Package {miapack}

Type: Package
Title: Marginalization over Incomplete Auxiliaries
Version: 0.2.0
Maintainer: Sean McGrath <sean.mcgrath514@gmail.com>
Description: Implements methods to estimate conditional outcome means in settings with missingness-not-at-random and incomplete auxiliary variables. Specifically, this package implements the marginalization over incomplete auxiliaries (MIA) method proposed by Mathur et al. (2026) <doi:10.13140/RG.2.2.30750.19524>. The package supports the iterative conditional expectation estimator and the noniterative conditional expectation estimator.
License: GPL (≥ 3)
Encoding: UTF-8
LazyData: true
RoxygenNote: 7.3.3
URL: https://github.com/stmcg/miapack
BugReports: https://github.com/stmcg/miapack/issues
Imports: boot, nnet, progress
Depends: R (≥ 2.10)
Suggests: testthat (≥ 3.0.0)
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2026-08-23 02:59:42 UTC; Sean
Author: Sean McGrath ORCID iD [aut, cre], Shaun Seaman ORCID iD [aut], Willi Zhang ORCID iD [aut], Ilya Shpitser ORCID iD [aut], Maya Mathur ORCID iD [aut]
Repository: CRAN
Date/Publication: 2026-08-23 10:30:02 UTC

Simulated data set

Description

This data set was simulated to reflect a setting with missingness-not-at-random and an incomplete auxiliary variable.

Usage

dat.sim

Format

A data frame that contains 9,297 rows and the following columns:

Y

A continuous outcome variable.

X1

A binary predictor variable.

X2

A binary predictor variable.

W

A binary auxiliary variable.

Details

Variable dependencies: The underlying values of the variables were generated as follows:

Missingness patterns: The missingness patterns were generated as follows:

See Also

mia_nice, mia_ice

Bootstrap-based confidence intervals for MIA

Description

This function applies nonparametric bootstrap to construct confidence intervals around the conditional mean estimates obtained by mia_nice or mia_ice. This function is a wrapper for the boot and boot.ci functions from the boot package.

Usage

get_CI(
  mia_res,
  n_boot = 1000,
  type = "perc",
  conf = 0.95,
  boot_args = list(),
  boot.ci_args = list(),
  show_progress = TRUE
)

Arguments

mia_res

Output from the mia_nice or mia_ice function.

n_boot

Numeric scalar specifying the number of bootstrap replicates to use

type

Character string specifying the type of confidence interval. The options are "norm", "basic", "perc", and "bca".

conf

Numeric scalar specifying the level of the confidence interval. The default is 0.95.

boot_args

A list of additional arguments to pass to the boot function. Note that this includes parallelization options.

boot.ci_args

A list of additional arguments to pass to the boot.ci function

show_progress

Logical scalar indicating whether to show a progress bar during bootstrap. Default is TRUE. The progress bar will not be displayed when parallelization is used.

Value

An object of class "mia_ci". This object is a list with the following elements:

ci_1

An object of class "boot.ci" which contains the output of the boot.ci function applied for the confidence interval around the mean under X_values_1 in mia_nice or mia_ice.

ci_2

An object of class "boot.ci" which contains the output of the boot.ci function applied for the confidence interval around the mean under X_values_2 in mia_nice or mia_ice. (if applicable).

ci_contrast

An object of class "boot.ci" which contains the output of the boot.ci function applied for the confidence interval around the contrast between mean under X_values_1 versus X_values_2 in mia_nice or mia_ice (if applicable).

bres

An object of class "boot" which contains the output of the boot function. Users can access the bootstrap replicates through the element t in this object.

...

additional elements

Mathur MB, Seaman S, Zhang W, McGrath S, Shpitser I. (2026). Estimating conditional means under missingness-not-at-random with incomplete auxiliary variables. doi:10.13140/RG.2.2.30750.19524.

Examples

set.seed(1234)
res <- mia_nice(data = dat.sim,
                X_names = c("X1", "X2"),
                X_values_1 = c(0, 1), X_values_2 = c(0, 0),
                Y_model = Y ~ W + X1 + X2, W_model = W ~ X1 + X2)
res_ci <- get_CI(mia_res = res, n_boot = 50, type = 'perc')
res_ci

## Example with parallelization
res_par <- get_CI(res, n_boot = 100, type = 'perc',
                 boot_args = list(parallel = "snow", ncpus = 2))

MIA Method via the Iterative Conditional Expectation Approach

Description

This function implements the marginalization over incomplete auxiliaries (MIA) method (Mathur et al. 2026) via an iterative conditional expectation (ICE) approach. For an outcome variable Y, predictor variable X, and auxiliary variable W, this function estimates the conditional outcome mean identified by

\mu_{\text{MIA}}(x) = \int_{w} E [ Y | X=x, W=w, M=1 ] p( w | X=x, R_W = R_X = 1 ) dw,

where R_W and R_X are indicators of non-missing values of W and X, respectively, and M is an indicator of a complete case pattern (i.e., Y, X, and W are non-missing). This function uses a plug-in estimator of the functional represented as

\mu_{\text{MIA}}(x) = E [ \, E [ Y | X, W, M=1 ] \mid X=x, R_W = R_X = 1 \, ]

The function supports estimating the identifying functionals of \mu_{\text{MIA}}(x_1) and \mu_{\text{MIA}}(x_2) as well as contrasts between them (differences, ratios).

Usage

mia_ice(
  data,
  X_names,
  X_values_1,
  X_values_2 = NULL,
  contrast_type,
  Y_model,
  Y_type,
  outer_model
)

Arguments

data

Data frame containing the observed data.

X_names

Vector of character strings specifying the name(s) of the predictor variable(s) X.

X_values_1

Numeric vector specifying the value of the predictor variable(s) X, i.e. x_1 in \mu_{\text{MIA}}(x_1).

X_values_2

(Optional) Numeric vector specifying an additional value of the predictor variable(s) X, i.e. x_2 in \mu_{\text{MIA}}(x_2).

contrast_type

(Optional) Character string specifying the type of contrast to use when comparing \mu_{\text{MIA}}(x_1) and \mu_{\text{MIA}}(x_2). Options are "difference", "ratio", and "none".

Y_model

Formula for the outcome model.

Y_type

(Optional) Character string specifying the "type" of the outcome variable. Options are "binary" and "continuous". If this is not supplied, the type will be inferred from the corresponding column in data.

outer_model

Formula for the outer regression of the fitted outcome means on the predictor(s) X. The left-hand side must be g_hat, which denotes the fitted outcome means \hat{E}[ Y | X, W, M = 1 ]. For example, g_hat ~ X1 * X2 specifies a model that is saturated with respect to binary predictors X1 and X2.

Details

Estimation algorithm:

Step 1: One fits a model for the conditional outcome mean g(x, w) = E [ Y | X=x, W=w, M=1 ] using the complete cases (i.e., units with Y, X, and W observed). Let \hat{g}(x, w) denote the fitted model.

Step 2: For every unit with X and W observed (i.e., R_X = R_W = 1), one computes the fitted outcome mean \hat{g}(X, W) at the unit's observed X and W.

Step 3: One regresses the fitted outcome means \hat{g}(X, W) on the predictor(s) X among units with R_X = R_W = 1, using the model specified by outer_model, and takes the prediction at X = x as the estimate of \mu_{\text{MIA}}(x). Note that when outer_model is saturated with respect to X (e.g., g_hat ~ X1 * X2 for binary predictors), this reduces to the sample mean of \hat{g}(x, w) among units with X = x and R_X = R_W = 1.

Value

An object of class "mia". This object is a list with the following elements:

mean_est_1

conditional outcome mean estimate under X_values_1

mean_est_2

conditional outcome mean estimate under X_values_2

contrast_est

contrast of conditional outcome mean estimates between X_values_1 and X_values_2

fit_Y

fitted model for Y

fit_outer

fitted outer regression of the fitted outcome means on X

...

additional elements

References

Mathur MB, Seaman S, Zhang W, McGrath S, Shpitser I. (2026). Estimating conditional means under missingness-not-at-random with incomplete auxiliary variables. doi:10.13140/RG.2.2.30750.19524.

See Also

print.mia, get_CI

Examples

set.seed(1234)
mia_ice(data = dat.sim,
        X_names = c("X1", "X2"),
        X_values_1 = c(0, 1), X_values_2 = c(0, 0),
        Y_model = Y ~ W + X1 + X2, outer_model = g_hat ~ X1 * X2)

MIA Method via the Noniterative Conditional Expectation (NICE) Approach

Description

This function implements the marginalization over incomplete auxiliaries (MIA) method (Mathur et al. 2026). For an outcome variable Y, predictor variable X, and auxiliary variable W, this function estimates the conditional outcome mean identified by

\mu_{\text{MIA}}(x) = \int_{w} E [ Y | X=x, W=w, M=1 ] p( w | X=x, R_W = R_X = 1 ) dw.

where R_W and R_X are indicators of non-missing values of W and X, respectively, and M is an indicator of a complete case pattern (i.e., Y, X, and W are non-missing). The function supports estimating the identifying functionals of \mu_{\text{MIA}}(x_1) and \mu_{\text{MIA}}(x_2) as well as contrasts between them (differences, ratios).

Usage

mia_nice(
  data,
  X_names,
  X_values_1,
  X_values_2 = NULL,
  contrast_type,
  Y_model,
  Y_type,
  W_model,
  W_type,
  n_mc = 10000,
  return_simulated_data = FALSE
)

Arguments

data

Data frame containing the observed data.

X_names

Vector of character strings specifying the name(s) of the predictor variable(s) X.

X_values_1

Numeric vector specifying the value of the predictor variable(s) X, i.e. x_1 in \mu_{\text{MIA}}(x_1).

X_values_2

(Optional) Numeric vector specifying an additional value of the predictor variable(s) X, i.e. x_2 in \mu_{\text{MIA}}(x_2).

contrast_type

(Optional) Character string specifying the type of contrast to use when comparing \mu_{\text{MIA}}(x_1) and \mu_{\text{MIA}}(x_2). Options are "difference", "ratio", and "none".

Y_model

Formula for the outcome model.

Y_type

(Optional) Character string specifying the "type" of the outcome variable. Options are "binary" and "continuous". If this is not supplied, the type will be inferred from the corresponding column in data.

W_model

Formula for the auxiliary variable model. If the auxiliary variable is multivariate, this argument should be a list of model formulas, one for each component. The components will be simulated in the order they appear in the list.

W_type

(Optional) Vector of character strings specifying the "type" of each auxiliary variable. Options are "binary", "categorical", and "normal". If this is not supplied, the type will be inferred from the corresponding column in data.

n_mc

Integer specifying the number of Monte Carlo samples to use.

return_simulated_data

Logical scalar indicating whether to return the simulated data set(s) containing the predictors and simulated auxiliary variable. Setting this argument to TRUE can substantially increase the size of the returned object, particularly when n_mc is large. The default is FALSE.

Details

Estimation algorithm:

Step 1: One fits a model for the conditional outcome mean E [ Y | X=x, W=w, M=1 ] and the conditional density of the auxiliary variables p( w | X=x, R_W = R_X = 1 ). When W is multivariate, i.e., W = (W_1, \dots, W_p)^\top, one uses the decomposition

p( w | X=x, R_W = R_X = 1 ) = \prod_{j = 1}^p p( w_j | X=x, w_1, \dots, w_{j-1}, R_W = R_X = 1 )

and fits models for the components p( w_j | X=x, w_1, \dots, w_{j-1}, R_W = R_X = 1 ).

Step 2: Monte Carlo integration is used to compute the integral in the identifying functional for \mu_{\text{MIA}}(x) based on the fitted models in the first step. More specifically, for iteration i, the following algorithm is performed. The value of W is first simulated from its estimated conditional distribution. When W is multivariate, the components of W are simulated sequentially from their fitted models. That is, W_1 is simulated conditional on x, W_2 is simulated conditional on x, W_1, and so on. Then, the mean of Y is estimated conditional on x, W. Finally, the average of the estimated means (across all iterations i) is taken as the estimate of \mu_{\text{MIA}}(x).

Value

An object of class "mia". This object is a list with the following elements:

mean_est_1

conditional outcome mean estimate under X_values_1

mean_est_2

conditional outcome mean estimate under X_values_2

contrast_est

contrast of conditional outcome mean estimates between X_values_1 and X_values_2

fit_W

a list of fitted model(s) for W

fit_Y

fitted model for Y

simulated_data

a list, where the first element is the simulated data set under X_values_1 and the second element is the simulated data set under X_values_2. The simulated data sets contain the predictors and simulated auxiliary variable. This element is set to NULL unless return_simulated_data is set to TRUE.

...

additional elements

References

Mathur MB, Seaman S, Zhang W, McGrath S, Shpitser I. (2026). Estimating conditional means under missingness-not-at-random with incomplete auxiliary variables. doi:10.13140/RG.2.2.30750.19524.

See Also

print.mia, get_CI

Examples

set.seed(1234)
mia_nice(data = dat.sim,
         X_names = c("X1", "X2"),
         X_values_1 = c(0, 1), X_values_2 = c(0, 0),
         Y_model = Y ~ W + X1 + X2, W_model = W ~ X1 + X2)

Print method for objects of class "mia"

Description

Print method for objects of class "mia"

Usage

## S3 method for class 'mia'
print(x, digits = 4, ...)

Arguments

x

Object of class "mia".

digits

Integer specifying the number of decimal places to display.

...

Other arguments (ignored).

Value

No value is returned.

See Also

mia_nice, mia_ice

Examples

res <- mia_nice(data = dat.sim,
                X_names = c("X1", "X2"),
                X_values_1 = c(0, 1), X_values_2 = c(0, 0),
                Y_model = Y ~ W + X1 + X2, W_model = W ~ X1 + X2)
print(res)

Print method for objects of class "mia_ci"

Description

Print method for objects of class "mia_ci"

Usage

## S3 method for class 'mia_ci'
print(x, digits = 4, ...)

Arguments

x

Object of class "mia_ci".

digits

Integer specifying the number of decimal places to display.

...

Other arguments (ignored).

Value

No value is returned.

See Also

get_CI

Examples

set.seed(1234)
res <- mia_nice(data = dat.sim,
           X_names = c("X1", "X2"),
           X_values_1 = c(0, 1), X_values_2 = c(0, 0),
           Y_model = Y ~ W + X1 + X2, W_model = W ~ X1 + X2)
res_ci <- get_CI(res, n_boot = 100, type = 'perc')
print(res_ci)