Package 'NMAR'

Default coefficients for NMAR results

Description

Returns missingness-model coefficients.

Usage

## S3 method for class 'nmar_result'
coef(object, ...)

Arguments

object	An 'nmar_result' object.
...	Ignored.

Value

A named numeric vector or 'NULL'.

---

Coefficient table for summary objects

Description

Returns a coefficients table (Estimate, Std. Error, statistic, p-value) from a 'summary_nmar_result*' object when missingness-model coefficients and a variance matrix are available. If the summary does not carry missingness-model coefficients, returns 'NULL'.

Usage

## S3 method for class 'summary_nmar_result'
coef(object, ...)

Arguments

object	An object of class 'summary_nmar_result' (or subclass).
...	Ignored.

Details

The statistic column is labelled "t value" when finite degrees of freedom are present in survey designs, otherwise it is labelled "z value".

Value

A data.frame with rows named by coefficient, or 'NULL' if not available.

---

Wald confidence interval for NMAR results

Description

Wald confidence interval for NMAR results

Usage

## S3 method for class 'nmar_result'
confint(object, parm, level = 0.95, ...)

Arguments

object	An object of class 'nmar_result'.
parm	Ignored.
level	Confidence level.
...	Ignored.

Value

A 1x2 numeric matrix with confidence limits.

---

Confidence intervals for summary objects

Description

Returns Wald-style confidence intervals for missingness-model coefficients from a 'summary_nmar_result*' object. Uses t-quantiles when finite degrees of freedom are available, otherwise normal quantiles.

Usage

## S3 method for class 'summary_nmar_result'
confint(object, parm, level = 0.95, ...)

Arguments

object	An object of class 'summary_nmar_result' (or subclass).
parm	A specification of which coefficients are to be given confidence intervals, either a vector of names or a vector of indices. By default, all coefficients are considered.
level	The confidence level required.
...	Ignored.

Value

A numeric matrix with columns giving lower and upper confidence limits for each parameter. Row names correspond to coefficient names. Returns 'NULL' if coefficients are unavailable.

---

Empirical likelihood engine for NMAR

Description

Constructs an engine specification for the empirical likelihood estimator of a full-data mean under nonignorable nonresponse.

Usage

el_engine(
  standardize = TRUE,
  trim_cap = Inf,
  on_failure = c("return", "error"),
  variance_method = c("bootstrap", "none"),
  bootstrap_reps = 500,
  auxiliary_means = NULL,
  control = list(),
  strata_augmentation = TRUE,
  n_total = NULL,
  start = NULL,
  family = c("logit", "probit")
)

Arguments

standardize	logical; standardize predictors. Default TRUE.
trim_cap	numeric; cap for EL weights (Inf = no trimming).
on_failure	character; "return" or "error" on solver failure.
variance_method	character; one of "bootstrap" or "none".
bootstrap_reps	integer; number of bootstrap replicates when variance_method = "bootstrap".
auxiliary_means	named numeric vector; population means for auxiliary design columns. Names must match the materialized model.matrix column names on the first RHS after formula expansion, e.g., factor indicator columns created by model.matrix() or transformed terms like I(X^2). Auxiliary intercepts are always dropped automatically, so do not supply (Intercept). If NULL (default) and the outcome contains at least one NA, auxiliary means are estimated from the full input (including nonrespondents): IID uses unweighted column means of the auxiliary design, while survey designs use the design-weighted means based on weights(design). This corresponds to the QLS case where $\mu_x$ is replaced by the full-sample mean $\bar X$ when auxiliary variables are observed for all sampled units.
control	Optional solver configuration forwarded to nleqslv::nleqslv(). Provide a single list that may include solver tolerances (e.g., xtol, ftol, maxit) and, optionally, top-level entries global and xscalm for globalization and scaling. Example: control = list(maxit = 500, xtol = 1e-10, ftol = 1e-10, global = "qline", xscalm = "auto").
strata_augmentation	logical; when TRUE (default), survey designs with an identifiable strata structure are augmented with stratum indicators and corresponding population shares in the auxiliary block (proposed by Wu 2005). Has no effect for data.frame inputs or survey designs without strata.
n_total	numeric; optional when supplying respondents-only data (no NA in the outcome). For data.frame inputs, set to the total number of sampled units before filtering to respondents. For survey.design inputs, set to the total design-weight total on the same analysis scale as weights(design) (default sum(weights(design))). If omitted and the outcome contains no NAs, the estimator errors, requesting n_total.
start	list; optional starting point for the solver. Fields: beta: named numeric vector of missingness-model coefficients on the original scale, including (Intercept). W or z: starting value for population response rate (0 < W < 1) or its logit (z). If both are provided, z takes precedence. lambda: named numeric vector of auxiliary multipliers on the original scale (names must match auxiliary design columns). Values are mapped to the scaled space internally.
family	Missingness model family. Either "logit" (default) or "probit", or a custom family object: a list with components name, linkinv, mu.eta, score_eta, and optionally d2mu.deta2. When d2mu.deta2 is absent the solver uses Broyden/numeric Jacobians.

Details

The implementation follows Qin, Leung, and Shao (2002): the response mechanism is modeled as $w(y, x; \beta) = P(R = 1 \mid Y = y, X = x)$ and the joint distribution of $(Y, X)$ is represented nonparametrically by respondent masses that satisfy empirical likelihood constraints. The mean is estimated as a respondent weighted mean with weights proportional to $\tilde w_i = a_i / D_i(\beta, W, \lambda)$, where $a_i$ are base weights ($a_i \equiv 1$ for IID data and $a_i = d_i$ for survey designs) and $D_i$ is the EL denominator.

For data.frame inputs the estimator solves the Qin-Leung-Shao estimating equations for $(\beta, W, \lambda_x)$ with $W$ reparameterized as $z = \operatorname{logit}(W)$, and profiles out the response multiplier $\lambda_W$ using the closed-form QLS identity (their Eq. 10). For survey.design inputs the estimator uses a design-weighted analogue (Chen and Sitter 1999, Wu 2005) with an explicit $\lambda_W$ and an additional linkage equation involving the nonrespondent design-weight total $T_0$.

Numerical stability:

• $W$ is optimized on the logit scale so $0 < W < 1$.

• The response-model linear predictor is capped and EL denominators $D_i$ are floored at a small positive value. The analytic Jacobian is consistent with this guard via an active-set mask.

• Optional trimming (trim_cap) is applied only after solving, to the unnormalized masses $\tilde w_i = a_i/D_i$. This changes the returned weights and therefore the point estimate.

Formula syntax and data constraints: nmar() accepts a partitioned right-hand side y_miss ~ auxiliaries | response_only. Variables left of | enter auxiliary moment constraints. Variables right of | enter only the response model. The outcome (LHS) is always included as a response-model predictor through the evaluated LHS expression. Explicit use of the outcome on the RHS is rejected. The response model always includes an intercept, while the auxiliary block never includes an intercept.

To include a covariate in both the auxiliary constraints and the response model, repeat it on both sides, e.g. y_miss ~ X | X.

Auxiliary means: If auxiliary_means = NULL (default) and the outcome contains at least one NA, auxiliary means are estimated from the full input and used as $\bar X$ in the QLS constraints. For respondents-only data (no NA in the outcome), n_total must be supplied, and if the auxiliary RHS is non-empty, auxiliary_means must also be supplied. When standardize = TRUE, supply auxiliary_means on the original data scale, the engine applies the same standardization internally.

Survey scale: For survey.design inputs, n_total must be on the same analysis scale as weights(design). The default is sum(weights(design)).

Convergence and identification: the stacked EL system can have multiple solutions. Adding response-only predictors (variables to the right of |) can make the problem sensitive to starting values. Inspect diagnostics such as jacobian_condition_number and consider supplying start = list(beta = ..., W = ...) when needed.

Variance: The EL engine supports bootstrap standard errors via variance_method = "bootstrap" or can skip variance with variance_method = "none".

Bootstrap uses no additional packages for IID resampling, and will run sequentially by default. If the suggested future.apply package is installed, IID bootstrap can use future.apply::future_lapply() according to the user's future::plan() for parallel execution. Bootstrap backend is controlled by the package option nmar.bootstrap_apply:

"auto"

(default) Use base::lapply() unless the current future plan has more than one worker, in which case use future.apply::future_lapply() if available.

"base"

Always use base::lapply(), even if future.apply is installed.

"future"

Always use future.apply::future_lapply().

For survey.design inputs, replicate-weight bootstrap requires the suggested packages survey and svrep.

Value

A list of class "nmar_engine_el" containing configuration fields to be supplied to nmar() together with a formula and data.

References

Qin, J., Leung, D., and Shao, J. (2002). Estimation with survey data under nonignorable nonresponse or informative sampling. Journal of the American Statistical Association, 97(457), 193-200. doi:10.1198/016214502753479338

Chen, J., and Sitter, R. R. (1999). A pseudo empirical likelihood approach for the effective use of auxiliary information in complex surveys. Statistica Sinica, 9, 385-406.

Wu, C. (2005). Algorithms and R codes for the pseudo empirical likelihood method in survey sampling. Survey Methodology, 31(2), 239-243.

See Also

nmar, weights.nmar_result, summary.nmar_result

Examples

set.seed(1)
n <- 200
X <- rnorm(n)
Y <- 2 + 0.5 * X + rnorm(n)
p <- plogis(-0.7 + 0.4 * scale(Y)[, 1])
R <- runif(n) < p
if (all(R)) R[1] <- FALSE
df <- data.frame(Y_miss = Y, X = X)
df$Y_miss[!R] <- NA_real_

# Estimate auxiliary mean from full data
eng <- el_engine(auxiliary_means = NULL, variance_method = "none")

# Put X in both the auxiliary block and the response model
fit <- nmar(Y_miss ~ X | X, data = df, engine = eng)
summary(fit)


# Response-only predictors can be placed to the right of |
Z <- rnorm(n)
df2 <- data.frame(Y_miss = Y, X = X, Z = Z)
df2$Y_miss[!R] <- NA_real_
eng2 <- el_engine(auxiliary_means = NULL, variance_method = "none")
fit2 <- nmar(Y_miss ~ X | Z, data = df2, engine = eng2)
print(fit2)

# Survey design usage
if (requireNamespace("survey", quietly = TRUE)) {
  des <- survey::svydesign(ids = ~1, weights = ~1, data = df)
  eng3 <- el_engine(auxiliary_means = NULL, variance_method = "none")
  fit3 <- nmar(Y_miss ~ X, data = des, engine = eng3)
  summary(fit3)
}

---

Extract engine configuration

Description

Extract engine configuration

Usage

engine_config(x)

Arguments

x	An object inheriting from class 'nmar_engine'.

Value

A named list of configuration fields.

---

Canonical engine name

Description

Returns identifier for an engine object.

Usage

engine_name(x)

Arguments

x	An object inheriting from class 'nmar_engine'.

Value

A single character string, e.g. "empirical_likelihood".

---

Exponential tilting engine for NMAR

Description

Constructs a configuration for the exponential tilting estimator under nonignorable nonresponse. The estimator solves $S_2(\boldsymbol{\phi}, \hat{\boldsymbol{\gamma}}) = 0,$ using nleqslv to apply EM algorithm.

Usage

exptilt_engine(
  standardize = FALSE,
  on_failure = c("return", "error"),
  variance_method = c("bootstrap", "none"),
  bootstrap_reps = 10,
  supress_warnings = FALSE,
  control = list(),
  family = c("logit", "probit"),
  y_dens = c("normal", "lognormal", "exponential", "binomial"),
  stopping_threshold = 1,
  sample_size = 2000
)

Arguments

standardize	logical; standardize predictors. Default TRUE.
on_failure	character; "return" or "error" on solver failure
variance_method	character; one of "bootstrap", or "none".
bootstrap_reps	integer; number of bootstrap replicates when variance_method = "bootstrap".
supress_warnings	Logical; suppress variance-related warnings.
control	Named list of control parameters passed to nleqslv::nleqslv. Common parameters include: maxit: Maximum number of iterations (default: 100) method: Solver method - "Newton" or "Broyden" (default: "Newton") global: Global strategy - "dbldog", "pwldog", "qline", "gline", "hook", or "none" (default: "dbldog") xtol: Tolerance for relative error in solution (default: 1e-8) ftol: Tolerance for function value (default: 1e-8) btol: Tolerance for backtracking (default: 0.01) allowSingular: Allow singular Jacobians (default: TRUE) See ?nleqslv::nleqslv for full details.
family	character; response model family, either "logit" or "probit", or a family object created by logit_family() / probit_family().
y_dens	Outcome density model ("auto", "normal", "lognormal", "exponential", or "binomial").
stopping_threshold	Numeric; early stopping threshold. If the maximum absolute value of the score function falls below this threshold, the algorithm stops early (default: 1).
sample_size	Integer; maximum sample size for stratified random sampling (default: 2000). When the dataset exceeds this size, a stratified random sample is drawn to optimize memory usage. The sampling preserves the ratio of respondents to non-respondents in the original data.

Details

The method is a robust Propensity-Score Adjustment (PSA) approach for Not Missing at Random (NMAR). It uses Maximum Likelihood Estimation (MLE), basing the likelihood on the observed part of the sample ($f(\boldsymbol{Y}_i | \delta_i = 1, \boldsymbol{X}_i)$), making it robust against outcome model misspecification. The propensity score is estimated by assuming an instrumental variable ($X_2$) that is independent of the response status given other covariates and the study variable. Estimator calculates fractional imputation weights $w_i$. The final estimator is a weighted average, where the weights are the inverse of the estimated response probabilities $\hat{\pi}_i$, satisfying the estimating equation:

$\sum_{i \in \mathcal{R}} \frac{\boldsymbol{g}(\boldsymbol{Y}_i, \boldsymbol{X}_i ; \boldsymbol{\theta})}{\hat{\pi}_i} = 0,$

where $\mathcal{R}$ is the set of observed respondents.

Value

An engine object of class c("nmar_engine_exptilt","nmar_engine"). This is a configuration list; it is not a fit. Pass it to nmar.

References

Minsun Kim Riddles, Jae Kwang Kim, Jongho Im A Propensity-score-adjustment Method for Nonignorable Nonresponse Journal of Survey Statistics and Methodology, Volume 4, Issue 2, June 2016, Pages 215–245.

Examples

generate_test_data <- function(
  n_rows = 500,
  n_cols = 1,
  case = 1,
  x_var = 0.5,
  eps_var = 0.9,
  a = 0.8,
  b = -0.2
) {
# Generate X variables - fixed to match comparison
  X <- as.data.frame(replicate(n_cols, rnorm(n_rows, 0, sqrt(x_var))))
  colnames(X) <- paste0("x", 1:n_cols)

# Generate Y - fixed coefficients to match comparison
  eps <- rnorm(n_rows, 0, sqrt(eps_var))
  if (case == 1) {
# Use fixed coefficient of 1 for all x variables to match: y = -1 + x1 + epsilon
    X$Y <- as.vector(-1 + as.matrix(X) %*% rep(1, n_cols) + eps)
  }
  else if (case == 2) {
    X$Y <- -2 + 0.5 * exp(as.matrix(X) %*% rep(1, n_cols)) + eps
  }
  else if (case == 3) {
    X$Y <- -1 + sin(2 * as.matrix(X) %*% rep(1, n_cols)) + eps
  }
  else if (case == 4) {
    X$Y <- -1 + 0.4 * as.matrix(X)^3 %*% rep(1, n_cols) + eps
  }

  Y_original <- X$Y

# Missingness mechanism - identical to comparison
  pi_obs <- 1 / (1 + exp(-(a + b * X$Y)))

# Create missing values
  mask <- runif(nrow(X)) > pi_obs
  mask[1] <- FALSE # Ensure at least one observation is not missing
  X$Y[mask] <- NA

  return(list(X = X, Y_original = Y_original))
}
res_test_data <- generate_test_data(n_rows = 500, n_cols = 1, case = 1)
x <- res_test_data$X

exptilt_config <- exptilt_engine(
  y_dens = 'normal',
  control = list(maxit = 10),
  stopping_threshold = 0.1,
  standardize = FALSE,
  family = 'logit',
  bootstrap_reps = 5
)
formula = Y ~ x1
res <- nmar(formula = formula, data = x, engine = exptilt_config, trace_level = 1)
summary(res)

---

Nonparametric exponential tilting engine for NMAR

Description

Constructs a configuration for the nonparametric exponential tilting estimator under nonignorable nonresponse. This engine implements the "Fully Nonparametric Approach" from **Appendix 2** of Riddles et al. (2016). The estimator uses an Expectation-Maximization (EM) algorithm to directly estimate the nonresponse odds $O(x_1, y)$ for aggregated, categorical data.

Usage

exptilt_nonparam_engine(refusal_col = "", max_iter = 100, tol_value = 1e-06)

Arguments

refusal_col	character; the column name in data that contains the aggregated counts of non-respondents (refusals).
max_iter	integer; the maximum number of iterations for the EM algorithm.
tol_value	numeric; the convergence tolerance for the EM algorithm. The loop stops when the sum of absolute changes in the odds matrix is less than this value.

Details

This engine is designed for cases where all variables (outcomes $Y$, response predictors $X_1$, and instrumental variables $X_2$) are categorical, and the input data is pre-aggregated into strata.

The method assumes an instrumental variable $X_2$ is available. The response probability is assumed to depend on $X_1$ and $Y$, but *not* on $X_2$.

The EM algorithm iteratively solves for the nonresponse odds:

$O^{(t+1)}(x_1^*, y^*) = \frac{M_{y^*x_1^*}^{(t)}}{N_{y^*x_1^*}}$

where $M_{y^*x_1^*}^{(t)}$ is the expected count of non-respondents (calculated in the E-step) and $N_{y^*x_1^*}$ is the observed count of respondents for a given stratum $(x_1, y)$.

The final output from the nmar call is an object containing data_to_return, an aggregated data frame where the original 'refusal' counts have been redistributed into the outcome columns (e.g., 'Voted_A', 'Voted_B') as expected non-respondent counts.

Value

An engine object of class c("nmar_engine_exptilt_nonparam","nmar_engine"). This is a configuration list; it is not a fit. Pass it to nmar.

References

Minsun Kim Riddles, Jae Kwang Kim, Jongho Im A Propensity-score-adjustment Method for Nonignorable Nonresponse Journal of Survey Statistics and Methodology, Volume 4, Issue 2, June 2016, Pages 215–245. (See **Appendix 2** for this specific method).

Examples

# Test data (Riddles 2016, Table 9)
voting_data_example <- data.frame(
  Gender = rep(c("Male", "Male", "Male", "Male", "Female", "Female", "Female", "Female"), 1),
  Age_group = c("20-29", "30-39", "40-49", ">=50", "20-29", "30-39", "40-49", "50+"),
  Voted_A = c(93, 104, 146, 560, 106, 129, 170, 501),
  Voted_B = c(115, 233, 295, 350, 159, 242, 262, 218),
  Other = c(4, 8, 5, 3, 8, 5, 5, 7),
  Refusal = c(28, 82, 49, 174, 62, 70, 69, 211),
  Total = c(240, 427, 495, 1087, 335, 446, 506, 937)
)

np_em_config <- exptilt_nonparam_engine(
  refusal_col = "Refusal",
  max_iter = 100,
  tol_value = 0.001
)

# Formula: Y1 + Y2 + ... ~ X1_vars | X2_vars
# Here, Y = Voted_A, Voted_B, Other
#      x1 = Gender (response model)
#      x2 = Age_group (instrumental variable)
em_formula <- Voted_A + Voted_B + Other ~ Gender | Age_group


results_em_np <- nmar(
  formula = em_formula,
  data = voting_data_example,
  engine = np_em_config,
  trace_level = 0
)

# View the final adjusted counts
# (Original counts + expected non-respondent counts)
print(results_em_np$data_final)

---

Default fitted values for NMAR results

Description

Returns fitted response probabilities.

Usage

## S3 method for class 'nmar_result'
fitted(object, ...)

Arguments

object	An 'nmar_result' object.
...	Ignored.

Value

A numeric vector (possibly length 0).

---

Formatter for engines

Description

Returns a single concise line summarizing an engine configuration.

Usage

## S3 method for class 'nmar_engine'
format(x, ...)

Arguments

x	An engine object inheriting from 'nmar_engine'.
...	Unused.

Value

A length-1 character vector.

---

Default formula for NMAR results

Description

Returns the estimation formula if available.

Usage

## S3 method for class 'nmar_result'
formula(x, ...)

Arguments

x	An 'nmar_result' object.
...	Ignored.

Value

A formula or 'NULL'.

---

Glance summary for NMAR results

Description

One-row diagnostics for NMAR fits.

Usage

## S3 method for class 'nmar_result'
glance(x, ...)

Arguments

x	An object of class 'nmar_result'.
...	Ignored.

Value

A one-row data frame with diagnostics and metadata.

---

Not Missing at Random Estimation

Description

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. 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 created by el_engine, exptilt_engine, or exptilt_nonparam_engine. This object defines the estimation method and tuning parameters.
trace_level	Integer 0-3; controls verbosity during estimation (default 0): 0: no output, 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)


# Exponential tilting engine
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)

# Survey design
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)
}

# Bootstrap variance usage
# future.apply is optional, if installed, bootstrap may run in parallel under
# the user's future::plan()
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)

---

Polish Household Budget Data with Simulated Nonignorable Nonresponse

Description

This dataset is derived from the 'h05' dataset (Polish household budgets for 2005) found in the 'RClas' package. The original data was cleaned to remove all rows with missing values.

Usage

polish_households

Format

A data frame with 19,330 rows and 17 columns. The key variables are:

class

TODO

voi

TODO

bio

TODO

type

TODO

d345

TODO

d347

TODO

d348

TODO

d36

TODO

d38

TODO

d61

TODO

noper

TODO

income

TODO

expenditure

TODO

y_exp

Numeric. The **true** scaled expenditure ('expenditure / mean(expenditure)'). This is the complete study variable without missingness.

resp

TODO

R

Integer. The simulated response indicator (1=responded, 0=nonresponse).

y_exp_miss

Numeric. The **observed** scaled expenditure, containing 7,778 'NA' values where 'R = 0'. This is the variable to be used as the NMAR-affected outcome.

Details

To create a realistic test case for nonignorable nonresponse (NMAR), a nonresponse mechanism was simulated and applied to the scaled expenditure variable ('y_exp').

The key simulation steps were: 1. 'y_exp' (true study variable) was created by scaling total expenditure. 2. A true response probability ('resp') was created using the logistic model: 'plogis(1 - 0.6 * y_exp)'. 3. A response indicator ('R') was simulated based on this probability. 4. The final variable 'y_exp_miss' was generated by setting 'y_exp' to 'NA' wherever 'R' was 0.

The response is **nonignorable** because the probability of missingness depends directly on the value of the expenditure variable itself.

Source

TODO

See Also

'riddles_case1', 'riddles_case2', 'riddles_case3', 'riddles_case4'

---

Print method for engines

Description

Compact summary for 'nmar_engine' objects.

Usage

## S3 method for class 'nmar_engine'
print(x, ...)

Arguments

x	An engine object inheriting from 'nmar_engine'.
...	Unused.

Value

'x', invisibly.

---

Print method for nmar_result

Description

Print method for nmar_result

Usage

## S3 method for class 'nmar_result'
print(x, ...)

Arguments

x	nmar_result object
...	Additional parameters

Value

'x', invisibly.

---

Print method for EL results

Description

Print for objects of class nmar_result_el.

Usage

## S3 method for class 'nmar_result_el'
print(x, ...)

Arguments

x	An object of class nmar_result_el.
...	Ignored.

Value

x, invisibly.

---

Print method for Exponential Tilting results (engine-specific)

Description

This print method is tailored for 'nmar_result_exptilt' objects and shows a concise, human-friendly summary of the estimation result together with exptilt-specific diagnostics (loss, iterations) and a compact view of the response coefficients stored in the fitted model.

Usage

## S3 method for class 'nmar_result_exptilt'
print(x, ...)

Arguments

x	An object of class 'nmar_result_exptilt'.
...	Ignored.

Value

'x', invisibly.

---

Print method for summary.nmar_result

Description

Print method for summary.nmar_result

Usage

## S3 method for class 'summary_nmar_result'
print(x, ...)

Arguments

x	summary_nmar_result object
...	Additional parameters

Value

'x', invisibly.

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Riddles Simulation, Case 1: Linear Mean

Description

A simulated dataset of 500 observations based on Simulation Study I (Model 1, Case 1) of Riddles, Kim, and Im (2016). The data features a nonignorable nonresponse (NMAR) mechanism where the response probability depends on the study variable 'y'.

Usage

riddles_case1

Format

A data frame with 500 rows and 4 variables:

x

Numeric. The auxiliary variable, x ~ Normal(0, 0.5).

y

Numeric. The study variable with nonignorable nonresponse. 'y' contains 'NA's for nonrespondents.

y_true

Numeric. The complete, true value of 'y' before missingness was introduced.

delta

Integer. The response indicator (1 = responded, 0 = nonresponse).

Details

This dataset was generated using the following model parameters (n = 500):

Density for x:

x ~ Normal(mean = 0, variance = 0.5)

Density for error:

e ~ Normal(mean = 0, variance = 0.9)

True Model (Case 1):

y_true = -1 + x + e

Response Model (NMAR):

logit(pi) = 0.8 - 0.2 * y_true

Source

Riddles, M. K., Kim, J. K., & Im, J. (2016). A Propensity-Score-Adjustment Method for Nonignorable Nonresponse. Journal of Survey Statistics and Methodology, 4(1), 1-31.

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Riddles Simulation, Case 2: Exponential Mean

Description

A simulated dataset of 500 observations based on Simulation Study I (Model 1, Case 2) of Riddles, Kim, and Im (2016). The data features a nonignorable nonresponse (NMAR) mechanism where the response probability depends on the study variable 'y'.

Usage

riddles_case2

Format

A data frame with 500 rows and 4 variables:

x

Numeric. The auxiliary variable, x ~ Normal(0, 0.5).

y

Numeric. The study variable with nonignorable nonresponse. 'y' contains 'NA's for nonrespondents.

y_true

Numeric. The complete, true value of 'y' before missingness was introduced.

delta

Integer. The response indicator (1 = responded, 0 = nonresponse).

Details

This dataset was generated using the following model parameters (n = 500):

Density for x:

x ~ Normal(mean = 0, variance = 0.5)

Density for error:

e ~ Normal(mean = 0, variance = 0.9)

True Model (Case 2):

y_true = -2 + 0.5 * exp(x) + e

Response Model (NMAR):

logit(pi) = 0.8 - 0.2 * y_true

Source

Riddles, M. K., Kim, J. K., & Im, J. (2016). A Propensity-Score-Adjustment Method for Nonignorable Nonresponse. Journal of Survey Statistics and Methodology, 4(1), 1-31.

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Riddles Simulation, Case 3: Sine Wave Mean

Description

A simulated dataset of 500 observations based on Simulation Study I (Model 1, Case 3) of Riddles, Kim, and Im (2016). The data features a nonignorable nonresponse (NMAR) mechanism where the response probability depends on the study variable 'y'.

Usage

riddles_case3

Format

A data frame with 500 rows and 4 variables:

x

Numeric. The auxiliary variable, x ~ Normal(0, 0.5).

y

Numeric. The study variable with nonignorable nonresponse. 'y' contains 'NA's for nonrespondents.

y_true

Numeric. The complete, true value of 'y' before missingness was introduced.

delta

Integer. The response indicator (1 = responded, 0 = nonresponse).

Details

This dataset was generated using the following model parameters (n = 500):

Density for x:

x ~ Normal(mean = 0, variance = 0.5)

Density for error:

e ~ Normal(mean = 0, variance = 0.9)

True Model (Case 3):

y_true = -1 + sin(2 * x) + e

Response Model (NMAR):

logit(pi) = 0.8 - 0.2 * y_true

Source

Riddles, M. K., Kim, J. K., & Im, J. (2016). A Propensity-Score-Adjustment Method for Nonignorable Nonresponse. Journal of Survey Statistics and Methodology, 4(1), 1-31.

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Riddles Simulation, Case 4: Cubic Mean

Description

A simulated dataset of 500 observations based on Simulation Study I (Model 1, Case 4) of Riddles, Kim, and Im (2016). The data features a nonignorable nonresponse (NMAR) mechanism where the response probability depends on the study variable 'y'.

Usage

riddles_case4

Format

A data frame with 500 rows and 4 variables:

x

Numeric. The auxiliary variable, x ~ Normal(0, 0.5).

y

Numeric. The study variable with nonignorable nonresponse. 'y' contains 'NA's for nonrespondents.

y_true

Numeric. The complete, true value of 'y' before missingness was introduced.

delta

Integer. The response indicator (1 = responded, 0 = nonresponse).

Details

This dataset was generated using the following model parameters (n = 500):

Density for x:

x ~ Normal(mean = 0, variance = 0.5)

Density for error:

e ~ Normal(mean = 0, variance = 0.9)

True Model (Case 4):

y_true = -1 + 0.4 * x^3 + e

Response Model (NMAR):

logit(pi) = 0.8 - 0.2 * y_true

Source

Riddles, M. K., Kim, J. K., & Im, J. (2016). A Propensity-Score-Adjustment Method for Nonignorable Nonresponse. Journal of Survey Statistics and Methodology, 4(1), 1-31.

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Extract standard error for NMAR results

Description

Returns the standard error of the primary mean estimate.

Usage

se(object, ...)

Arguments

object	An 'nmar_result' or subclass.
...	Ignored.

Value

Numeric scalar.

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Summary method for nmar_result

Description

Summary method for nmar_result

Usage

## S3 method for class 'nmar_result'
summary(object, conf.level = 0.95, ...)

Arguments

object	nmar_result object
conf.level	Confidence level for intervals.
...	Additional parameters

Value

An object of class 'summary_nmar_result'.

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Summary method for EL results

Description

Summarize estimation, standard error and missingness-model coefficients.

Usage

## S3 method for class 'nmar_result_el'
summary(object, ...)

Arguments

object	An object of class nmar_result_el.
...	Ignored.

Value

An object of class summary_nmar_result_el.

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Summary method for Exponential Tilting results (engine-specific)

Description

Summarize estimation, standard error and model coefficients.

Usage

## S3 method for class 'nmar_result_exptilt'
summary(object, conf.level = 0.95, ...)

Arguments

object	An object of class 'nmar_result_exptilt'.
conf.level	Confidence level for confidence interval (default 0.95).
...	Ignored.

Value

An object of class 'summary_nmar_result_exptilt'.

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Tidy summary for NMAR results

Description

Return a data frame with the primary estimate and missingness-model coefficients.

Usage

## S3 method for class 'nmar_result'
tidy(x, conf.level = 0.95, ...)

Arguments

x	An object of class 'nmar_result'.
conf.level	Confidence level for the primary estimate.
...	Ignored.

Value

A data frame with one row for the primary estimate and, when available, additional rows for the response-model coefficients.

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Variance-covariance for NMAR results

Description

Variance-covariance for NMAR results

Usage

## S3 method for class 'nmar_result'
vcov(object, ...)

Arguments

object	An object of class 'nmar_result'.
...	Ignored.

Value

A 1x1 numeric matrix (the variance of the primary estimate).

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Aggregated Exit Poll Data for Gangdong-Gap (2012)

Description

This dataset contains the aggregated exit poll results for the Gangdong-Gap district in Seoul from the 2012 nineteenth South Korean legislative election. The data is transcribed directly from Table 9 of Riddles, Kim, and Im (2016).

Usage

voting

Format

A data frame with 8 rows and 7 variables:

Gender

Factor. The gender of the voter ("Male", "Female").

Age_group

Character. The age group of the voter.

Voted_A

Numeric. Count of respondents voting for Party A.

Voted_B

Numeric. Count of respondents voting for Party B.

Other

Numeric. Count of respondents voting for another party.

Refusal

Numeric. Count of sampled individuals who refused to respond (this is the nonresponse count).

Total

Numeric. Total individuals sampled in the group (Responders + Refusals).

Details

In the paper's application, 'Gender' is used as the nonresponse instrumental variable and 'Age_group' is the primary auxiliary variable .

Source

Riddles, M. K., Kim, J. K., & Im, J. (2016). A Propensity-Score-Adjustment Method for Nonignorable Nonresponse. *Journal of Survey Statistics and Methodology*, 4(1), 1–31. (Data from Table 9, p. 20).

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Extract weights from an 'nmar_result'

Description

Return analysis weights stored in an 'nmar_result' as either probability-scale (summing to 1) or population-scale (summing to 'sample$n_total'). The function normalizes stored masses and attaches informative attributes.

Usage

## S3 method for class 'nmar_result'
weights(object, scale = c("probability", "population"), ...)

Arguments

object	An 'nmar_result' object.
scale	One of '"probability"' (default) or '"population"'.
...	Additional arguments (ignored).

Value

Numeric vector of weights with length equal to the number of respondents.

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