SimDesign (version 2.2)

rHeadrick: Generate non-normal data with Headrick's (2002) method

Description

Generate multivariate non-normal distributions using the fifth-order polynomial method described by Headrick (2002).

Usage

rHeadrick(
  n,
  mean = rep(0, nrow(sigma)),
  sigma = diag(length(mean)),
  skew = rep(0, nrow(sigma)),
  kurt = rep(0, nrow(sigma)),
  gam3 = NaN,
  gam4 = NaN,
  return_coefs = FALSE,
  coefs = NULL,
  control = list(trace = FALSE, max.ntry = 15, obj.tol = 1e-10, n.valid.sol = 1)
)

Arguments

n

number of samples to draw

mean

a vector of k elements for the mean of the variables

sigma

desired k x k covariance matrix between bivariate non-normal variables

skew

a vector of k elements for the skewness of the variables

kurt

a vector of k elements for the kurtosis of the variables

gam3

(optional) explicitly supply the gamma 3 value? Default computes this internally

gam4

(optional) explicitly supply the gamma 4 value? Default computes this internally

return_coefs

logical; return the estimated coefficients only? See below regarding why this is useful.

coefs

(optional) supply previously estimated coefficients? This is useful when there must be multiple data sets drawn and will avoid repetitive computations. Must be the object returned after passing return_coefs = TRUE

control

a list of control parameters when locating the polynomial coefficients

Details

This function is primarily a wrapper for the code written by Oscar L. Olvera Astivia (last edited Feb 26, 2015) with some modifications (e.g., better starting values for the Newton optimizer, passing previously saved coefs, etc).

References

Chalmers, R. P., & Adkins, M. C. (2020). Writing Effective and Reliable Monte Carlo Simulations with the SimDesign Package. The Quantitative Methods for Psychology, 16(4), 248-280. 10.20982/tqmp.16.4.p248

Sigal, M. J., & Chalmers, R. P. (2016). Play it again: Teaching statistics with Monte Carlo simulation. Journal of Statistics Education, 24(3), 136-156. 10.1080/10691898.2016.1246953

Headrick, T. C. (2002). Fast fifth-order polynomial transforms for generating univariate and multivariate nonnormal distributions. Computational Statistics & Data Analysis, 40, 685-711.

Olvera Astivia, O. L., & Zumbo, B. D. (2015). A Cautionary Note on the Use of the Vale and Maurelli Method to Generate Multivariate, Nonnormal Data for Simulation Purposes. Educational and Psychological Measurement, 75, 541-567.

Examples

# NOT RUN {
# }
# NOT RUN {
set.seed(1)

N <- 200
mean <- c(rep(0,4))
Sigma <- matrix(.49, 4, 4)
diag(Sigma) <- 1
skewness <- c(rep(1,4))
kurtosis <- c(rep(2,4))

nonnormal <- rHeadrick(N, mean, Sigma, skewness, kurtosis)
# cor(nonnormal)
# psych::describe(nonnormal)

#-----------
# compute the coefficients, then supply them back to the function to avoid
# extra computations

cfs <- rHeadrick(N, mean, Sigma, skewness, kurtosis, return_coefs = TRUE)
cfs

# compare
system.time(nonnormal <- rHeadrick(N, mean, Sigma, skewness, kurtosis))
system.time(nonnormal <- rHeadrick(N, mean, Sigma, skewness, kurtosis,
                                   coefs=cfs))
# }
# NOT RUN {
# }