Wald Test for Model Parameters

Performs Wald tests for individual parameters or linear combinations of parameters in a fitted model.

Usage

wald_test(object, ...)

# S3 method for class 'femtofit'
wald_test(object, parm = NULL, null_value = 0, ...)

# Default S3 method
wald_test(object, se, null_value = 0, ...)

Arguments

object

A femtofit object, or for the generic: the parameter estimate.

...

Additional arguments.

parm

Parameter name(s) or indices to test. If NULL, tests all parameters.

null_value

The null hypothesis value(s). Default is 0.

se

Standard error (for default method)

Value

For single parameter tests, a wald_test object (also inherits from hypothesis_test) containing:

stat

The Wald chi-squared statistic

p.value

P-value from chi-squared(1) distribution

dof

Degrees of freedom (1 for single parameter)

z

The z-score

estimate

Parameter estimate

se

Standard error

null_value

The null hypothesis value

For multiple parameters, returns a list of wald_test objects.

Details

The Wald test statistic for a single parameter is: $$W = \left(\frac{\hat{\theta} - \theta_0}{SE(\hat{\theta})}\right)^2$$

which follows a chi-squared distribution with 1 degree of freedom under H0.

Methods (by class)

• wald_test(femtofit): Wald test for femtofit objects

• wald_test(default): Wald test from raw estimate and SE

Examples

if (FALSE) { # \dontrun{
set.seed(42)
x <- rnorm(100, mean = 5, sd = 2)

result <- fit(
  function(mu, log_sigma) loglik_normal(mu, exp(log_sigma), x),
  params = c(mu = 0, log_sigma = 0)
)

# Test if mu = 0
test <- wald_test(result, "mu")
pval(test)

# Test if mu = 5
wald_test(result, "mu", null_value = 5)

# Test all parameters
wald_test(result)
} # }