Not Missing at Random (NMAR) Estimation

High-level interface for NMAR estimation.

nmar() validates basic inputs and dispatches to an engine (for example el_engine). The engine controls the estimation method and interprets formula; see the engine documentation for model-specific requirements.

Usage

nmar(formula, data, engine, trace_level = 0)

Arguments

formula

A two-sided formula. Many engines support a partitioned right-hand side via |, for example y_miss ~ block1_vars | block2_vars. The meaning of these blocks is engine-specific (see the engine documentation). In the common "missing values indicate nonresponse" workflow, the left-hand side is the outcome with NA values for nonrespondents.

data

A data.frame or a survey.design containing the variables referenced by formula.

engine

An NMAR engine configuration object, typically created by el_engine, exptilt_engine, or exptilt_nonparam_engine. This object defines the estimation method and tuning parameters and must inherit from class "nmar_engine".

trace_level

Integer 0-3; controls verbosity during estimation (default 0):

• 0: no output (silent mode);

• 1: major steps only (initialization, convergence, final results);

• 2: iteration summaries and key diagnostics;

• 3: full diagnostic output.

Value

An object of class "nmar_result" with an engine-specific subclass (for example "nmar_result_el"). Use summary(), se, confint(), weights(), coef(), fitted(), and generics::tidy() / generics::glance() to access estimates, standard errors, weights, and diagnostics.

See also

el_engine, exptilt_engine, exptilt_nonparam_engine, summary.nmar_result, weights.nmar_result

Examples

set.seed(1)
n <- 200
x1 <- rnorm(n)
z1 <- rnorm(n)
y_true <- 0.5 + 0.3 * x1 + 0.2 * z1 + rnorm(n, sd = 0.3)
resp <- rbinom(n, 1, plogis(2 + 0.1 * y_true + 0.1 * z1))
if (all(resp == 1)) resp[sample.int(n, 1)] <- 0L
y_obs <- ifelse(resp == 1, y_true, NA_real_)

# Empirical likelihood engine
df_el <- data.frame(Y_miss = y_obs, X = x1, Z = z1)
eng_el <- el_engine(variance_method = "none")
fit_el <- nmar(Y_miss ~ X | Z, data = df_el, engine = eng_el)
summary(fit_el)
#> NMAR Model Summary
#> =================
#> Y_miss mean: 0.527456
#> Converged: TRUE 
#> Variance method: none 
#> Variance notes: Variance skipped (variance_method='none') 
#> Total units: 200 
#> Respondents: 179 
#> Call: nmar(Y_miss ~ X | Z, data = <data.frame: N=200>, engine = empirical_likelihood)
#> 
#> Missingness-model coefficients:
#>              Estimate
#> (Intercept)  2.460382
#> Y_miss       0.118914
#> Z           -0.875952

# \donttest{
# Exponential tilting engine (illustrative)
dat_et <- data.frame(y = y_obs, x2 = z1, x1 = x1)
eng_et <- exptilt_engine(
  y_dens = "normal",
  family = "logit",
  variance_method = "none"
)
fit_et <- nmar(y ~ x2 | x1, data = dat_et, engine = eng_et)
summary(fit_et)
#> NMAR Model Summary (Exponential tilting)
#> =================================
#> y mean: 0.515218
#> Converged: TRUE 
#> Variance method: none 
#> Call: nmar(y ~ x2 | x1, data = <data.frame: N=?>, engine = exponential_tilting)
#> 
#> Response-model (theta) coefficients:
#>   (Intercept)          : 2.214475
#>   x1                   : 0.120835
#>   y                    : -0.161063

# Survey design example (same outcome, random weights)
if (requireNamespace("survey", quietly = TRUE)) {
  w <- runif(n, 0.5, 2)
  des <- survey::svydesign(ids = ~1, weights = ~w,
                           data = data.frame(Y_miss = y_obs, X = x1, Z = z1))
  eng_svy <- el_engine(variance_method = "none")
  fit_svy <- nmar(Y_miss ~ X | Z, data = des, engine = eng_svy)
  summary(fit_svy)
}
#> NMAR Model Summary
#> =================
#> Y_miss mean: 0.516401
#> Converged: TRUE 
#> Variance method: none 
#> Variance notes: Variance skipped (variance_method='none') 
#> Total units: 253.0348 
#> Respondents: 179 
#> Call: nmar(Y_miss ~ X | Z, data = <survey.design: N=253.035>, engine = empirical_likelihood)
#> 
#> Missingness-model coefficients:
#>              Estimate
#> (Intercept)  1.938651
#> Y_miss       0.265915
#> Z           -0.046734

# Bootstrap variance usage
if (requireNamespace("future.apply", quietly = TRUE)) {
  set.seed(2)
  eng_boot <- el_engine(
    variance_method = "bootstrap",
    bootstrap_reps = 20
  )
  fit_boot <- nmar(Y_miss ~ X | Z, data = df_el, engine = eng_boot)
  se(fit_boot)
}
#> [1] 0.0298057
# }