Wald test statistic and p-value — wald

Given the parameter estimates and their variance-covariance matrix, wald_test calculates the Wald test statistic and p-value for a set of linear constraints on the parameters.

Usage

wald_test(
  gamma_hat,
  var_gamma_hat,
  R = diag(length(gamma_hat)),
  c = default_test(R)
)

Arguments

gamma_hat: L x 1 vector of parameter estimates
var_gamma_hat: L x L variance-covariance matrix of parameter estimates
R: Q x L matrix of linear constraints to be tested. Defaults to identity matrix of size L
c: Q x 1 vector of test values for the linear constraints. Defaults to a vector of zeros of length Q to test that all the contrasts are equal to zero.

Value

A list with the following elements:

W: Wald test statistic
p_value: p-value for the Wald test (\(\chi^2_Q\) distribution)

Examples

# test that union workers earn the same as non-union workers
cps$union <- as.numeric(cps$unionstatus == "Union")
model <- lm(earnwk ~ union, data = cps)
gamma_hat <- coef(model)
var_gamma_hat <- vcov(model)
wald_test(gamma_hat, var_gamma_hat, R = c(0, 1))
#> $W
#> [1] 28.14252
#> 
#> $p_value
#> [1] 1.127022e-07
#> 

# test that non-union workers make 900/week
# *and* union workers make 1000/week
wald_test(
  gamma_hat,
  var_gamma_hat,
  R = matrix(c(0, 1, 1, 1), nrow = 2),
  c = c(900, 1000)
)
#> $W
#> [1] 3273.083
#> 
#> $p_value
#> [1] 0
#>