Simulating Multiple Vectors

library(tidyverse)
library(faux)

I’m working on a package for simulations called faux. (Update: faux is now on CRAN!)

The first function, rnorm_multi, makes multiple normally distributed vectors with specified relationships and takes the following arguments:

n = the number of samples required (required)
vars = the number of variables to return (default = 3)
cors = the correlations among the variables (can be a single number, vars*vars matrix, vars*vars vector, or a vars*(vars-1)/2 vector; default = 0)
mu = a vector giving the means of the variables (numeric vector of length 1 or vars; default = 0)
sd = the standard deviations of the variables (numeric vector of length 1 or vars; default = 1)
varnames = optional names for the variables (string vector of length vars; default = NULL)
empirical = logical. If true, mu, sd and cors specify the empirical not population mean, sd and covariance (default = FALSE)

Example 1

The following example creates a 100-row dataframe of 3 columns names A, B, and C, with means = 0, SDs = 1, and where r_AB = 0.2, r_AC = -0.5, and r_BC = 0.5.

ex1 <- rnorm_multi(100, 3, c(0.2, -0.5, 0.5), varnames=c("A", "B", "C"))

Correlation Matrix of Sample Data

	A	B	C
A	1.0000000	0.0505608	0.0821478
B	0.0505608	1.0000000	-0.1303736
C	0.0821478	-0.1303736	1.0000000

Example 2

The following example calculates the correlation matrix, means, and SDs from the iris dataset and uses them to simulate a dataset of 100 rows with the same parameters.

dat <- select_if(iris, is.numeric)

iris_sim <- rnorm_multi(
  n = 100, 
  vars = ncol(dat), 
  r = cor(dat),
  mu = summarise_all(dat, mean) %>% t(), 
  sd = summarise_all(dat, sd) %>% t(), 
  varnames = names(dat)
)

Correlation Matrix of Original Data

	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width
Sepal.Length	1.0000000	-0.1175698	0.8717538	0.8179411
Sepal.Width	-0.1175698	1.0000000	-0.4284401	-0.3661259
Petal.Length	0.8717538	-0.4284401	1.0000000	0.9628654
Petal.Width	0.8179411	-0.3661259	0.9628654	1.0000000

Correlation Matrix of Sample Data

	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width
Sepal.Length	1.0000000	-0.0829264	0.8656481	0.8150830
Sepal.Width	-0.0829264	1.0000000	-0.4334276	-0.4177735
Petal.Length	0.8656481	-0.4334276	1.0000000	0.9700393
Petal.Width	0.8150830	-0.4177735	0.9700393	1.0000000