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Missing-not-at-random sensitivity analysis for a coordinate mean

Source: R/impute_sensitivity.R
proxy_mnar_sensitivity.Rd

Sweeps the missing-not-at-random sensitivity slope beta over a grid and, at each value, multiply-imputes coord under the selection model \(P(\text{missing}\mid y) = g(\alpha + \beta y)\) and pools its mean by Rubin's rules. The result traces how the estimate and its confidence interval move as the assumed dependence of missingness on the unobserved value strengthens, so an analyst can read off the value of beta at which a conclusion would change. beta = 0 is the missing-at-random anchor.

Usage

proxy_mnar_sensitivity(
  data,
  coord,
  beta_grid = seq(0, 1, by = 0.25),
  link = c("logit", "probit"),
  N = NULL,
  m = 20L,
  seed = NULL,
  ...
)

Arguments

data

A numeric matrix or data frame with NA in coord only (its other columns must be fully observed).

coord

Name or index of the coordinate the mechanism acts on.

beta_grid

Numeric vector of sensitivity slopes. Positive values make larger unobserved values more likely to be missing.

Selection link, "logit" (the default) or "probit".

N, m, seed, ...

Passed to gmm_impute(); a single seed makes the whole sweep reproducible and keeps the curve smooth across the grid.

Value

A data frame with one row per grid value: beta, estimate, std.error, conf.low, conf.high, fmi.

Details

The slope is a sensitivity parameter, not an estimate: the data do not identify it. Report the curve, not a single point.

See also

gmm_impute(), mnar().

Other imputation: as_mids(), gmm_complete(), gmm_imputation(), gmm_impute(), mechanism, proxy_fmi(), proxy_pool()

Examples

set.seed(1)
x1 <- rnorm(300)
y <- x1 + rnorm(300)
y[runif(300) < plogis(-0.4 + 0.8 * y)] <- NA      # MNAR on y
dat <- data.frame(x1 = x1, y = y)
proxy_mnar_sensitivity(dat, "y", beta_grid = c(0, 0.4, 0.8, 1.2), m = 10L, seed = 1L)
#>   beta   estimate  std.error    conf.low   conf.high       fmi
#> 1  0.0 -0.2114708 0.09202746 -0.39312678 -0.02981479 0.2294043
#> 2  0.4  0.0105841 0.09663433 -0.17992398  0.20109218 0.2079950
#> 3  0.8  0.1755879 0.10466714 -0.03128688  0.38246275 0.2494541
#> 4  1.2  0.3315785 0.11298771  0.10764312  0.55551396 0.2872016