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I want to simulate correlated categorical and continuous data. How to achieve that in R?

#For example, how to simulate the data in a way that these two variable are correlated?
x <- sample( LETTERS[1:4], 1000, replace=TRUE, prob=c(0.1, 0.2, 0.65, 0.05) ) #Categorical variable
y <- runif(1000,1,5) #Continuous variable

Any ideas will be greatly appreciated!

cliu
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2 Answers2

5

Does this give you something like what you're looking for? You can change the sd value to modify the amount of correlation.

k <- 1:4
n <- 1000
x <- sample( LETTERS[k], n, replace=TRUE, prob=c(0.1, 0.2, 0.65, 0.05) ) 
y <- as.vector(sapply(k,function(x) rnorm(round(n/length(k)),mean=x,sd=2)))
rdodhia
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0

Here's a method using copulas. Use larger values of alpha for higher correlation.

library(copula)
n <- 1000
alpha <- 5
u <- rCopula(n, claytonCopula(alpha))
u1 <- u[,1]
u2 <- u[,2]
x <- ifelse(u1 < 0.1, "A", 
     ifelse(u1 < 0.3, "B", 
     ifelse(u1 < 0.95, "C", "D")))
y <- qunif(u2, 1, 5)
plot(factor(x), y)


plot(factor(x))


plot(density(y))

Created on 2021-02-21 by the reprex package (v0.3.0)

user2554330
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  • Thanks for the answer@user2554330. Any ways to specify the correlation coefficient in the code though? – cliu Feb 21 '21 at 21:13
  • What kind of correlation coefficient do you mean? The usual one needs numeric data. – user2554330 Feb 21 '21 at 21:22
  • Yes, let's say we change `x` to this `x <- ifelse(u1 < 0.1, 1, ifelse(u1 < 0.3, 2, ifelse(u1 < 0.95, 3, 4)))`. If I want to fix r=0.2, how to specify that? – cliu Feb 21 '21 at 21:25
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    Change the value of `alpha`. The relation between `alpha` and the correlation will depend on the distributions in some ugly way; I'd do it by simulation (i.e. compute correlation for large samples with a few values of `alpha`, and interpolate). For your distributions it looks like `alpha <- 0.3` will come close to `r=0.2`. – user2554330 Feb 21 '21 at 21:32