### README - Quick Start

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/MANIFEST.txt

The README file provides a quick overview and reference for getting started with the mediation package.

```APIDOC
## README

Provides an overview and quick reference for the mediation package.

### Getting Started

1. Read `README.md` for overview and quick reference.
2. Pick a function from the function index.
3. Read the corresponding `api-*.md` file for function details.
4. Refer to `types.md` for output structures.
5. Check `configuration.md` for settings.
```

--------------------------------

### Example 3: Parallel Processing (Non-Windows)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-ivmediate.md

Shows how to utilize multicore processing for faster computations on non-Windows systems.

```APIDOC
## Example 3: Parallel Processing (Non-Windows)

### Description
This example enables parallel processing using the `multicore` and `mc.cores` arguments for potentially faster simulation and bootstrapping, particularly on Unix-like systems.

### Usage
```r
library(parallel)

result_parallel <- ivmediate(
  model_t, model_m, model_y,
  sims = 2000,
  boot = TRUE,
  enc = "treat",
  treat = "comply",
  mediator = "job_dich",
  multicore = TRUE,
  mc.cores = 4
)

summary(result_parallel)
```
```

--------------------------------

### Example 2: Using Nonparametric Bootstrap

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-ivmediate.md

Illustrates how to enable nonparametric bootstrapping for confidence interval estimation.

```APIDOC
## Example 2: Using Nonparametric Bootstrap

### Description
This example demonstrates the use of nonparametric bootstrapping within the `ivmediate` function to obtain confidence intervals for the mediation effects.

### Usage
```r
# Same models as above
result_boot <- ivmediate(
  model_t, model_m, model_y,
  sims = 1000,
  boot = TRUE,
  enc = "treat",
  treat = "comply",
  mediator = "job_dich"
)

summary(result_boot)
plot(result_boot)
```
```

--------------------------------

### Example 5: Continuous Mediator (Simple Case)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-ivmediate.md

Illustrates mediation analysis with a continuous mediator in a simplified model setting.

```APIDOC
## Example 5: Continuous Mediator (Simple Case)

### Description
This example handles a continuous mediator. It's applicable when the mediator is continuous and the regression models for the mediator and outcome include only the encouragement and treatment variables as predictors, alongside the mediator itself in the outcome model.

### Usage
```r
# When mediator is continuous but models contain
# only encouragement and treatment as predictors

model_m_cont <- lm(job_hours ~ comply + treat, data = jobs)

# Simple outcome model
model_y_cont <- lm(depress2 ~ job_hours + (comply + treat), data = jobs)

result_cont <- ivmediate(
  model_t, model_m_cont, model_y_cont,
  sims = 1000,
  boot = TRUE,
  enc = "treat",
  treat = "comply",
  mediator = "job_hours"
)

summary(result_cont)
```
```

--------------------------------

### Example 6: Different Encouragement Values and Confidence Level

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-ivmediate.md

Shows how to customize the confidence level for the intervals and implies handling of different encouragement variable values.

```APIDOC
## Example 6: Different Encouragement Values

### Description
This example demonstrates how to specify a custom confidence level (e.g., 90%) for the calculated intervals. It also implicitly covers scenarios where the encouragement variable might have different values, though the example uses the default 0/1 binary encouragement.

### Usage
```r
# If using binary encouragement variable with values 0/1
# (default in most designs)

# Customize confidence level
result_custom <- ivmediate(
  model_t, model_m, model_y,
  sims = 1000,
  boot = FALSE,
  enc = "treat",
  treat = "comply",
  mediator = "job_dich",
  conf.level = 0.90  # 90% confidence intervals instead of 95%
)

summary(result_custom)
```
```

--------------------------------

### Setup Multiple Mediations

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Configure multiple mediation analyses by defining datasets, treatment variables, mediators, outcomes, and covariates. Ensure dataset names start with their corresponding treatment variable names.

```r
# Dataset naming convention
datasets <- list(
  T1 = data1,  # Name must start with treatment variable name
  T2 = data2
)

treatment <- c("T1", "T2")  # Must match dataset name prefixes
mediators <- c("M1", "M2")
outcome <- c("Y1")
covariates <- "X1 + X2 + X3"  # Single string for all models

result <- mediations(
  datasets = datasets,
  treatment = treatment,
  mediators = mediators,
  outcome = outcome,
  covariates = covariates,
  families = c("gaussian", "gaussian"),
  sims = 1000
)
```

--------------------------------

### Example 4: Point Estimates Only (No Confidence Intervals)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-ivmediate.md

Demonstrates how to obtain only point estimates by disabling confidence interval calculations.

```APIDOC
## Example 4: Point Estimates Only (No Confidence Intervals)

### Description
This example shows how to request only point estimates (disabling confidence intervals) by setting `ci = FALSE`. This can be useful for exploratory analysis or when computational speed is critical.

### Usage
```r
# For exploratory analysis or when computation speed critical
result_point <- ivmediate(
  model_t, model_m, model_y,
  ci = FALSE,
  enc = "treat",
  treat = "comply",
  mediator = "job_dich"
)

# Only returns point estimates (dc0, dc1, zc0, zc1, tauc)
summary(result_point)
```
```

--------------------------------

### Example 1: Binary Mediator and Continuous Outcome

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-ivmediate.md

Demonstrates a typical use case with a binary mediator and a continuous outcome, using standard regression models.

```APIDOC
## Example 1: Binary Mediator and Continuous Outcome

### Description
This example shows how to perform an IV mediation analysis when the mediator is binary and the outcome is continuous. It sets up three regression models and then calls `ivmediate`.

### Usage
```r
library(mediation)
data(jobs)

# Model for actual treatment (encouraged vs. not)
model_t <- lm(comply ~ treat + sex + age + marital + nonwhite + educ + income, data = jobs)

# Model for mediator (binary job discrimination)
model_m <- glm(job_dich ~ comply + treat + sex + age + marital + nonwhite + educ + income, data = jobs, family = binomial)

# Model for outcome
model_y <- lm(depress2 ~ job_dich * (comply + treat) + sex + age + marital + nonwhite + educ + income, data = jobs)

# IV mediation analysis
result <- ivmediate(
  model_t, model_m, model_y,
  sims = 1000,
  boot = FALSE,
  enc = "treat",
  treat = "comply",
  mediator = "job_dich"
)

summary(result)
plot(result)
```
```

--------------------------------

### Output Structure Example

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

Illustrates the naming convention for elements within the returned list of mediate objects, based on outcome, treatment, and mediator variable names.

```R
output$outcome.treatment.mediator1
output$outcome.treatment.mediator2
```

--------------------------------

### Usage Example for test.modmed

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-testing-functions.md

Demonstrates how to use the `test.modmed` function to compare mediation effects for different moderator values. Requires fitting mediation models first.

```r
library(mediation)
data(jobs)

# Fit models with covariate interactions
mediator_int <- lm(job_seek ~ treat*age + econ_hard + sex, data = jobs)
outcome_int <- lm(depress2 ~ treat*job_seek*age + econ_hard + sex, data = jobs)

# Mediation analysis
result <- mediate(mediator_int, outcome_int,
                  sims = 1000, treat = "treat", mediator = "job_seek")

# Test difference for age = 20 vs age = 70
test_result <- test.modmed(
  result,
  covariates.1 = list(age = 20),
  covariates.2 = list(age = 70)
)

# View results
print(test_result)
summary(test_result)
```

--------------------------------

### Enable speedglm for Bootstrap

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Demonstrates how to enable the use of the speedglm package for faster model fitting during bootstrap iterations within the mediate() function. Requires speedglm to be installed.

```r
# Enable speedglm for bootstrap iterations
use_speed <- TRUE  # In mediate() call
```

--------------------------------

### Mediation Analysis with Weights

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

This example shows how to incorporate survey weights into the mediation analysis. Provide the name of the weight variable in the 'weights' argument.

```r
datasets <- list(treat = jobs)
treatment <- "treat"
mediators <- c("job_seek", "job_dich")
outcome <- c("depress2")
covariates <- "econ_hard + sex + age"

result <- mediations(
  datasets,
  treatment,
  mediators,
  outcome,
  covariates = covariates,
  families = c("gaussian", "gaussian"),
  weights = "sample_weight",  # Variable in data frame
  sims = 1000
)

summary(result)
```

--------------------------------

### Binary Probit Models for Mediators and Outcome

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

Use this example when both your mediators and outcome variables are binary. Specify 'binomial' for each in the 'families' argument.

```r
datasets <- list(treat = jobs)
treatment <- "treat"
mediators <- c("job_disc", "job_dich")
outcome <- "work1"
covariates <- "econ_hard + sex + age"

result <- mediations(
  datasets,
  treatment,
  mediators,
  outcome,
  covariates = covariates,
  families = c("binomial", "binomial"),  # Binary mediators and outcome
  sims = 1000
)

summary(result)
```

--------------------------------

### Mediator Model with Treatment-Mediator Interaction

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate.md

Shows how to include a treatment-mediator interaction term in the outcome model to estimate effects when the mediator's effect on the outcome depends on the treatment. Uses the same setup as the linear model example.

```r
outcome_int <- lm(depress2 ~ treat + job_seek + treat:job_seek + econ_hard + sex + age, 
                   data = jobs)

result_int <- mediate(
  mediator_model, outcome_int,
  sims = 1000, 
  treat = "treat", 
  mediator = "job_seek"
)

summary(result_int)
```

--------------------------------

### API Reference - Core Functions

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/MANIFEST.txt

Detailed documentation for each of the 13 main functions available in the mediation package. This includes function signatures, parameter descriptions, and usage examples.

```APIDOC
## API Reference

This section provides detailed documentation for each function in the mediation package.

### Function Index

- **Basic mediation**: `api-mediate.md`
- **Sensitivity analysis**: `api-medsens.md`
- **Noncompliance mediation**: `api-ivmediate.md`
- **Multiple mediators**: `api-multimed.md`
- **Design-based mediation**: `api-mediate-designs.md`
- **Batch processing**: `api-mediations.md`
- **Testing functions**: `api-testing-functions.md`

Each `api-*.md` file contains:
- Function signature
- Parameter details (from roxygen comments)
- Usage examples with output patterns
- Error handling documentation
- Return value structures
```

--------------------------------

### Single Experiment Design with SI and Bootstrap

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate-designs.md

Example demonstrating the use of the nonparametric bootstrap method within mediate.sed for estimating ACME when the sequential ignorability assumption holds. Allows for more simulations.

```r
result_boot <- mediate.sed("depress2", "job_disc", "treat", jobs, 
                           SI = TRUE, boot = TRUE, sims = 1000)
summary(result_boot)
```

--------------------------------

### Get Standard Mediation Summary

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Generate a standard summary of the mediation analysis results. This output includes p-values.

```r
# Standard summary
summary(result)
```

--------------------------------

### Ordered Probit Outcome Model

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

This example demonstrates how to use an ordered probit model for the outcome variable. Ensure the outcome variable is an ordered factor and specify 'oprobit' in the 'families' argument for the outcome.

```r
# Assuming job_disc is ordered factor with 3 levels
jobs$job_disc_ord <- factor(jobs$job_disc, ordered = TRUE)

datasets <- list(treat = jobs)
treatment <- "treat"
mediators <- c("job_seek", "job_dich")
outcome <- "job_disc_ord"
covariates <- "econ_hard + sex + age"

result <- mediations(
  datasets,
  treatment,
  mediators,
  outcome,
  covariates = covariates,
  families = c("gaussian", "oprobit"),  # Linear mediators, ordered outcome
  sims = 1000
)

# Result has class mediations.order
class(result)
summary(result)
plot(result)
```

--------------------------------

### Quantile Regression for Outcome

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

This example shows how to perform quantile regression for the outcome variable. Specify 'quantile' in the 'families' argument and set 'tau.y' to the desired quantile (e.g., 0.5 for the median).

```r
datasets <- list(treat = jobs)
treatment <- "treat"
mediators <- c("job_seek")
outcome <- c("depress2")
covariates <- "econ_hard + sex + age"

# Median regression
result <- mediations(
  datasets,
  treatment,
  mediators,
  outcome,
  covariates = covariates,
  families = c("gaussian", "quantile"),  # Quantile outcome
  tau.y = 0.5,  # Median
  sims = 1000
)

summary(result)
```

--------------------------------

### Single Experiment Design with SI Assumption (Point Estimates)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate-designs.md

Example of using mediate.sed to calculate nonparametric point estimates for ACME under the sequential ignorability assumption. Uses the 'jobs' dataset.

```r
data(jobs)
result_si <- mediate.sed("depress2", "job_disc", "treat", jobs, SI = TRUE)
summary(result_si)
```

--------------------------------

### R: Mediation Analysis Workflow

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/overview.md

This R code demonstrates a typical workflow for mediation analysis using the 'mediation' package. It includes fitting linear models for the mediator and outcome, performing the mediation analysis, summarizing results, plotting, conducting sensitivity analysis, and testing for moderated mediation. Ensure the 'mediation' package and its dependencies are installed.

```r
library(mediation)
data(jobs)

# 1. Fit models
model.m <- lm(job_seek ~ treat + econ_hard + sex + age, data = jobs)
model.y <- lm(depress2 ~ treat + job_seek + econ_hard + sex + age, data = jobs)

# 2. Mediation analysis
result <- mediate(model.m, model.y, 
                  sims = 1000, 
                  treat = "treat", 
                  mediator = "job_seek")

# 3. Summarize results
summary(result)
plot(result)

# 4. Sensitivity analysis
sens <- medsens(result, rho.by = 0.1)
summary(sens)
plot(sens)

# 5. Test for interaction
test.TMint(result)

# 6. Moderated mediation
test.modmed(result, 
            covariates.1 = list(age = 20),
            covariates.2 = list(age = 70))
```

--------------------------------

### Multiple Treatments, Multiple Mediators, Single Outcome

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

This example demonstrates mediation analysis with multiple treatment variables, multiple mediators, and a single outcome. Set 'interaction = TRUE' to include treatment-mediator interactions in the model.

```r
# Hypothetical data with multiple treatment variables
datasets <- list(
  treat1 = jobs,  # Data frame containing treat1 variable
  treat2 = jobs   # Data frame containing treat2 variable
)
treatment <- c("treat1", "treat2")
mediators <- c("job_seek", "job_dich")
outcome <- c("depress2")
covariates <- "econ_hard + sex + age"

result <- mediations(
  datasets, 
  treatment, 
  mediators, 
  outcome,
  covariates = covariates,
  families = c("gaussian", "gaussian"),
  interaction = TRUE,  # Include T-M interaction
  sims = 1000
)

# Access results for specific combinations
summary(result$depress2.treat1.job_seek)
summary(result$depress2.treat2.job_dich)

# Summary of all
summary(result)
```

--------------------------------

### Multiple Outcomes, Treatments, and Mediators

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

This example shows how to perform mediation analysis with multiple outcome variables, multiple treatment variables, and multiple mediators. The 'families' argument should specify the model type for each mediator and outcome combination.

```r
# Three different outcome variables
datasets <- list(
  educ = jobs,
  income = jobs
)
treatment <- c("educ", "income")
mediators <- c("job_seek", "job_dich")
outcome <- c("depress2", "work1")
covariates <- "sex + age"

result <- mediations(
  datasets,
  treatment,
  mediators,
  outcome,
  covariates = covariates,
  families = c("gaussian", "binomial"),  # Linear mediator, binary outcome
  sims = 1000,
  boot = TRUE
)

# Accessing 2x2x2 = 8 different mediation analyses
names(result)
```

--------------------------------

### Get Mediation Summary by Group

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Generate a mediation summary organized by group, providing an overview of mediation effects within different subgroups.

```r
summary(result, output = "bygroup")   # Organized by group
```

--------------------------------

### Single Experiment Design without SI Assumption (Bounds)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate-designs.md

Example of using mediate.sed to compute nonparametric bounds for ACME when the sequential ignorability assumption is not made. Requires a subset of the data.

```r
library(mediation)
data(boundsdata)

# Single experiment design without SI assumption (bounds)
data_sed <- subset(boundsdata, manip == 0)
result_bounds <- mediate.sed("out", "med", "ttt", data_sed, SI = FALSE)
summary(result_bounds)
```

--------------------------------

### Pooling Mediation Results Across Imputations

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-testing-functions.md

This example demonstrates how to use the 'amelidiate' function to pool mediation analysis results. It first creates multiply imputed datasets using the 'mice' package, then runs mediation analyses on each imputed dataset, and finally pools the results using 'amelidiate'. This is useful when your data has missing values that have been handled through multiple imputation.

```r
library(mediation)
library(mice)  # For imputation example
data(jobs)

# Create multiply imputed datasets
# (Example uses mice package; any imputation method acceptable)
imputed_data <- mice(jobs, m = 5)  # 5 imputations
datasets <- list()

for (i in 1:5) {
  datasets[[i]] <- complete(imputed_data, i)
}

# Run mediations on each imputed dataset
results_list <- list()

for (i in 1:5) {
  results_list[[i]] <- mediations(
    datasets = list(treat = datasets[[i]]),
    treatment = "treat",
    mediators = "job_seek",
    outcome = "depress2",
    covariates = "econ_hard + sex + age",
    families = c("gaussian", "gaussian"),
    sims = 1000
  )
}

# Pool results across imputations
pool <- amelidiate(results_list)

# Use standard summary and plot methods
summary(pooled)
plot(pooled)
```

--------------------------------

### Configure Bootstrap CI Method (BCA)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Sets the bootstrap confidence interval method to Bias-Corrected and Accelerated (BCA). Requires boot = TRUE.

```r
# Bias-corrected and accelerated
result <- mediate(..., boot = TRUE, boot.ci.type = "bca")
```

--------------------------------

### Configure Parallel Processing on Linux/Mac

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Demonstrates enabling multicore processing on Linux or Mac systems using ivmediate() with multicore = TRUE and specifying the number of cores.

```r
# On Linux/Mac: can use
result <- ivmediate(..., multicore = TRUE, mc.cores = 4)
```

--------------------------------

### Configure Bootstrap CI Method (Percentile)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Sets the bootstrap confidence interval method to the percentile method, which is the default behavior when boot = TRUE.

```r
# Percentile method (default)
result <- mediate(..., boot = TRUE, boot.ci.type = "perc")
```

--------------------------------

### Configuration

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/MANIFEST.txt

Information on how to customize the behavior of the mediation package.

```APIDOC
## Configuration

Customize the behavior of the mediation package.

### Settings

- Details on configuration options are available in `configuration.md`.
- Includes information on default parameters.
```

--------------------------------

### Summarize Mediation Design Results

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate-designs.md

Use `summary.mediate.design` to get a tabular summary of mediation analysis results. The `print.summary.mediate.design` function displays these results.

```r
summary.mediate.design(object, ...)
print.summary.mediate.design(x, ...)
```

--------------------------------

### Basic Mediation and Sensitivity Analysis in R

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/README.md

This workflow demonstrates the basic steps for estimating mediation effects, testing their statistical significance, assessing robustness to unmeasured confounding, and testing for interaction between treatment and mediator. Requires prior fitting of mediator and outcome models.

```r
# 1. Estimate effects
result <- mediate(model.m, model.y, sims = 1000, 
                  treat = "T", mediator = "M")

# 2. Test statistical significance
summary(result)

# 3. Assess robustness
sens <- medsens(result)
summary(sens)

# 4. Test for interaction
test.TMint(result)
```

--------------------------------

### Tobit Censored Outcome Model

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediations.md

Use this example for outcome variables that are censored. Specify 'tobit' in the 'families' argument and provide the 'LowerY' or 'UpperY' bounds.

```r
datasets <- list(treat = jobs)
treatment <- "treat"
mediators <- c("job_seek")
outcome <- c("income")
covariates <- "econ_hard + sex + age"

result <- mediations(
  datasets,
  treatment,
  mediators,
  outcome,
  covariates = covariates,
  families = c("gaussian", "tobit"),  # Tobit outcome model
  LowerY = 0,  # Lower bound (income >= 0)
  sims = 1000
)

summary(result)
```

--------------------------------

### Get Mediation Summary by Effect Type

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Generate a mediation summary organized by effect type, useful for detailed analysis of different components of the mediation.

```r
# Summary with specific output type (merMod)
summary(result, output = "byeffect")  # Organized by effect type
```

--------------------------------

### Retrieve Default Cores Option

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Shows how to retrieve the 'mc.cores' option, defaulting to 2 if not explicitly set. This is used internally by parallel functions.

```r
mc.cores = getOption("mc.cores", 2L)  # Retrieves option or defaults to 2
```

--------------------------------

### S3 Methods (summary, plot, print)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/README.md

Provides standard S3 methods for summarizing, visualizing, and printing mediation analysis results. These methods offer convenient ways to inspect and present the output from mediation functions.

```APIDOC
## S3 Methods

### Description
Standard S3 methods for mediation objects.

### Methods
- `summary()`: Provides tabular results.
- `plot()`: Generates graphical summaries.
- `print()`: Displays formatted output.
```

--------------------------------

### Load mediation Package

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Loads the mediation package into the R session. This is a prerequisite for using any of its functions.

```r
library(mediation)
```

--------------------------------

### Sensitivity Analysis for Linear-Linear Models

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Configure the FGLS convergence tolerance for sensitivity analysis in linear-linear models.

```r
sens <- medsens(med_result, eps = 1e-7)  # FGLS convergence tolerance
```

--------------------------------

### Fine-Grained Sensitivity Analysis with R2 Increments

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-multimed.md

Perform a more detailed sensitivity analysis by specifying finer increments for the R-squared parameter. This allows for a more granular sweep of sensitivity parameters, with `R2.by` controlling the step size.

```r
# More detailed sensitivity parameter sweeps
result_fine <- multimed(
  outcome = "immigr",
  med.main = "emo",
  med.alt = "p_harm",
  treat = "treat",
  covariates = c("age", "educ", "gender", "income"),
  data = framing,
  design = "single",
  sims = 2000,
  R2.by = 0.05  # Finer increments than default 0.1
)

summary(result_fine)
plot(result_fine, type = "R2-total")
```

--------------------------------

### Coarser Grid Sensitivity Analysis

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Use a coarser grid for faster sensitivity analysis computation by increasing the `rho.by` parameter.

```r
# Coarser grid for faster computation
sens <- medsens(med_result, rho.by = 0.2)
```

--------------------------------

### Sensitivity Analysis Visualization

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-multimed.md

Visualize sensitivity to interaction heterogeneity and R-squared values for mediation analysis. Useful for understanding the robustness of mediation results to unobserved confounding.

```r
# Visualize sensitivity to interaction heterogeneity
plot(result, type = "sigma", tgroup = "average")
plot(result, type = "R2-total", tgroup = "average")
```

--------------------------------

### Multiple Imputation Workflow for Mediation Analysis

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-testing-functions.md

This workflow demonstrates how to perform mediation analysis with missing data using the `mice` package. It involves imputing missing data, running mediation on each imputed dataset, and then pooling the results using `amelidiate`.

```r
library(mice)

# 1. Impute missing data
imputed <- mice(original_data, m = 10)

# 2. Run mediation on each imputed dataset
results <- list()
for (i in 1:10) {
  results[[i]] <- mediations(
    datasets = list(treat = complete(imputed, i)),
    treatment = "treat",
    mediators = "mediator",
    outcome = "outcome",
    covariates = "X1 + X2",
    families = c("gaussian", "gaussian"),
    sims = 1000
  )
}

# 3. Pool across imputations
final <- amelidiate(results)
summary(final)
```

--------------------------------

### Binary Outcome with Nonparametric Bootstrap

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate.md

Demonstrates mediation analysis with binary outcome and mediator variables using generalized linear models (probit link). Employs nonparametric bootstrapping for inference by setting `boot = TRUE`.

```r
mediator_bin <- glm(job_dich ~ treat + econ_hard + sex + age, 
                     data = jobs, family = binomial(link = "probit"))
outcome_bin <- glm(work1 ~ treat + job_dich + econ_hard + sex + age, 
                    data = jobs, family = binomial(link = "probit"))

result_boot <- mediate(
  mediator_bin, outcome_bin,
  sims = 1000,
  boot = TRUE,
  treat = "treat",
  mediator = "job_dich"
)

summary(result_boot)
```

--------------------------------

### Basic Mediation Analysis in R

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/README.md

Perform a basic mediation analysis by fitting linear models for the mediator and outcome, then using the `mediate` function. Requires the `mediation` package and a dataset like `jobs`.

```r
library(mediation)
data(jobs)

# Fit models
mediator_model <- lm(job_seek ~ treat + econ_hard + sex + age, data = jobs)
outcome_model <- lm(depress2 ~ treat + job_seek + econ_hard + sex + age, data = jobs)

# Estimate mediation effects
result <- mediate(mediator_model, outcome_model,
                  sims = 1000,
                  treat = "treat",
                  mediator = "job_seek")

# Summary and visualization
summary(result)
plot(result)
```

--------------------------------

### Linear Outcome and Mediator Model

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate.md

Demonstrates fitting linear models for mediator and outcome, then estimating causal mediation effects using the mediate function. Requires the 'mediation' package and 'jobs' dataset.

```r
library(mediation)
data(jobs)

# Fit mediator and outcome models
mediator_model <- lm(job_seek ~ treat + econ_hard + sex + age, data = jobs)
outcome_model <- lm(depress2 ~ treat + job_seek + econ_hard + sex + age, data = jobs)

# Estimate causal mediation effects
result <- mediate(
  mediator_model, outcome_model,
  sims = 1000, 
  treat = "treat", 
  mediator = "job_seek"
)

summary(result)
plot(result)
```

--------------------------------

### Configure Censored Outcome Models (Tobit)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Use the 'tobit' family for outcome models when dealing with censored data. Specify 'LowerY' and 'UpperY' to define the censoring bounds. Set 'UpperY' to NULL for a one-sided tobit model.

```r
# Tobit outcome (censored)
result <- mediations(
  ...,
  families = c("gaussian", "tobit"),
  LowerY = 0,    # Lower bound (censoring point)
  UpperY = NULL  # No upper bound
)

# Two-sided Tobit
result <- mediations(
  ...,
  families = c("gaussian", "tobit"),
  LowerY = 0,    # Lower bound
  UpperY = 100   # Upper bound
)
```

--------------------------------

### Run SED Mediation Design

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-mediate-designs.md

Execute the Simplest Experimental Design (SED) for mediation analysis. This requires specifying the treatment, mediator, and outcome variables, along with the dataset. Set `SI = TRUE` to assume Sequential Ignorability.

```r
result <- mediate.sed("out", "med", "treat", data, SI = TRUE)
summary(result)  # Tabular summary
```

--------------------------------

### Sensitivity Analysis for Binary Models

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Specify the number of Monte Carlo draws for sensitivity analysis when working with binary models.

```r
sens <- medsens(med_result, sims = 2000)  # MC draws for binary models
```

--------------------------------

### Configure Parallel Processing on Windows

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Specifies how to disable multicore processing on Windows systems, where it is not supported, by setting multicore = FALSE in ivmediate().

```r
# On Windows: multicore = FALSE
result <- ivmediate(..., multicore = FALSE)
```

--------------------------------

### Configure Quantile Regression Models

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Specify 'quantile' family for mediator or outcome models to perform quantile regression. Use 'tau.m' for mediator quantiles and 'tau.y' for outcome quantiles.

```r
# Quantile mediator model
result <- mediations(
  ...,
  families = c("quantile", "gaussian"),
  tau.m = 0.5  # Median
)

# Quantile outcome model
result <- mediations(
  ...,
  families = c("gaussian", "quantile"),
  tau.y = 0.75  # 75th percentile
)
```

--------------------------------

### Type Reference

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/MANIFEST.txt

Documentation for data structures and types used within the mediation package, essential for understanding output patterns.

```APIDOC
## Type Reference

This section details the data structures and types used in the mediation package.

### Data Structures

- **Output Structures**: Defined in `types.md`.
- **Class Definitions**: Derived from source code.
```

--------------------------------

### Parallel Processing for IV Mediation (Non-Windows)

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/api-ivmediate.md

Enables parallel processing for faster computation of IV mediation analysis on non-Windows systems. Specify the number of cores to use for parallel computation.

```r
library(parallel)

result_parallel <- ivmediate(
  model_t, model_m, model_y,
  sims = 2000,
  boot = TRUE,
  enc = "treat",
  treat = "comply",
  mediator = "job_dich",
  multicore = TRUE,
  mc.cores = 4
)

summary(result_parallel)
```

--------------------------------

### Set Default Confidence Interval Level

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Illustrates setting the confidence level for interval estimation in mediate(). The default is 0.95 (95%).

```r
result <- mediate(..., conf.level = 0.95)  # Default
result <- mediate(..., conf.level = 0.90)  # 90% CI
result <- mediate(..., conf.level = 0.99)  # 99% CI
```

--------------------------------

### Integrate Multiple Imputation with Mediation

Source: https://github.com/kosukeimai/mediation/blob/master/_autodocs/configuration.md

Run mediation analyses on multiple imputed datasets and pool the results. Requires the 'mice' package for imputation.

```r
library(mice)

# Create imputed datasets
imputed <- mice(original_data, m = 10)

# Run mediations on each
results <- lapply(1:10, function(i) {
  mediations(
    datasets = list(treat = complete(imputed, i)),
    treatment = "treat",
    mediators = "mediator",
    outcome = "outcome",
    covariates = "X1 + X2",
    families = c("gaussian", "gaussian"),
    sims = 1000
  )
})

# Pool using amelidiate
pooled <- amelidiate(results)
```