targa targa - 17 days ago 14
R Question

Arrange monte carlo p-value into a matrix for different sample size and variance estimators

The following code works out quite well (based on my previous question). But I have to change the variance estimator (

ols
,
hc0
,
hc1
,
hc2
,
hc3
) every time before I run the code. I would like to solve this problem with a loop.

Hereafter, I briefly describe the code. Within the code, 1000 regression models for each sample size (
n = 25, 50, 100, 250, 500, 1000
) are created. Then, each regression model out of the 1000 is estimated by OLS. After that, I calculate t-statistics based on the different beta values of
x3
out of the 1000 samples. The null hypothesis reads:
H0: beta03 = beta3
, that is the calculated beta value of
x3
equals the 'real' value which I defined as 1. In the last step, I check how often the null hypothesis is rejected (significance level = 0.05). My final goal is to create a code which spits out the procentual rejection rate of the null hypothesis for each sample size and variance estimator. Thus, the result should be a matrix whereas right now I get a vector as a result. I would be pleased if anyone of you could help me with that. Here you can see my code:

library(car)
sample_size = c("n=25"=25, "n=50"=50, "n=100"=100, "n=250"=250, "n=500"=500, "n=1000"=1000)

B <- 1000
beta0 <- 1
beta1 <- 1
beta2 <- 1
beta3 <- 1
alpha <- 0.05

simulation <- function(n, beta3h0){
t.test.values <- rep(NA, B)
#simulation of size
for(rep in 1:B){
#data generation
d1 <- runif(n, 0, 1)
d2 <- rnorm(n, 0, 1)
d3 <- rchisq(n, 1, ncp=0)
x1 <- (1 + d1)
x2 <- (3*d1 + 0.6*d2)
x3 <- (2*d1 + 0.6*d3)
# homoskedastic error term: exi <- rchisq(n, 4, ncp = 0)
exi <- sqrt(x3 + 1.6)*rchisq(n, 4, ncp = 0)
y <- beta0 + beta1*x1 + beta2*x2 + beta3*x3 + exi
mydata <- data.frame(y, x1, x2, x3)
#ols estimation
lmobj <- lm(y ~ x1 + x2 + x3, mydata)
#extraction
betaestim <- coef(lmobj)[4]
betavar <- vcov(lmobj)[4,4]
#robust variance estimators: hc0, hc1, hc2, hc3
betavar0 <- hccm(lmobj, type="hc0")[4,4]
betavar1 <- hccm(lmobj, type="hc1")[4,4]
betavar2 <- hccm(lmobj, type="hc2")[4,4]
betavar3 <- hccm(lmobj, type="hc3")[4,4]
#t statistic
t.test.values[rep] <- (betaestim - beta3h0)/sqrt(betavar)
}
mean(abs(t.test.values) > qt(p=c(1-alpha/2), df=n-4))
}

sapply(sample_size, simulation, beta3h0 = 1)

Answer

You don't need a double nested loop. Just make sure you get a matrix inside your loop. Update your current simulation with the following:

## set up a matrix
## replacing `t.test.values <- rep(NA, B)`
t.test.values <- matrix(nrow = 5, ncol = B)  ## 5 estimators

## update / fill a column
## replacing `t.test.values[rep] <- (betaestim - beta3h0)/sqrt(betavar)`
t.test.values[, rep] <- abs(betaestim - beta3h0) / sqrt(c(betavar, betavar0, betavar1, betavar2, betavar3))

## row means
## replacing `mean(abs(t.test.values) > qt(p=c(1-alpha/2), df=n-4))`
rowMeans(t.test.values > qt(1-alpha/2, n-4))

Now, simulation would return a vector of length 5. For each sample size, the monte carlo estimate of t-statistic p-value is returned for all 5 variance estimators. Then, when you call sapply, you get a matrix result:

sapply(sample_size, simulation, beta3h0 = 1)
#      n=25  n=50 n=100 n=250 n=500 n=1000
#[1,] 0.132 0.237 0.382 0.696 0.917  0.996
#[2,] 0.198 0.241 0.315 0.574 0.873  0.994
#[3,] 0.157 0.220 0.299 0.569 0.871  0.994
#[4,] 0.119 0.173 0.248 0.545 0.859  0.994
#[5,] 0.065 0.122 0.197 0.510 0.848  0.993