I want to create 1000 samples of 200 bivariate normally distributed vectors
set.seed(42) # for sake of reproducibility
mu <- c(1, 1)
S <- matrix(c(0.56, 0.4,
0.4, 1), nrow=2, ncol=2, byrow=TRUE)
bivn <- mvrnorm(200, mu=mu, Sigma=S)
so that I can run OLS regressions on each sample and therefore get 1000 estimators. I tried this
library(MASS)
bivn_1000 <- replicate(1000, mvrnorm(200, mu=mu, Sigma=S), simplify=FALSE)
but I am stuck there, because now I don't know how to proceed to run the regression for each sample.
I would appreciate the help to know how to run these 1000 regressions and then extract the coefficients.
We could write a custom regression function.
regFun1 <- function(x) summary(lm(x[, 1] ~ x[, 2]))
which we can loop over the data with lapply:
l1 <- lapply(bivn_1000, regFun1)
The coefficients are saved inside a list and can be extracted like so:
l1[[1]]$coefficients # for the first regression
# Estimate Std. Error t value Pr(>|t|)
# (Intercept) 0.5554601 0.06082924 9.131466 7.969277e-17
# x[, 2] 0.4797568 0.04255711 11.273246 4.322184e-23
If we solely want the estimators without statistics, we adjust the output of the function accordingly.
regFun2 <- function(x) summary(lm(x[, 1] ~ x[, 2]))$coef[, 1]
Since we may want the output in matrix form we use sapply next.
m2 <- t(sapply(bivn_1000, regFun2))
head(m2)
# (Intercept) x[, 2]
# [1,] 0.6315558 0.4389721
# [2,] 0.5514555 0.4840933
# [3,] 0.6782464 0.3250800
# [4,] 0.6350999 0.3848747
# [5,] 0.5899311 0.3645237
# [6,] 0.6263678 0.3825725
where
dim(m2)
# [1] 1000 2
assures us that we have our 1,000 estimates.