Introduction to faux

Lisa DeBruine

2019-02-19

It is useful to be able to simulate data with a specified structure. The faux package provides some functions to make this process easier.

rnorm_multi

This function makes multiple normally distributed vectors with specified parameters and relationships.

For example, the following creates a sample that has 100 observations of 3 variables, drawn from a population where where A correlates with B and C with r = 0.5, and B and C correlate with r = 0.25. A has a mean of 0 and SD of 1, while B and C have means of 20 and SDs of 5.

dat <- rnorm_multi(n = 100, 
                  cors = c(0.5, 0.5, 0.25), 
                  mu = c(0, 20, 20),
                  sd = c(1, 5, 5),
                  varnames = c("A", "B", "C"),
                  empirical = FALSE)

Sample stats

var	A	B	C	mean	sd
A	1.00	0.45	0.49	0.03	0.99
B	0.45	1.00	0.33	20.01	4.89
C	0.49	0.33	1.00	19.76	4.02

Specify cors

You can specify the correlations in one of four ways:

• A single r for all pairs
• A vars by vars matrix
• A vars*vars length vector
• A vars*(vars-1)/2 length vector

One Number

If you want all the pairs to have the same correlation, just specify a single number.

bvn <- rnorm_multi(100, 5, .3, varnames = letters[1:5])

Sample stats from a single rho

var	a	b	c	d	e	mean	sd
a	1.00	0.35	0.22	0.45	0.37	-0.04	1.09
b	0.35	1.00	0.19	0.36	0.28	-0.05	0.83
c	0.22	0.19	1.00	0.26	0.20	0.01	1.08
d	0.45	0.36	0.26	1.00	0.24	0.00	1.00
e	0.37	0.28	0.20	0.24	1.00	0.04	0.97

Matrix

If you already have a correlation matrix, such as the output of cor(), you can specify the simulated data with that.

cmat <- cor(iris[,1:4])
bvn <- rnorm_multi(100, 4, cmat, 
                  varnames = colnames(cmat))

Sample stats from a correlation matrix

var	Sepal.Length	Sepal.Width	Petal.Length	Petal.Width	mean	sd
Sepal.Length	1.00	-0.10	0.88	0.83	-0.01	1.05
Sepal.Width	-0.10	1.00	-0.38	-0.29	-0.19	1.09
Petal.Length	0.88	-0.38	1.00	0.96	-0.01	1.02
Petal.Width	0.83	-0.29	0.96	1.00	-0.05	0.98

Vector (vars*vars)

You can specify your correlation matrix by hand as a vars*vars length vector, which will include the correlations of 1 down the diagonal.

cmat <- c(1, .3, .5,
          .3, 1, 0,
          .5, 0, 1)
bvn <- rnorm_multi(100, 3, cmat, 
                  varnames = c("first", "second", "third"))

Sample stats from a vars*vars vector

var	first	second	third	mean	sd
first	1.00	0.33	0.45	-0.12	1.01
second	0.33	1.00	-0.04	-0.01	1.04
third	0.45	-0.04	1.00	-0.11	1.00

Vector (vars*(vars-1)/2)

You can specify your correlation matrix by hand as a vars*(vars-1)/2 length vector, skipping the diagonal and lower left duplicate values.

rho1_2 <- .3
rho1_3 <- .5
rho1_4 <- .5
rho2_3 <- .2
rho2_4 <- 0
rho3_4 <- -.3
cmat <- c(rho1_2, rho1_3, rho1_4, rho2_3, rho2_4, rho3_4)
bvn <- rnorm_multi(100, 4, cmat, 
                  varnames = letters[1:4])

Sample stats from a (vars*(vars-1)/2) vector

var	a	b	c	d	mean	sd
a	1.00	0.35	0.55	0.50	-0.13	1.01
b	0.35	1.00	0.16	0.09	-0.10	1.05
c	0.55	0.16	1.00	-0.21	-0.19	0.91
d	0.50	0.09	-0.21	1.00	0.12	0.97

empirical

If you want your samples to have the exact correlations, means, and SDs you entered, set empirical to TRUE.

bvn <- rnorm_multi(100, 5, .3, 
                  varnames = letters[1:5], 
                  empirical = T)

Sample stats with empirical = TRUE

var	a	b	c	d	e	mean	sd
a	1.0	0.3	0.3	0.3	0.3	0	1
b	0.3	1.0	0.3	0.3	0.3	0	1
c	0.3	0.3	1.0	0.3	0.3	0	1
d	0.3	0.3	0.3	1.0	0.3	0	1
e	0.3	0.3	0.3	0.3	1.0	0	1