lr_test: Likelihood-Ratio Test for Informative Survey Weights (In production)

Description

Implements the Breidt-Herndon likelihood-ratio test for assessing whether survey weights are informative in linear regression models. The test compares maximized log-likelihoods under equal weights (null) and survey weights (alternative), with an asymptotic distribution given by a weighted chi-squared mixture.

Usage

lr_test(
  model,
  coef_subset = NULL,
  na.action = stats::na.omit,
  likelihood = c("pseudo", "scaled")
)
# S3 method for lr_test
print(x, ...)
# S3 method for lr_test
summary(object, ...)
# S3 method for lr_test
tidy(x, ...)
# S3 method for lr_test
glance(x, ...)

Value

An object of class "lr_test" containing:

statistic: Likelihood-ratio test statistic (non-negative)
p.value: P-value for the test (Satterthwaite approximation)
df: Approximate degrees of freedom
eigvals: Eigenvalues of the Gamma matrix
logLik_null: Maximized log-likelihood under equal weights
logLik_alt: Maximized log-likelihood under survey weights
method: Name of the test performed
call: Function call

Arguments

model: An object of class svyglm.
coef_subset: Optional character vector of coefficient names to include in the test. Defaults to all coefficients.
na.action: Function to handle missing data before testing.
likelihood: Character string specifying the likelihood form: "pseudo" (default) for raw weighted likelihood, or "scaled" to normalize weights by their mean.
x: An object of class lr_test
...: Additional arguments passed to methods
object: An object of class lr_test

Details

The null hypothesis is that survey weights are not informative (equal weights suffice). The alternative allows weights to affect the likelihood. The asymptotic null distribution is a weighted chi-squared mixture; here we approximate the p-value using a Satterthwaite moment-matching approach.

References

Breidt, F. J., & Opsomer, J. D. (1997). Testing for informativeness in analytic inference from complex surveys. *Survey Methodology*, 23(1), 1-11.