Tests: The Linear Regression Model (Variance-Covariance Matrix of Estimates of Regression Coefficients)

Ivan Jacob Agaloos Pesigan

2020-12-31

# The Linear Regression Model: Variance-Covariance Matrix of Estimates of Regression Coefficients {#linreg-estimation-vcov-example}

Data

See jeksterslabRdatarepo::wages.matrix() for the data set used in this example.

X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
y <- jeksterslabRdatarepo::wages.matrix[["y"]]
head(X)
#>      constant gender race union education experience
#> [1,]        1      1    0     0        12         20
#> [2,]        1      0    0     0         9          9
#> [3,]        1      0    0     0        16         15
#> [4,]        1      0    1     1        14         38
#> [5,]        1      1    1     0        16         19
#> [6,]        1      1    0     0        12          4
head(y)
#>      wages
#> [1,] 11.55
#> [2,]  5.00
#> [3,] 12.00
#> [4,]  7.00
#> [5,] 21.15
#> [6,]  6.92

Variance-Covariance Matrix of Estimates of Regression Coefficients

n <- nrow(X)
k <- ncol(X)
sigma2hatepsilonhat <- sigma2hatepsilonhat(
  X = X,
  y = y
)
result_vcovhatbetahat1 <- .vcovhatbetahat(
  sigma2hatepsilonhat = sigma2hatepsilonhat,
  X = X
)
result_vcovhatbetahat1 <- as.vector(result_vcovhatbetahat1)
result_vcovhatbetahat2 <- .vcovhatbetahat(
  X = X,
  y = y
)
result_vcovhatbetahat2 <- as.vector(result_vcovhatbetahat2)
result_vcovhatbetahat3 <- vcovhatbetahat(
  X = X,
  y = y
)
result_vcovhatbetahat3 <- as.vector(result_vcovhatbetahat3)

Variance-Covariance Matrix of Estimates of Regression Coefficients (biased)

sigma2hatepsilonhatbiased <- sigma2hatepsilonhatbiased(
  X = X,
  y = y
)
result_vcovhatbetahatbiased1 <- .vcovhatbetahatbiased(
  sigma2hatepsilonhatbiased = sigma2hatepsilonhatbiased,
  X = X
)
result_vcovhatbetahatbiased1 <- as.vector(result_vcovhatbetahatbiased1)
result_vcovhatbetahatbiased2 <- .vcovhatbetahatbiased(
  X = X,
  y = y
)
result_vcovhatbetahatbiased2 <- as.vector(result_vcovhatbetahatbiased2)
result_vcovhatbetahatbiased3 <- vcovhatbetahatbiased(
  X = X,
  y = y
)
result_vcovhatbetahatbiased3 <- as.vector(result_vcovhatbetahatbiased3)

lm() function

lmobj <- lm(
  wages ~ gender + race + union + education + experience,
  data = jeksterslabRdatarepo::wages
)
lm_vcov <- as.vector(vcov(lmobj))

context("Test linreg-estimation-vcov")
test_that("unbiased", {
  for (i in 1:length(lm_vcov)) {
    expect_equivalent(
      result_vcovhatbetahat1[i],
      lm_vcov[i]
    )
    expect_equivalent(
      result_vcovhatbetahat1[i],
      lm_vcov[i]
    )
    expect_equivalent(
      result_vcovhatbetahat1[i],
      lm_vcov[i]
    )
  }
})
#> Test passed 🎉
test_that("biased", {
  for (i in 1:length(lm_vcov)) {
    expect_equivalent(
      round(result_vcovhatbetahatbiased1[i], digits = 1),
      round(lm_vcov[i], digits = 1)
    )
    expect_equivalent(
      round(result_vcovhatbetahatbiased1[i], digits = 1),
      round(lm_vcov[i], digits = 1)
    )
    expect_equivalent(
      round(result_vcovhatbetahatbiased1[i], digits = 1),
      round(lm_vcov[i], digits = 1)
    )
  }
})
#> Test passed 🥇