Use the DuMouchel-Duncan (1983) test to assess the need for sampling weights in your linear regression analysis.

wgttest(model, weights, data = NULL, model_output = FALSE,
test = NULL, digits = getOption("jtools-digits", default = 3))

## Arguments

model The unweighted linear model (must be lm, glm, see details for other types) you want to check. 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 FALSE since the output can be very long for complex models. 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. 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.

## Details

This is designed to be similar to the wgttest macro for Stata (http://fmwww.bc.edu/repec/bocode/w/wgttest.html). This method, advocated for by DuMouchel and Duncan (1983), is fairly straightforward. To decide whether weights are needed, the weights are added to the linear model as a predictor and interaction with each other predictor. Then, an omnibus test of significance is performed to compare the weights-added model to the original; if insignificant, weights are not significantly related to the result and you can use the more efficient estimation from unweighted OLS.

It can be helpful to look at the created model using model_output = TRUE to see which variables might be the ones affected by inclusion of weights.

This test can support most GLMs in addition to LMs, a use validated by Nordberg (1989). This, to my knowledge, is different from the Stata macro. It does not work for mixed models (e.g., lmer or lme) though it could plausibly be implemented. However, there is no scholarly consensus how to properly incorporate weights into mixed models. There are other types of models that may work, but have not been tested. The function is designed to be compatible with as many model types as possible, but the user should be careful to make sure s/he understands whether this type of test is appropriate for the model being considered. DuMouchel and Duncan (1983) were only thinking about linear regression when the test was conceived. Nordberg (1989) validated its use with generalized linear models, but to this author's knowledge it has not been tested with other model types.

## References

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.

Winship, C. & Radbill, L. (1994). Sampling weights and regression analysis. Sociological Methods and Research, 23, 230-257.

Other survey tools: pf_sv_test, svycor, svysd, weights_tests

## Examples

# First, let's create some fake sampling weights
wts <- runif(50, 0, 5)
# Create model
fit <- lm(Income ~ Frost + Illiteracy + Murder,
data = as.data.frame(state.x77))
# See if the weights change the model
wgttest(fit, weights = wts)#> DuMouchel-Duncan test of model change with weights
#>
#> F(4,42) = 1.665
#> p = 0.176
#>
#> Lower p values indicate greater influence of the weights.
#>
# With a GLM
wts <- runif(100, 0, 2)
x <- rnorm(100)
y <- rbinom(100, 1, .5)
fit <- glm(y ~ x, family = binomial)
wgttest(fit, wts)#> DuMouchel-Duncan test of model change with weights
#>
#> Deviance (2) = 1.164
#> p = 0.559
#>
#> Lower p values indicate greater influence of the weights.
#> ## Can specify test manually
wgttest(fit, weights = wts, test = "Rao")#> DuMouchel-Duncan test of model change with weights
#>
#> Rao (2,96) = 1.156
#> p = 0.561
#>
#> Lower p values indicate greater influence of the weights.
#>
# Quasi family is treated differently than likelihood-based
## Dobson (1990) Page 93: Randomized Controlled Trial (plus some extra values):
counts <- c(18,17,15,20,10,20,25,13,12,18,17,15,20,10,20,25,13,12)
outcome <- gl(3,1,18)
treatment <- gl(3,6)
glm.D93 <- glm(counts ~ outcome + treatment, family = quasipoisson)
wts <- runif(18, 0, 3)
wgttest(glm.D93, weights = wts)#> DuMouchel-Duncan test of model change with weights
#>
#> F(5,8) = 0.304
#> p = 0.897
#>
#> Lower p values indicate greater influence of the weights.
#>