Package {mixedsubjects}

mixedsubjects: Causal Inference in Experiments with Mixed-Subjects Designs

Description

Implements seven estimators for average treatment effect (ATE) estimation in mixed-subjects designs (MSDs), where human subjects data is augmented with predictions from large language models (LLMs). Includes Difference-in-Means, GREG, PPI++, Doubly-Tuned, Difference-in-Predictions (DiP), DiP++, and D-T DiP estimators. Provides point estimates, variance estimation via delta-method or bootstrap, and optimal design selection for budget allocation between human observations and LLM predictions.

Author(s)

Maintainer: Klint Kanopka klint.kanopka@nyu.edu

Authors:

• Austin van Loon avanloon@mit.edu

Other contributors:

• Yuan Huang yh2741@nyu.edu [contributor]

See Also

Useful links:

• https://klintkanopka.com/mixedsubjects/

• Report bugs at https://github.com/klintkanopka/mixedsubjects/issues

Variance Estimation for Mixed-Subjects Design

Description

Variance estimation methods including fold-respecting bootstrap. Bootstrap Variance Estimation

Computes bootstrap variance estimates for MSD estimators using a fold-respecting resampling procedure.

Usage

bootstrap_variance(
  data,
  estimator = c("dim", "greg", "ppi", "dt", "dip", "dip_pp", "dt_dip"),
  n_bootstrap = 1000,
  n_folds = 2,
  conf_level = 0.95,
  seed = NULL
)

Arguments

Details

The fold-respecting bootstrap resamples within each stratum:

1. Resample observed treatment units with replacement

2. Resample observed control units with replacement

3. Resample unlabeled units with replacement

4. Recompute the estimator on the bootstrap sample

For cross-fit estimators, the fold assignments are regenerated for each bootstrap replicate to properly account for the cross-fitting variance.

Value

A list containing:

Examples

# Create sample data
obs_df <- data.frame(
  Y = rnorm(100),
  S0 = rnorm(100),
  S1 = rnorm(100),
  D = rep(c(1, 0), each = 50)
)
unobs_df <- data.frame(
  S0 = rnorm(200),
  S1 = rnorm(200),
  D = rep(c(1, 0), each = 100)
)
msd <- msd_data(observed = obs_df, unobserved = unobs_df)

# Bootstrap variance for D-T DiP
boot_result <- bootstrap_variance(msd, "dt_dip", n_bootstrap = 100, seed = 1)
print(boot_result)

Compare variance estimates across methods

Description

Computes and compares variance estimates using both delta-method and bootstrap for a given estimator.

Usage

compare_variance_methods(
  data,
  estimator,
  n_bootstrap = 1000,
  n_folds = 2,
  seed = NULL
)

Arguments

Value

A data frame comparing variance estimates

Examples

obs_df <- data.frame(
  Y = rnorm(100), S0 = rnorm(100), S1 = rnorm(100),
  D = rep(c(1, 0), each = 50)
)
unobs_df <- data.frame(
  S0 = rnorm(200), S1 = rnorm(200), D = rep(c(1, 0), each = 100)
)
msd <- msd_data(observed = obs_df, unobserved = unobs_df)
comparison <- compare_variance_methods(msd, "dt_dip", n_bootstrap = 100, seed = 1)
print(comparison)

Estimate all available estimators

Description

Runs all applicable estimators on the data and returns a summary table.

Usage

estimate_all(data, n_folds = 2, conf_level = 0.95)

Arguments

Value

A data frame with estimates from all applicable estimators

Examples

obs_df <- data.frame(
  Y = rnorm(100), S0 = rnorm(100), S1 = rnorm(100),
  D = rep(c(1, 0), each = 50)
)
unobs_df <- data.frame(
  S0 = rnorm(200), S1 = rnorm(200), D = rep(c(1, 0), each = 100)
)
msd <- msd_data(observed = obs_df, unobserved = unobs_df)
all_estimates <- estimate_all(msd)
print(all_estimates)

Data Preparation for Mixed-Subjects Design

Description

Create and validate data objects for MSD estimation. Create an MSD data object

Creates a validated data object for mixed-subjects design estimation. Accepts either a single combined dataframe or two separate dataframes for observed and unobserved units. Column names default to "Y", "D", "S0", "S1" and can be overridden explicitly.

Usage

msd_data(
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  outcome = "Y",
  treatment = "D",
  pred_control = "S0",
  pred_treated = "S1",
  obs_outcome = NULL,
  obs_treatment = NULL,
  obs_pred_control = NULL,
  obs_pred_treated = NULL,
  unobs_treatment = NULL,
  unobs_pred_control = NULL,
  unobs_pred_treated = NULL
)

Arguments

Details

The function supports flexible column name specification:

Default column names: By default, the function expects columns named "Y" (outcome), "D" (treatment), "S0" (control prediction), and "S1" (treatment prediction). Override these using the outcome, treatment, pred_control, and pred_treated arguments.

Global specification: Use outcome, treatment, pred_control, pred_treated to set column names that apply to both observed and unobserved dataframes.

Per-dataframe specification: Use obs_* and unobs_* arguments when column names differ between observed and unobserved dataframes. These override global settings.

Two input modes:

Mode 1: Single combined dataframe Provide a single dataframe via the data argument. The function will automatically split it into observed and unobserved based on whether Y is NA.

Mode 2: Separate dataframes Provide two separate dataframes via observed and unobserved.

Value

An S3 object of class "msd_data" containing:

Examples

# Default column names (Y, D, S0, S1)
obs_df <- data.frame(
  Y = c(1.2, 0.8, 1.5, 0.9),
  S0 = c(1.0, 0.7, 1.3, 0.8),
  S1 = c(1.1, 0.9, 1.4, 1.0),
  D = c(1, 0, 1, 0)
)
msd <- msd_data(observed = obs_df)

# Custom column names (same in both dataframes)
obs_df2 <- data.frame(
  response = c(1.2, 0.8, 1.5, 0.9),
  pred_ctrl = c(1.0, 0.7, 1.3, 0.8),
  pred_trt = c(1.1, 0.9, 1.4, 1.0),
  treated = c(1, 0, 1, 0)
)
unobs_df2 <- data.frame(
  pred_ctrl = c(1.1, 0.9),
  pred_trt = c(1.2, 1.0),
  treated = c(1, 0)
)
msd2 <- msd_data(
  observed = obs_df2,
  unobserved = unobs_df2,
  outcome = "response",
  treatment = "treated",
  pred_control = "pred_ctrl",
  pred_treated = "pred_trt"
)

# Different column names in observed vs unobserved
obs_df3 <- data.frame(
  outcome = c(1.2, 0.8),
  claude_pred_0 = c(1.0, 0.7),
  claude_pred_1 = c(1.1, 0.9),
  treatment = c(1, 0)
)
unobs_df3 <- data.frame(
  s0_claude = c(1.1, 0.9),
  s1_claude = c(1.2, 1.0),
  D = c(1, 0)
)
msd3 <- msd_data(
  observed = obs_df3,
  unobserved = unobs_df3,
  obs_outcome = "outcome",
  obs_treatment = "treatment",
  obs_pred_control = "claude_pred_0",
  obs_pred_treated = "claude_pred_1",
  unobs_treatment = "D",
  unobs_pred_control = "s0_claude",
  unobs_pred_treated = "s1_claude"
)

Difference-in-Means Estimator

Description

Classical difference-in-means estimator for ATE. Difference-in-Means Estimator

Computes the classical difference-in-means estimator for the average treatment effect (ATE). This estimator uses only observed (labeled) data and does not incorporate any predictions.

Usage

msd_dim(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  conf_level = 0.95
)

Arguments

Details

The difference-in-means estimator is:

\hat{\tau}^{DiM} = \bar{Y}_1 - \bar{Y}_0

where \bar{Y}_d is the sample mean of outcomes in arm d.

The variance is estimated as:

\widehat{Var}(\hat{\tau}^{DiM}) = \frac{s^2_{Y(1)}}{n_1} + \frac{s^2_{Y(0)}}{n_0}

where s^2_{Y(d)} is the sample variance of outcomes in arm d.

Value

An msd_result object containing:

Examples

# Using msd_data object (standard interface)
obs_df <- data.frame(
  Y = c(1.2, 1.4, 0.8, 0.6, 1.1, 0.9, 1.3, 0.7),
  S0 = c(1.0, 1.2, 0.7, 0.5, 1.0, 0.8, 1.1, 0.6),
  S1 = c(1.1, 1.3, 0.9, 0.7, 1.1, 0.9, 1.2, 0.8),
  D = c(1, 1, 0, 0, 1, 0, 1, 0)
)
msd <- msd_data(observed = obs_df)

result <- msd_dim(msd)
print(result)

# Using formula interface with custom column names
df <- data.frame(
  response = c(1.2, 1.4, 0.8, 0.6),
  treated = c(1, 1, 0, 0)
)
result2 <- msd_dim(response ~ treated, observed = df)

DiP (Difference-in-Predictions) Estimator

Description

DiP estimator for ATE using paired predictions. DiP (Difference-in-Predictions) Estimator

Computes the Difference-in-Predictions (DiP) estimator for the average treatment effect (ATE). This estimator uses both treatment and control predictions for each unlabeled unit, computing the contrast S^(1) - S^(0) at the unit level.

Usage

msd_dip(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  conf_level = 0.95
)

Arguments

Details

The DiP estimator is:

\hat{\tau}^{DiP} = \frac{1}{|\mathcal{U}|}\sum_{i \in \mathcal{U}} (S_i^{(1)} - S_i^{(0)}) + \frac{1}{n_1}\sum_{i \in \mathcal{O}_1} (Y_i - S_i^{(1)}) - \frac{1}{n_0}\sum_{i \in \mathcal{O}_0}(Y_i - S_i^{(0)})

Value

An msd_result object containing:

Note

DiP requires BOTH S0 and S1 predictions for ALL units. The key advantage of DiP over GREG is that when S^(1) and S^(0) are positively correlated, the variance of their difference is smaller.

Examples

# Using msd_data object
obs_df <- data.frame(
  Y = c(1.2, 1.4, 0.8, 0.6),
  S0 = c(1.0, 1.2, 0.7, 0.5),
  S1 = c(1.1, 1.3, 0.9, 0.7),
  D = c(1, 1, 0, 0)
)
unobs_df <- data.frame(
  S0 = c(1.1, 0.9, 1.0, 0.8),
  S1 = c(1.2, 1.0, 1.1, 0.9),
  D = c(1, 1, 0, 0)
)
msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_dip(msd)

# Using formula interface
result2 <- msd_dip(Y ~ D | S1 + S0, observed = obs_df, unobserved = unobs_df)

DiP++ Estimator

Description

Power-tuned Difference-in-Predictions estimator for ATE. DiP++ Estimator

Computes the DiP++ (power-tuned difference-in-predictions) estimator for the average treatment effect (ATE). This estimator uses paired predictions S^(1) and S^(0) for each unlabeled unit, with a single tuning parameter lambda estimated via cross-fitting.

Usage

msd_dip_pp(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  n_folds = 2,
  conf_level = 0.95,
  seed = NULL
)

Arguments

Details

The DiP++ estimator is:

\hat{\tau}^{DiP++}(\lambda) = \frac{\lambda}{|\mathcal{U}|} \sum_{i \in \mathcal{U}} (S_i^{(1)} - S_i^{(0)}) + \frac{1}{n_1}\sum_{i \in \mathcal{O}_1}(Y_i - \lambda S_i^{(1)}) - \frac{1}{n_0}\sum_{i \in \mathcal{O}_0}(Y_i - \lambda S_i^{(0)})

Value

An msd_result object containing:

Note

DiP++ requires BOTH S0 and S1 predictions for ALL units. For arm-specific tuning, use msd_dt_dip.

Examples

# Using msd_data object
set.seed(123)
n <- 100
obs_df <- data.frame(
  Y = rnorm(n),
  D = rep(c(1, 0), each = n/2)
)
obs_df$Y <- obs_df$Y + 0.3 * obs_df$D
obs_df$S1 <- 0.5 * obs_df$Y + rnorm(n, 0, 0.5)
obs_df$S0 <- 0.5 * obs_df$Y + rnorm(n, 0, 0.5) - 0.1

unobs_df <- data.frame(
  S0 = rnorm(200, 0, 0.5),
  S1 = rnorm(200, 0.2, 0.5),
  D = rep(c(1, 0), each = 100)
)

msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_dip_pp(msd)

# Using formula interface
result2 <- msd_dip_pp(Y ~ D | S1 + S0, observed = obs_df, unobserved = unobs_df)

D-T (Doubly-Tuned) Estimator

Description

D-T estimator with arm-specific tuning parameters for ATE. D-T (Doubly-Tuned) Estimator

Computes the Doubly-Tuned (D-T) estimator for the average treatment effect (ATE). This estimator uses arm-specific tuning parameters (lambda_1 and lambda_0) estimated via cross-fitting.

Usage

msd_dt(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  n_folds = 2,
  conf_level = 0.95,
  seed = NULL
)

Arguments

Details

The D-T estimator uses arm-specific tuning parameters:

\hat{\mu}_d^{D-T}(\lambda_d) = \bar{Y}_{\mathcal{O}_d} + \lambda_d(\bar{S}^{(d)}_{\mathcal{U}_d} - \bar{S}^{(d)}_{\mathcal{O}_d})

Each lambda_d is chosen to minimize the variance in arm d:

\lambda_d^* = \frac{Cov(Y(d), S^{(d)}) / n_d}{Var(S^{(d)})(1/m_d + 1/n_d)}

The tuning parameters are estimated via cross-fitting to avoid bias.

Value

An msd_result object containing:

Note

D-T differs from PPI++ by using separate tuning parameters for each arm, which can improve efficiency when the prediction quality differs between treatment and control.

Examples

# Create sample data
set.seed(123)
n <- 100
obs_df <- data.frame(
  Y = rnorm(n),
  S0 = rnorm(n, 0, 0.5),
  S1 = rnorm(n, 0.2, 0.5),
  D = rep(c(1, 0), each = n/2)
)
obs_df$Y <- obs_df$Y + 0.3 * obs_df$D
obs_df$S1[obs_df$D == 1] <- obs_df$S1[obs_df$D == 1] + 0.5 * obs_df$Y[obs_df$D == 1]
obs_df$S0[obs_df$D == 0] <- obs_df$S0[obs_df$D == 0] + 0.5 * obs_df$Y[obs_df$D == 0]

unobs_df <- data.frame(
  S0 = rnorm(200, 0, 0.5),
  S1 = rnorm(200, 0.2, 0.5),
  D = rep(c(1, 0), each = 100)
)

msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_dt(msd)

# Using formula interface
result2 <- msd_dt(Y ~ D | S1 + S0, observed = obs_df, unobserved = unobs_df)

D-T DiP (Doubly-Tuned Difference-in-Predictions) Estimator

Description

D-T DiP estimator with arm-specific tuning for ATE. D-T DiP (Doubly-Tuned Difference-in-Predictions) Estimator

Computes the D-T DiP estimator for the average treatment effect (ATE). This estimator uses paired predictions S^(1) and S^(0) for each unlabeled unit, with arm-specific tuning parameters (lambda_1 and lambda_0) estimated via cross-fitting.

Usage

msd_dt_dip(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  n_folds = 2,
  conf_level = 0.95,
  seed = NULL
)

Arguments

Details

The D-T DiP estimator is:

\hat{\tau}^{D-T DiP} = \frac{1}{|\mathcal{U}|} \sum_{i \in \mathcal{U}} (\lambda_1 S_i^{(1)} - \lambda_0 S_i^{(0)}) + \frac{1}{n_1}\sum_{i \in \mathcal{O}_1}(Y_i - \lambda_1 S_i^{(1)}) - \frac{1}{n_0}\sum_{i \in \mathcal{O}_0}(Y_i - \lambda_0 S_i^{(0)})

The tuning parameters (\lambda_1, \lambda_0) are chosen jointly to minimize the total variance. Because the two arms share the unobserved pool, the variance is jointly quadratic in (\lambda_1, \lambda_0) with a cross-term from Cov(S^{(1)}, S^{(0)}), so the optimum solves a coupled 2x2 linear system rather than two independent regressions.

The tuning parameters are estimated via cross-fitting:

1. Split labeled data into K folds

2. For each fold k, estimate (lambda_1, lambda_0) on opposite folds

3. Compute the fold-k estimate using estimated lambdas

4. Average across folds with equal weights

Value

An msd_result object containing:

Note

D-T DiP requires BOTH S0 and S1 predictions for ALL units. This corresponds to 2 predictions per unlabeled unit.

D-T DiP combines the benefits of:

• DiP: exploiting positive correlation between S^(1) and S^(0)

• D-T: arm-specific tuning for heterogeneous prediction quality

Examples

# Create sample data with both predictions
set.seed(123)
n <- 100
obs_df <- data.frame(
  Y = rnorm(n),
  D = rep(c(1, 0), each = n/2)
)
obs_df$Y <- obs_df$Y + 0.3 * obs_df$D
obs_df$S1 <- 0.6 * obs_df$Y + rnorm(n, 0, 0.4)
obs_df$S0 <- 0.4 * obs_df$Y + rnorm(n, 0, 0.5)

unobs_df <- data.frame(
  S0 = rnorm(300, 0, 0.5),
  S1 = rnorm(300, 0.2, 0.4),
  D = rep(c(1, 0), 150)
)
# Add correlation between S0 and S1
unobs_df$S1 <- unobs_df$S1 + 0.5 * unobs_df$S0

msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_dt_dip(msd)

# Using formula interface
result2 <- msd_dt_dip(Y ~ D | S1 + S0, observed = obs_df, unobserved = unobs_df)

GREG Estimator

Description

Generalized Regression (GREG) calibration estimator for ATE. GREG Estimator

Computes the Generalized Regression (GREG) calibration estimator for the average treatment effect (ATE). This is the untuned calibration estimator with tuning parameter \lambda = 1. GREG, the original Prediction-Powered Inference (PPI) estimator, and Design-based Supervised Learning (DSL) are all the same untuned (\lambda = 1) estimator. It is distinct from the power-tuned PPI++ estimator in msd_ppi, which estimates \lambda via cross-fitting to minimize variance.

Usage

msd_greg(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  conf_level = 0.95
)

Arguments

Details

The GREG estimator for arm d is:

\hat{\mu}_d^{GREG} = \bar{S}^{(d)}_{\mathcal{U}_d} + (\bar{Y}_{\mathcal{O}_d} - \bar{S}^{(d)}_{\mathcal{O}_d})

The ATE estimate is:

\hat{\tau}^{GREG} = \hat{\mu}_1^{GREG} - \hat{\mu}_0^{GREG}

The variance is:

\widehat{Var}(\hat{\tau}^{GREG}) = \sum_{d \in \{0,1\}} \left[\frac{s^2_{S^{(d)}}}{m_d} + \frac{Var(Y(d) - S^{(d)})}{n_d}\right]

Value

An msd_result object containing:

Note

GREG requires predictions for each unit's assigned arm:

• Treatment arm units need S1

• Control arm units need S0

Examples

# Using msd_data object
obs_df <- data.frame(
  Y = c(1.2, 1.4, 0.8, 0.6),
  S0 = c(1.0, 1.2, 0.7, 0.5),
  S1 = c(1.1, 1.3, 0.9, 0.7),
  D = c(1, 1, 0, 0)
)
unobs_df <- data.frame(
  S0 = c(1.1, 0.9, 1.0, 0.8),
  S1 = c(1.2, 1.0, 1.1, 0.9),
  D = c(1, 1, 0, 0)
)
msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_greg(msd)

# Using formula interface
result2 <- msd_greg(Y ~ D | S1 + S0, observed = obs_df, unobserved = unobs_df)

PPI++ Estimator

Description

Power-tuned Prediction-Powered Inference estimator for ATE. PPI++ Estimator

Computes the PPI++ (power-tuned prediction-powered inference) estimator for the average treatment effect (ATE). This estimator uses a single tuning parameter lambda that is estimated via cross-fitting to minimize variance.

Usage

msd_ppi(
  formula_or_data,
  data = NULL,
  observed = NULL,
  unobserved = NULL,
  n_folds = 2,
  conf_level = 0.95,
  seed = NULL
)

Arguments

Details

The PPI++ estimator uses a single tuning parameter lambda across both arms:

\hat{\mu}_d^{PPI}(\lambda) = \bar{Y}_{\mathcal{O}_d} + \lambda(\bar{S}^{(d)}_{\mathcal{U}_d} - \bar{S}^{(d)}_{\mathcal{O}_d})

The tuning parameter is estimated via cross-fitting:

1. Split labeled data into K folds

2. For each fold k, estimate lambda on the opposite folds

3. Compute the fold-k estimate using the estimated lambda

4. Average across folds

Lambda is chosen to minimize the combined variance across arms.

Value

An msd_result object containing:

Note

PPI++ uses a single lambda across arms, unlike D-T which uses arm-specific tuning parameters. For arm-specific tuning, use msd_dt.

Examples

# Create sample data
set.seed(123)
n <- 100
obs_df <- data.frame(
  Y = rnorm(n),
  S0 = rnorm(n, 0, 0.5),
  S1 = rnorm(n, 0.2, 0.5),
  D = rep(c(1, 0), each = n/2)
)
obs_df$Y <- obs_df$Y + 0.3 * obs_df$D
obs_df$S1[obs_df$D == 1] <- obs_df$S1[obs_df$D == 1] + 0.5 * obs_df$Y[obs_df$D == 1]
obs_df$S0[obs_df$D == 0] <- obs_df$S0[obs_df$D == 0] + 0.5 * obs_df$Y[obs_df$D == 0]

unobs_df <- data.frame(
  S0 = rnorm(200, 0, 0.5),
  S1 = rnorm(200, 0.2, 0.5),
  D = rep(c(1, 0), each = 100)
)

msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_ppi(msd)

# Using formula interface
result2 <- msd_ppi(Y ~ D | S1 + S0, observed = obs_df, unobserved = unobs_df)

Optimal Design for Mixed-Subjects Experiments

Description

Find optimal budget allocation between human observations and predictions. Optimal Design Selection

Determines the optimal allocation of budget between human observations and LLM predictions, and recommends the best estimator for the given pilot data.

Usage

optimal_design(
  pilot_data,
  budget,
  cost_human,
  cost_prediction,
  treatment_prob = 0.5,
  estimators = "all",
  min_observed = 20,
  n_grid = 100
)

Arguments

Details

The function uses grid search to find the optimal (n_O, n_U) allocation that minimizes expected variance given the budget constraint:

n_O \times cost_{human} + n_U \times (k \times cost_{prediction}) \leq budget

where k is the number of predictions per unit:

• k = 0 for DiM (no predictions)

• k = 1 for GREG, PPI++, D-T (one prediction per arm)

• k = 2 for DiP, DiP++, D-T DiP (both S^(0) and S^(1))

The expected variance is computed using population moments estimated from the pilot data.

Value

An S3 object of class "msd_design" containing:

Examples

# Pilot study data
pilot_obs <- data.frame(
  Y = rnorm(50),
  S0 = rnorm(50),
  S1 = rnorm(50),
  D = rep(c(1, 0), each = 25)
)
pilot_unobs <- data.frame(
  S0 = rnorm(100),
  S1 = rnorm(100),
  D = rep(c(1, 0), each = 50)
)
pilot <- msd_data(observed = pilot_obs, unobserved = pilot_unobs)

# Find optimal design with $10,000 budget
design <- optimal_design(
  pilot_data = pilot,
  budget = 10000,
  cost_human = 10,      # $10 per human observation
  cost_prediction = 0.01 # $0.01 per prediction
)
print(design)

Print method for msd_data

Description

Print method for msd_data

Usage

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

Arguments

Value

Invisibly returns x

Print method for msd_design

Description

Print method for msd_design

Usage

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

Arguments

Value

Invisibly returns x.

Print method for msd_result

Description

Print method for msd_result

Usage

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

Arguments

Value

Invisibly returns x

Print method for msd_summary

Description

Print method for msd_summary

Usage

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

Arguments

Value

Invisibly returns x.

Print method for summary.msd_result

Description

Produces nicely formatted output similar to summary.lm, designed for applied social scientists.

Usage

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

Arguments

Value

Invisibly returns x

Summary method for msd_design

Description

Summary method for msd_design

Usage

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

Arguments

Value

Invisibly returns object.

Summary method for msd_result

Description

Produces a detailed summary of the MSD estimation results, including the coefficient table with z-statistics and p-values, sample size information, and interpretation guidance.

Usage

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

Arguments

Value

A summary.msd_result object (invisibly when printed)

Examples

obs_df <- data.frame(
  Y = rnorm(100), S0 = rnorm(100), S1 = rnorm(100),
  D = rep(c(1, 0), each = 50)
)
unobs_df <- data.frame(
  S0 = rnorm(200), S1 = rnorm(200), D = rep(c(1, 0), each = 100)
)
msd <- msd_data(observed = obs_df, unobserved = unobs_df)
result <- msd_dt_dip(msd, seed = 1)
summary(result)