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Extreme Value Bounds with Double Sampling with Sensitivity

Source: R/user_facing_functions.R
estimator_ds_sens.Rd

This function yields extreme value bounds under the assumption that the outcomes of 1-delta of the missing second-round units are ignorable, that is, that they are drawn from an unknown distribution with mean and variance equal to the observed second-round groups.

Usage

estimator_ds_sens(
  Y,
  Z,
  R1,
  Attempt,
  R2,
  minY,
  maxY,
  delta,
  strata = NULL,
  alpha = 0.05,
  data
)

Arguments

Y

The (unquoted) outcome variable, or a formula outcome ~ treatment for use with declare_estimator(.method = estimator_ds_sens). Must be numeric.

Z

The (unquoted) assignment indicator variable. Must be numeric and take values 0 or 1. Ignored when Y is a formula.

R1

The initial sample response indicator: unquoted column name, or a quoted string column name when using the formula interface. Must be numeric and take values 0 or 1.

Attempt

The follow-up attempt indicator: unquoted column name, or quoted string. Must be numeric and take values 0 or 1.

R2

The follow-up response indicator: unquoted column name, or quoted string. Must be numeric and take values 0 or 1.

minY

The minimum possible value of the outcome (Y) variable.

maxY

The maximum possible value of the outcome (Y) variable.

delta

Sensitivity parameter in [0, 1]. At delta = 1 (default) worst-case bounds apply; at delta = 0 ignorability holds for all follow-up non-responders.

strata

Stratification variable: unquoted column name or a quoted string column name.

alpha

The desired significance level. 0.05 by default.

data

A dataframe

Value

A named numeric vector with elements ci_lower and ci_upper, the joint Imbens-Manski confidence interval; low_est and upp_est, the bound point estimates; and low_var and upp_var, their variances. Pass to tidy() for a data frame.

Examples

set.seed(343)
N <- 1000
Y_0 <- sample(1:5, N, replace = TRUE, prob = c(0.1, 0.3, 0.3, 0.2, 0.1))
Y_1 <- sample(1:5, N, replace = TRUE, prob = c(0.1, 0.1, 0.4, 0.3, 0.1))
Z <- rbinom(N, 1, 0.5)
Y_star <- Z * Y_1 + (1 - Z) * Y_0
R1 <- rbinom(N, 1, prob = 0.7 + 0.1 * Z)
Y <- Y_star
Y[R1 == 0] <- NA

# Follow up intensively with a random half of the initial non-responders
Attempt <- rep(0, N)
Attempt[R1 == 0] <- rbinom(sum(R1 == 0), 1, 0.5)
R2 <- rep(0, N)
R2[Attempt == 1] <- rbinom(sum(Attempt == 1), 1, 0.9)
Y[Attempt == 1 & R2 == 1] <- Y_star[Attempt == 1 & R2 == 1]
df <- data.frame(Y, Z, R1, Attempt, R2)

# delta = 1 reproduces the worst-case double-sampling bounds
estimator_ds_sens(Y, Z, R1, Attempt, R2, minY = 1, maxY = 5, delta = 1, data = df)
#>      ci_lower      ci_upper       low_est       upp_est       low_var 
#> -0.0003261488  0.5435113299  0.1356982015  0.4100265693  0.0068387546 
#>       upp_var 
#>  0.0065857778 

# delta = 0 assumes ignorability among follow-up non-responders
estimator_ds_sens(Y, Z, R1, Attempt, R2, minY = 1, maxY = 5, delta = 0, data = df)
#>    ci_lower    ci_upper     low_est     upp_est     low_var     upp_var 
#> 0.128264350 0.433193885 0.280729118 0.280729118 0.006051218 0.006051218