svytest (version 1.1.0)

diff_in_coef_test: Difference-in-Coefficients Test for Survey Weights

Description

Implements the Hausman-Pfeffermann Difference-in-Coefficients test to assess whether survey weights significantly affect regression estimates.

Usage

diff_in_coef_test(
  model,
  lower.tail = FALSE,
  var_equal = TRUE,
  robust_type = c("HC0", "HC1", "HC2", "HC3"),
  coef_subset = NULL,
  na.action = stats::na.omit
)
# S3 method for diff_in_coef_test
print(x, ...)
# S3 method for diff_in_coef_test
summary(object, ...)
# S3 method for diff_in_coef_test
tidy(x, ...)
# S3 method for diff_in_coef_test
glance(x, ...)

Value

An object of class "diff_in_coef_test" containing:

statistic

Chi-squared test statistic

parameter

Degrees of freedom

p.value

P-value for the test

betas_unweighted

Unweighted coefficient estimates

betas_weighted

Weighted coefficient estimates

vcov_diff

Estimated variance-covariance matrix of coefficient differences

diff_betas

Vector of coefficient differences

call

Function call

Arguments

model

An object of class svyglm.

lower.tail

Logical; passed to pchisq().

var_equal

Logical; assume equal residual variance between models. If FALSE, a heteroskedasticity-robust variance estimator is used.

robust_type

Character; type of heteroskedasticity-robust variance estimator to use if var_equal = FALSE. Options are "HC0", "HC1", "HC2", "HC3" as used in `sandwich` package.

coef_subset

Character vector of coefficient names to include in the test. Defaults to all coefficients.

na.action

Function to handle missing data before fitting the test.

x

An object of class diff_in_coef_test

...

Additional arguments passed to methods

object

An object of class diff_in_coef_test

Details

Let \(X\) denote the design matrix and \(y\) the response vector. Define the unweighted OLS estimator $$\hat\beta_{U} = (X^\top X)^{-1} X^\top y,$$ and the survey-weighted estimator $$\hat\beta_{W} = (X^\top W X)^{-1} X^\top W y,$$ where \(W = \mathrm{diag}(w_1, \ldots, w_n)\) is the diagonal matrix of survey weights.

The test statistic is based on the difference $$d = \hat\beta_{W} - \hat\beta_{U}.$$

Under the null hypothesis that weights are not informative, \(d\) has mean zero and variance \(V_d\). The test statistic is $$T = d^\top V_d^{-1} d,$$ which is asymptotically \(\chi^2_p\) distributed with \(p\) equal to the number of coefficients tested.

If var_equal = TRUE, \(V_d\) is estimated assuming equal residual variance across weighted and unweighted models. If var_equal = FALSE, a heteroskedasticity-robust estimator (e.g. HC0–HC3) is used.

This test is a survey-weighted adaptation of the Hausman specification test (Hausman, 1978), as proposed by Pfeffermann (1993).

References

Hausman, J. A. (1978). Specification Tests in Econometrics. *Econometrica*, 46(6), 1251-1271. tools:::Rd_expr_doi("10.2307/1913827")

Pfeffermann, D. (1993). The Role of Sampling Weights When Modeling Survey Data. *International Statistical Review*, 61(2), 317-337. tools:::Rd_expr_doi("10.2307/1403631")

See Also

svytestCE for the curated Consumer Expenditure dataset included in this package, which can be used to demonstrate the Difference-in-Coefficients test.

@importFrom survey svyglm

Examples

# Load in survey package (required) and load in example data
library(survey)
data(api, package = "survey")

# Create a survey design and fit a weighted regression model
des <- svydesign(id = ~1, strata = ~stype, weights = ~pw, data = apistrat)
fit <- svyglm(api00 ~ ell + meals, design = des)

# Run difference-in-coefficients diagnostic test versions with different variance assumptions
# and reports Chi-Squared statistic, df, and p-value
summary(diff_in_coef_test(fit, var_equal = TRUE))
summary(diff_in_coef_test(fit, var_equal = FALSE, robust_type = "HC3"))