This function implements the bias correction of the ranking distribution using a paired anchor question, using the IPW estimator.
Usage
imprr_weights(
data,
J = NULL,
main_q,
anc_correct = NULL,
population = "non-random",
assumption = "contaminated",
weight = NULL,
ranking = "ranking",
p_random = NULL
)Arguments
- data
The input dataset with ranking data.
- J
The number of items in the ranking question. Defaults to NULL, in which case it will be inferred from the data.
- main_q
Ranking question to be analyzed. When `main_q` is a single column name or unquoted symbol such as `app_identity`, the function looks for `app_identity_1`, `app_identity_2`, `app_identity_3`, and so on. You may also supply `main_q` directly as a character vector or unquoted `c(...)` expression of ranking columns such as `c(party, gender, race, religion)`.
- anc_correct
Optional indicator for passing the anchor question. If `NULL`, `p_random` is used when supplied; otherwise the function defaults to `p_random = 0` and applies no correction.
- population
Choice of the target population out of non-random respondents (default) or all respondents.
- assumption
Choice of identifying assumption when `population = "all"`: `uniform` assumes random respondents would have uniform counterfactual preferences, while `contaminated` assumes their counterfactual preferences match those of non-random respondents.
- weight
The name of the weight column in `data`. Defaults to `NULL`, which uses equal weights. This can also be supplied as a numeric vector or as an unquoted column name.
- ranking
The name of the column that will store the full ranking profile. Defaults to "ranking". If `main_q` exists in the data, the produced column should be identical to `main_q`. However, the function defaults to creating another column by combining marginal rankings, just in case.
- p_random
Optional fixed proportion of random/inattentive respondents. When supplied, this overrides `anc_correct` and a message is shown if both are provided.
Value
A list with three elements:
- est_p_random
A numeric value representing the estimated proportion of random responses.
- results
A data frame with the original data augmented with a
weightscolumn containing inverse probability weights and arankingcolumn with unified ranking patterns.- rankings
A data frame with ranking patterns, observed proportions (
prop_obs), bias-corrected proportions (prop_bc), and inverse probability weights (weights) for each permutation.
Details
`imprr_weights()` enumerates the full permutation space of rankings, so its computational cost grows factorially in `J`. In practice, it is best suited to small or moderate ranking questions. For larger `J`, prefer `imprr_direct()` or `imprr_direct_rcpp()`.
Examples
out <- imprr_weights(
identity,
main_q = "app_identity",
anc_correct = "anc_correct_identity"
)
#> No weight column supplied; using equal weights for all observations.
head(out$results)
#> # A tibble: 6 × 18
#> weights s_weight app_identity app_identity_1 app_identity_2 app_identity_3
#> <dbl> <dbl> <chr> <dbl> <dbl> <dbl>
#> 1 1.02 0.844 1423 1 4 2
#> 2 1.02 0.886 1423 1 4 2
#> 3 1.27 2.96 3412 3 4 1
#> 4 1.02 0.987 1423 1 4 2
#> 5 1.10 1.76 4132 4 1 3
#> 6 1.02 0.469 3124 3 1 2
#> # ℹ 12 more variables: app_identity_4 <dbl>, anc_identity <chr>,
#> # anc_identity_1 <dbl>, anc_identity_2 <dbl>, anc_identity_3 <dbl>,
#> # anc_identity_4 <dbl>, anc_correct_identity <dbl>,
#> # app_identity_recorded <chr>, anc_identity_recorded <chr>,
#> # app_identity_row_rnd <chr>, anc_identity_row_rnd <chr>, ranking <chr>
head(out$rankings)
#> ranking n prop_obs prop_bc weights prop_bc_raw prop_bc_adj
#> 1 1234 14 0.012939002 0.000000000 0.0000000 -0.0003526508 0.000000000
#> 2 1243 11 0.010166359 0.000000000 0.0000000 -0.0044081345 0.000000000
#> 3 1324 14 0.012939002 0.000000000 0.0000000 -0.0003526508 0.000000000
#> 4 1342 7 0.006469501 0.000000000 0.0000000 -0.0098154461 0.000000000
#> 5 1423 50 0.046210721 0.046944603 1.0158812 0.0483131539 0.048313154
#> 6 1432 20 0.018484288 0.007538549 0.4078355 0.0077583167 0.007758317