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Use the tests proposed in Pfeffermann and Sverchkov (1999) and DuMouchel and Duncan (1983) to check whether a regression model is specified correctly without weights.


  model_output = TRUE,
  test = NULL,
  sims = 1000,
  digits = getOption("jtools-digits", default = 2)



The fitted model, without weights


The name of the weights column in model's data frame or a vector of weights equal in length to the number of observations included in model.


The data frame with the data fed to the fitted model and the weights


Should a summary of the model with weights as predictor be printed? Default is TRUE, but you may not want it if you are trying to declutter a document.


Which type of test should be used in the ANOVA? The default, NULL, chooses based on the model type ("F" for linear models). This argument is passed to anova.


The number of bootstrap simulations to use in estimating the variance of the residual correlation. Default is 1000, but for publications or when computing power/time is sufficient, a higher number is better.


An integer specifying the number of digits past the decimal to report in the output. Default is 3. You can change the default number of digits for all jtools functions with options("jtools-digits" = digits) where digits is the desired number.


This function is a wrapper for the two tests implemented in this package that test whether your regression model is correctly specified. The first is wgttest, an R adaptation of the Stata macro of the same name. This test can otherwise be referred to as the DuMouchel-Duncan test. The other test is the Pfeffermann-Sverchkov test, which can be accessed directly with pf_sv_test.

For more details on each, visit the documentation on the respective functions. This function just runs each of them for you.


DuMouchel, W. H. & Duncan, D.J. (1983). Using sample survey weights in multiple regression analyses of stratified samples. Journal of the American Statistical Association, 78. 535-543.

Nordberg, L. (1989). Generalized linear modeling of sample survey data. Journal of Official Statistics; Stockholm, 5, 223-239.

Pfeffermann, D., & Sverchkov, M. (1999). Parametric and semi-parametric estimation of regression models fitted to survey data. Sankhya: The Indian Journal of Statistics, 61. 166-186.

See also

Other survey tools: pf_sv_test(), svycor(), svysd(), wgttest()


# Note: This is a contrived example to show how the function works,
# not a case with actual sammpling weights from a survey vendor
if (requireNamespace("boot")) {
  states <-
  states$wts <- runif(50, 0, 3)
  fit <- lm(Murder ~ Illiteracy + Frost, data = states)
  weights_tests(model = fit, data = states, weights = wts, sims = 100)
#> DuMouchel-Duncan test of model change with weights
#> F(3,44) = 0.674
#> p = 0.572
#> Lower p values indicate greater influence of the weights.
#> Standard errors: OLS
#> ---------------------------------------------------
#>                         Est.   S.E.   t val.      p
#> -------------------- ------- ------ -------- ------
#> (Intercept)             2.68   4.80     0.56   0.58
#> Illiteracy              5.01   1.93     2.60   0.01
#> wts                     1.01   2.78     0.36   0.72
#> Frost                  -0.00   0.03    -0.15   0.88
#> Illiteracy:wts         -0.96   1.17    -0.83   0.41
#> wts:Frost              -0.00   0.01    -0.24   0.81
#> ---------------------------------------------------
#> ---
#> Pfeffermann-Sverchkov test of sample weight ignorability 
#> Residual correlation = -0.16, p = 0.33
#> Squared residual correlation = 0.25, p = 0.11
#> Cubed residual correlation = -0.00, p = 1.00
#> A significant correlation may indicate biased estimates
#> in the unweighted model.