determined with parallel:detectCores()

Value

If a feasible solution was found, a vine to be used for simulation

References

Grønneberg, S., Foldnes, N., & Marcoulides, K. M. (2021). covsim: An r package for simulating non-normal data for structural equation models using copulas. Journal of Statistical Software. doi:10.18637/jss.v102.i03

Examples

set.seed(1)# define a target covariance. 3 dimensions.
sigma.target <- cov(MASS::mvrnorm(10, mu=rep(0,3), Sigma=diag(1, 3)))

#normal margins that match the covariances:
marginsnorm <- lapply(X=sqrt(diag(sigma.target)),function(X) list(distr="norm", sd=X) )

#calibrate with a default D-vine, with rather low precision (default Nmax is 10^6)
# if cores=1 is removed, all cores are used, with a speed gain
calibrated.vine <- vita(marginsnorm, sigma.target =sigma.target, Nmax=10^5, cores=1)
#check
#round(cov(rvinecopulib::rvine(10^5, calibrated.vine))-sigma.target, 3)

#margins are normal but dependence structure is not
#pairs(rvinecopulib::rvine(500, calibrated.vine))

---