SimCorMultRes (version 1.9.0)

rnorta: Simulating Random Vectors using the NORTA Method

Description

Utility function to simulate random vectors with predefined marginal distributions via the NORTA method.

Usage

rnorta(R = R, cor.matrix = cor.matrix, distr = distr,
  qparameters = NULL)

Value

Returns R random vectors of size ncol(cor.matrix) with marginal distributions specified by distr (and qparameters).

Arguments

R

integer indicating the sample size.

cor.matrix

matrix indicating the correlation matrix of the multivariate normal distribution employed in the NORTA method.

distr

character string vector of length ncol(cor.matrix) naming the quantile functions of the desired marginal distributions.

qparameters

list of ncol(cor.matrix) lists indicating the parameter values of the quantile functions specified by distr.

Author

Anestis Touloumis

Details

Checks are made to ensure that cor.matrix is a positive definite correlation matrix. The positive definiteness of cor.matrix is assessed via eigenvalues.

The \(t\)-th character string in distr indicates the quantile function of the \(t\)-th marginal distribution. See Distributions for the most common distributions. Quantile functions supported by other R packages are allowed provided that these packages have been uploaded first. However, note that no checks are made to ensure that the character strings in distr correspond to valid names of quantile functions.

If qparameters = NULL then the default parameter values for the quantile functions specified by distr are used. Otherwise, qparameters should be provided as a list of ncol(cor.matrix) lists such that the \(t\)-th list contains the desired parameter values of the \(t\)-th quantile function.

References

Cario, M. C. and Nelson, B. L. (1997) Modeling and generating random vectors with arbitrary marginal distributions and correlation matrix. Technical Report, Department of Industrial Engineering and Management Sciences, Northwestern University, Evanston, Illinois.

Li, S. T. and Hammond, J. L. (1975) Generation of pseudorandom numbers with specified univariate distributions and correlation coefficients. IEEE Transactions on Systems, Man and Cybernetics 5, 557--561.

Touloumis, A. (2016) Simulating Correlated Binary and Multinomial Responses under Marginal Model Specification: The SimCorMultRes Package. The R Journal 8, 79--91.

Examples

## An example with standard logistic as marginal distribution.
set.seed(1)
sample_size <- 1000
latent_correlation_matrix <- toeplitz(c(1, rep(0.8, 2)))
latent_correlation_matrix
common_marginal_distribution <- rep("qlogis", 3)
simulated_logistic_responses <- rnorta(R = sample_size,
  cor.matrix = latent_correlation_matrix,
  distr = common_marginal_distribution)

## The following lines exemplify the NORTA method.
set.seed(1)
simulated_normal_responses <- rsmvnorm(R = sample_size,
  cor.matrix = latent_correlation_matrix)
norta_simulated <- qlogis(pnorm(simulated_normal_responses))
all(simulated_logistic_responses == norta_simulated)

## Change the marginal distributions to standard normal, standard
## logistic and standard extreme value distribution.
set.seed(1)
different_marginal_distributions <- c("qnorm", "qlogis", "qgumbel")
simulated_logistic_responses <- rnorta(R = sample_size,
  cor.matrix = latent_correlation_matrix,
  distr = different_marginal_distributions)
cor(simulated_logistic_responses)
colMeans(simulated_logistic_responses)
apply(simulated_logistic_responses, 2, sd)

## Same as above but using parameter values other than the default ones.
set.seed(1)
qpars <- list(c(mean = 1, sd = 9), c(location = 2, scale = 1),
  c(loc = 3, scale = 1))
simulated_logistic_responses <- rnorta(R = sample_size,
  cor.matrix = latent_correlation_matrix,
  distr = different_marginal_distributions, qparameters = qpars)
cor(simulated_logistic_responses)
colMeans(simulated_logistic_responses)
apply(simulated_logistic_responses, 2, sd)