Pseudo-weights for a non-probability sample against a reference

For a non-probability sample (opt-in panel, volunteer or river sample) with no design weights, step_pseudoweight() estimates each unit's participation propensity \(\hat p\) against a probability reference_sample() and assigns the pseudo-weight \((1 - \hat{p})/\hat{p}\) (the participation odds; Elliott and Valliant 2017), which inflates each unit to the population so the weights sum to the reference's estimated population size. It stacks the non-probability sample and the reference internally (the participation indicator and the two samples' weights are built for you), fits the propensity, and returns the pseudo-weight on the non-probability units only; the reference is used to train the model and then dropped.

Usage

step_pseudoweight(
  spec,
  reference,
  formula,
  engine = c("logit", "tree", "forest", "boost"),
  num_classes = NULL,
  crossfit = NULL,
  crossfit_seed = NULL,
  id = NULL
)

Arguments

spec

a non-probability weighting_spec.

reference

a reference_sample() (the probability reference with its design weights). Pass the reference's replicate weights through reference_sample(replicates = ) to propagate its sampling variance through the recipe-aware bootstrap: each replicate refits the propensity from the paired reference replicate. Without them the reference is treated as fixed, so the bootstrap reflects only the variability of the non-probability sample (which it resamples as a with-replacement sample of units, a slightly conservative approximation when that sample is a large fraction of the population).

formula

one-sided formula of the covariates shared by both samples, e.g. ~ sex + age + region.

engine

propensity learner: "logit" (default), "tree", "forest" or "boost".

num_classes

NULL (default, direct 1/pi) or an integer: group the fitted propensities into that many quantile classes and use the class-average pseudo-weight, which is more robust to a misspecified model.

crossfit, crossfit_seed

optional K-fold cross-fitting of the propensity (recommended for the flexible learners), and its seed.

id

optional stable step id.

Value

the input weighting_spec with this step appended.

Details

The recipe must be a non-probability spec: weighting_spec(..., nonprob = TRUE). This step is the inverse-propensity (IPW) route; you can instead, or additionally, calibrate to a reference_sample() with step_calibrate() / step_model_calibration() (mass imputation / model-based), and combining both gives the doubly robust estimator.

References

Elliott, M. R. and Valliant, R. (2017). Inference for non-probability samples. Statistical Science 32(2), 249-264.

See also

reference_sample(), step_calibrate(), step_model_calibration()

Other weighting steps: step_assert(), step_calibrate(), step_cre(), step_drop_ineligible(), step_model_calibration(), step_nonresponse(), step_nr_sensitivity(), step_rescale(), step_round(), step_select_within(), step_subsample(), step_trim(), step_trim_calibrated(), step_trim_weights(), step_unknown_eligibility()

Examples

set.seed(1)
N   <- nrow(population)
# a biased volunteer sample (men over-participate) and a probability reference
vol <- population[rbinom(N, 1, plogis(-2 + 0.9 * (population$sex == "M"))) == 1,
                  c("region", "sex", "income")]
ref <- population[sample(N, 600), c("region", "sex")]
ref$d <- N / 600                                   # its design weights
fit <- weighting_spec(vol, base_weights = NULL, nonprob = TRUE) |>
  step_pseudoweight(reference = reference_sample(ref, "d"),
                    formula = ~ region + sex, engine = "logit") |>
  prep()
# the pseudo-weighted mean corrects the volunteer bias
c(naive = mean(vol$income),
  pseudo = weighted.mean(vol$income, fit$final_weight),
  truth = mean(population$income))
#>    naive   pseudo    truth 
#> 19353.58 18936.79 19298.11