Tidy helper function for estimator_AS function — estimator_AS

Runs the Aronow and Samii estimator from the 'interference' package and returns Horvitz-Thompson and Hajek estimates of the total, direct, and indirect effects. Exposure is defined by one-hop neighbours in adj_matrix. The data must contain the treatment as Z and the outcome as Y.

Usage

estimator_AS_tidy(
  data,
  permutatation_matrix = NULL,
  adj_matrix,
  obs_prob_exposure = NULL
)

Arguments

data

A data frame with columns Z and Y.

permutatation_matrix

(The spelling is the published one and is kept so existing code runs.) A matrix of random treatment assignments with one row per permutation of the treatment vector and one column per unit, as returned by t(obtain_permutation_matrix(declaration)). The exposure probabilities are computed from it unless obs_prob_exposure is supplied.

adj_matrix

An adjacency matrix defining the network structure. This can be created, for example, as follows:


adjacency <- fairfax |>
  as("Spatial") |>
  spdep::poly2nb(queen = TRUE) |>
  spdep::nb2mat(style = "B", zero.policy = TRUE)

obs_prob_exposure

Optional exposure probabilities. They depend only on the permutation matrix and the network, so in a simulation they are the same on every draw; computing them once and passing them here avoids recomputing them each time. For example:


prob_exposure <- interference::make_exposure_prob(
  potential_tr_vector = permutatation_matrix,
  adj_matrix = adjacency,
  exposure_map_fn = interference::make_exposure_map_AS,
  exposure_map_fn_add_args = list(hop = 1)
)

When NULL, the default, they are computed from permutatation_matrix.

Value

A data frame with six rows (three inquiries by two estimators) and columns term, inquiry, estimator, estimate, std.error, p.value, conf.low, and conf.high. Each effect is a contrast with the no exposure condition. The Hajek rows use the Hajek variance estimator. The Horvitz-Thompson rows use the conservative estimator of Aronow and Samii (2017), the larger of the Horvitz-Thompson variance and the constant-effects variance, because the Horvitz-Thompson variance of a difference can be negative. The p-values and 95 percent confidence intervals use a normal approximation. When an exposure condition is rare the variance estimates are noisy and the intervals can undercover: in 300 simulations of the book's Fairfax design with 10 percent of units treated, the total effect's intervals covered 82 percent of the time (Horvitz-Thompson) and 90 percent (Hajek); the direct and indirect effects' covered 94 to 98 percent.

Details

The function requires the 'interference' package, which is not available on CRAN.

To use this function, install it with remotes::install_github('szonszein/interference')

Without it the function returns nothing and explains why, so a design that includes it still declares and diagnoses.

See https://book.declaredesign.org/experimental-causal.html#experiments-over-networks

Examples


set.seed(343)
# A ring of 20 units, each adjacent to the units on either side of it
N <- 20
adjacency <- matrix(0, N, N)
adjacency[cbind(1:N, c(2:N, 1))] <- 1
adjacency <- adjacency + t(adjacency)
Z <- randomizr::complete_ra(N)

# 100 possible assignments, one per row
permutations <- t(replicate(100, randomizr::complete_ra(N)))

dat <- data.frame(Z = Z, Y = Z + rnorm(N))
estimator_AS_tidy(dat, permutatation_matrix = permutations, adj_matrix = adjacency)
#> # A tibble: 6 × 8
#>   term     inquiry      estimator  estimate std.error p.value conf.low conf.high
#>   <chr>    <chr>        <chr>         <dbl>     <dbl>   <dbl>    <dbl>     <dbl>
#> 1 dir_ind1 total_ATE    Horvitz-T…     2.08     1.55  0.178     -0.951      5.11
#> 2 isol_dir direct_ATE   Horvitz-T…     1.42     2.00  0.479     -2.51       5.35
#> 3 ind1     indirect_ATE Horvitz-T…     1.53     1.38  0.267     -1.17       4.23
#> 4 dir_ind1 total_ATE    Hajek          2.11     0.810 0.00911    0.525      3.70
#> 5 isol_dir direct_ATE   Hajek          1.33     1.25  0.288     -1.12       3.77
#> 6 ind1     indirect_ATE Hajek          1.46     0.579 0.0119     0.322      2.59