Storing data in long or array format in simulation - r

Question

I have a simulation study which I would eventually like to plot the results of using ggplot2. However, this requires the data to be in long format, which I find not very convenient when doing a simulation study which naturally employs a kind of factorial design. My question concerns how to approach this.
Here's a dummy example just to illustrate it all. Suppose we want to compare the OLS estimator for the slope in a simple linear regression with and without intercept included for two sample sizes for R replications. We can store this using:
an R x 2 x 2 array (replications x estimators x sample sizes)
a data frame (tibble) with variables Replication, Sample size, Estimator and Value
Here's the array and data frame in R:
library(tidyverse)
# Settings
R <- 10
est <- c("OLS1", "OLS2")
n <- c(50, 100)
# Initialize array
res <- array(NA,
dim = c(R, length(est), length(n)),
dimnames = list(Replication = 1:R,
Estimator = est,
Sample_size = n))
tibb <- as_tibble(expand.grid(Replication = 1:R, Sample_size = n, Estimator = est)) %>%
mutate(Value = NA)
To fill these with values, here's the main body of the simulation:
for (i in seq_along(n)) {
nn <- n[i]
x <- rnorm(nn)
for (j in 1:R) {
y <- 1 * x + rnorm(nn)
mod1 <- lm(y ~ 0 + x)
mod2 <- lm(y ~ 1 + x)
res[j, 1, i] <- mod1$coefficients[1]
res[j, 2, i] <- mod2$coefficients[2]
tibb[tibb$Replication == j & tibb$Sample_size == nn & tibb$Estimator == "OLS1", "Value"] <- mod1$coefficients[1]
tibb[tibb$Replication == j & tibb$Sample_size == nn & tibb$Estimator == "OLS2", "Value"] <- mod2$coefficients[2]
}
}
Now, tibb is immediately ready for plotting with ggplot2. However, that row selection that is going on is pretty awkward. On the other hand, while filling the array feels natural and intuitive, it needs more work to be transformed into the appropriate format for plotting.
So how should I best approach this? (Also bearing in mind that real simulations would usually have more dimensions than what I used here.) Are there other, better ways to do this?

Answer 1

First of all, I suggest reading the good blog about tidy data
Keeping in mind, that
Each column is a variable.
Each row is an observation.
you can build upa datafram containing all planned simulations. Define your simulation as a function and apply this function to every row of the dataframe:
library(dplyr)
library(ggplot2)
# pre-define your simulations
df = expand.grid(Replication=1:10, Sample_size=c(50,100), Estimator=c("OLS1", "OLS2"))
# your simulation in a function
sim <- function(n, est) {
x = rnorm(n)
y = 1 * x + rnorm(n)
ic = rep(ifelse(est=="OLS1",0,1), n)
lm(y ~ ic + x)$coefficients["x"]
}
# simulate and plot
df %>%
rowwise() %>%
mutate(coefs= sim(Sample_size, Estimator)) %>%
ggplot(aes(x=Replication, y=coefs, colour=as.factor(Sample_size), shape=Estimator)) +
geom_point()