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

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,
  max_iter = 500L,
  ...
)

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.

link

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.

max_iter

Maximum EM iterations per fit, passed to gmm_impute(). Default 500L; fits near missing at random can need more than the gmm_impute() default of 100.

Value

A data frame with one row per grid value: beta, estimate, std.error, conf.low, conf.high, fmi, loglik (the observed-data log-likelihood of the selection model at the fitted mixture and intercept) and converged (whether the point fit converged). A warning names any slope whose fit did not converge.

Details

The mixture is refitted at each slope. Under this selection model the observed data carry information about the slope, but only through the assumed shape of the outcome distribution; a different shape can fit the observed data equally well at a different slope. The loglik column shows how strongly the data favour one slope over another under the mixture. Treat a large difference as a consequence of the model's shape, not as evidence about the missingness mechanism itself, and report the whole curve.

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(200)
y <- x1 + rnorm(200)
y[runif(200) < 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, 0.5, 1), m = 5L, seed = 1L)
#>   beta   estimate std.error   conf.low   conf.high       fmi    loglik
#> 1  0.0 -0.3588626 0.1471407 -0.6864382 -0.03128708 0.6304986 -557.7112
#> 2  0.5 -0.1233208 0.1261837 -0.3886618  0.14202015 0.4743556 -552.2003
#> 3  1.0  0.1370836 0.1242975 -0.1173614  0.39152868 0.3752030 -552.1423
#>   converged
#> 1      TRUE
#> 2      TRUE
#> 3      TRUE