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.
weights_tests(model, weights, data, model_output = TRUE, test = NULL, sims = 1000, digits = getOption("jtoolsdigits", default = 2))
model  The fitted model, without weights 

weights  The name of the weights column in 
data  The data frame with the data fed to the fitted model and the weights 
model_output  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. 
test  Which type of test should be used in the ANOVA? The default,

sims  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. 
digits  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

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 DuMouchelDuncan test. The
other test is the PfeffermannSverchkov 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. 535543.
Nordberg, L. (1989). Generalized linear modeling of sample survey data. Journal of Official Statistics; Stockholm, 5, 223239.
Pfeffermann, D., & Sverchkov, M. (1999). Parametric and semiparametric estimation of regression models fitted to survey data. Sankhya: The Indian Journal of Statistics, 61. 166186.
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 < as.data.frame(state.x77) set.seed(100) states$wts < runif(50, 0, 3) fit < lm(Murder ~ Illiteracy + Frost, data = states) weights_tests(model = fit, data = states, weights = wts, sims = 100) }#> DuMouchelDuncan 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 #> #>  #> PfeffermannSverchkov test of sample weight ignorability #> #> Residual correlation = 0.16, p = 0.34 #> Squared residual correlation = 0.25, p = 0.16 #> Cubed residual correlation = 0.00, p = 1.00 #> #> A significant correlation may indicate biased estimates #> in the unweighted model.