random seeds

TLDR: I explain why researchers should not use the same random seed to generate variables that should not be correlated.

I have been working on a simulation for a spatial transcriptomics project. During the process of debugging the simulation, I came across an issue with setting seeds that I wanted to explore further. Setting a seed initializes a value that is used by a pseudorandom number generator.

Comparing these two lines of code shows us how a seed functions:

set.seed(10); runif(2); runif(2)

[1] 0.5074782 0.3067685

[1] 0.4269077 0.6931021

set.seed(10); runif(4)

[1] 0.5074782 0.3067685 0.4269077 0.6931021

For this reason, we want to refrain from using the same random seed to generate variables that should not be correlated. For example,

set.seed(1)
alpha <- runif(50, 1, 2)

set.seed(1)
beta <- runif(25, 0.5, 4)
beta <- append(beta, runif(25, 4, 8))

plot(alpha, beta)

cor(alpha[1:25], beta[1:25])

[1] 1

cor(alpha[26:50], beta[26:50])

[1] 1

It is very clear when I write it in simple code like this, but I was not aware of this concern before. The same issue occurs when selecting values from any distribution.

set.seed(100)
vals1 <- rnorm(100, mean = 3, sd = 1)

set.seed(100)
vals2 <- rnorm(100, mean = 0.5, sd = 10)

plot(vals1, vals2)

cor(vals1, vals2)

[1] 1

To make sure this result is not by chance, I replicated it with 50 different seeds and summarized the correlation.

correlation_list <- c()

for(i in c(1:50)){
  set.seed(i)
  vals1 <- rnorm(100, mean = i, sd = 1)

  set.seed(i)
  vals2 <- rnorm(100, mean = 0.5, sd = i)

  correlation_list <- append(correlation_list, cor(vals1, vals2))
}

correlation_list

 [1] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
[39] 1 1 1 1 1 1 1 1 1 1 1 1

Best Practices

From now on, I will be implementing a better practice of setting the seed just once at the beginning (Morris and Crowther 2019).

I was under the assumption that using the same seed to simulate, say, normal and uniform data would produce correlated data as well. I found that this is actually not the case and that this correlation does not occur when selecting values from different distributions.

set.seed(9)
normal <- rnorm(100)

set.seed(9)
uniform <- runif(100)

plot(normal, uniform)

cor(normal, uniform)

[1] 0.06719044

This finding is counterintuitive to me as I thought that generating values from the normal distribution was just transformation of randomly generated uniform values to the normal distribution. I’m reading about the Mersenne Twister, a modern random number generator that is used in R and other languages (“Mersenne Twister” 2023), in hopes of understanding this. I would love to hear if anyone knows of an explanation for this.

Big thanks to Boyi Guo for his insights on this post!

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References

“Mersenne Twister.” 2023. https://en.m.wikipedia.org/wiki/Mersenne_Twister.

Morris, White, T., and M. Crowther. 2019. “Using Simulation Studies to Evaluate Statistical Methods.” https://onlinelibrary.wiley.com/doi/10.1002/sim.8086.