Tests: Estimates of Regression Coefficients from summary matrices

Ivan Jacob Agaloos Pesigan

2020-12-31

# Estimates of Regression Coefficients from summary matrices {#linreg-estimation-betahat_matrix}

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

Unstandardized

data <- X
data[, 1] <- y
Sigmahat <- cov(data)
SigmaXhat <- Sigmahat[-1, -1]
sigmayX <- as.vector(Sigmahat[, 1])
sigmayX <- sigmayX[-1]
result1_slopes <- .slopeshat(
  SigmaXhat = SigmaXhat,
  sigmayX = sigmayX
)
result2_slopes <- .slopeshat(
  X = X,
  y = y
)
result3_slopes <- slopeshat(
  X = X,
  y = y
)
result1_intercept <- .intercepthat(
  slopeshat = result1_slopes,
  muyhat = mean(y),
  muXhat = colMeans(X[, -1])
)
result2_intercept <- .intercepthat(
  X = X,
  y = y
)
result3_intercept <- .intercepthat(
  X = X,
  y = y
)
result1_betahat <- c(result1_intercept, as.vector(result1_slopes))
result2_betahat <- c(result2_intercept, as.vector(result2_slopes))
result3_betahat <- c(result3_intercept, as.vector(result3_slopes))

Standardized

Rhat <- cor(data)
RXhat <- Rhat[-1, -1]
ryXhat <- as.vector(Rhat[, 1])
ryXhat <- ryXhat[-1]
result1_std.slopes <- .slopeshatprime(
  X = X,
  y = y
)
result2_std.slopes <- .slopeshatprime(
  RXhat = RXhat,
  ryXhat = ryXhat
)
result3_std.slopes <- slopeshatprime(
  X = X,
  y = y
)
result1_betahatprime <- c(0, as.vector(result1_std.slopes))
result2_betahatprime <- c(0, as.vector(result2_std.slopes))
result3_betahatprime <- c(0, as.vector(result3_std.slopes))

lm() function

The lm() function is the default option for fitting a linear model in R.

lmobj <- lm(
  wages ~ gender + race + union + education + experience,
  data = jeksterslabRdatarepo::wages
)
lmscaledobj <- lm(
  wages ~ gender + race + union + education + experience,
  data = as.data.frame(scale(jeksterslabRdatarepo::wages))
)
lm_betahat <- coef(lmobj)
lm_betahatprime <- coef(lmscaledobj)

context("Test Coefficients")
test_that("unstandardized.", {
  expect_equivalent(
    length(lm_betahat),
    length(result1_betahat),
    length(result2_betahat),
    length(result3_betahat)
  )
  for (i in seq_along(result1_betahat)) {
    expect_equivalent(
      lm_betahat[i],
      result1_betahat[i]
    )
    expect_equivalent(
      lm_betahat[i],
      result2_betahat[i]
    )
    expect_equivalent(
      lm_betahat[i],
      result3_betahat[i]
    )
  }
})
#> Test passed 🥳
test_that("standardized.", {
  expect_equivalent(
    length(lm_betahatprime),
    length(result1_betahatprime),
    length(result2_betahatprime),
    length(result3_betahatprime)
  )
  for (i in seq_along(result1_betahatprime)) {
    expect_equivalent(
      lm_betahatprime[i],
      result1_betahatprime[i]
    )
    expect_equivalent(
      lm_betahatprime[i],
      result2_betahatprime[i]
    )
    expect_equivalent(
      lm_betahatprime[i],
      result3_betahatprime[i]
    )
  }
})
#> Test passed 🎉