# FastRerandomize Package Tutorial

#### 2025-01-13

## Introduction

This vignette demonstrates how to use the fastrerandomize package for generating and testing experimental designs in an agricultural study setting based on:

- Burchardi, K.B., Gulesci, S., Lerva, B. and Sulaiman, M., 2019. Moral hazard: Experimental Evidence from Tenancy Contracts. The Quarterly Journal of Economics, 134(1), pp.281-347.

We will walk through:

- Generating synthetic covariate data
- Creating candidate randomizations
- Exploring the S3 methods for printing, summarizing, and plotting randomization objects
- Conducting a randomization-based inference test

Note: This tutorial assumes you have installed the fastrerandomize package, either from source or via GitHub:

    # If you haven't installed or set up the package:
    # devtools::install_github("cjerzak/fastrerandomize-software/fastrerandomize")

    # (Done once) Optionally build the JAX backend if needed
    # fastrerandomize::build_backend()

    # note that this vignette can be found like so:
    # vignette(package = "fastrerandomize")

## 1. Obtain Pre-treatment Covariate Data

For illustration, we use several pre-treatment covariates from the original experiment.

    library(fastrerandomize)

    # Obtain pre-treatment covariates
    data(QJEData, package = "fastrerandomize")
    myCovariates <- c("children","married","hh_size","hh_sexrat")
    QJEData <- QJEData[!is.na(rowSums(QJEData[,myCovariates])),]
    X <- QJEData[,myCovariates]

    # Analysis parameters
    n_units   <- nrow(X)
    n_treated <- round(nrow(X)/2)

## 2. Generate Randomizations

We now create our candidate randomizations using the function `generate_randomizations()` from fastrerandomize. Depending on the scale and complexity of your experiment, you may choose either exact enumeration (“exact”) or Monte Carlo (“monte_carlo”) randomization.

In this example, we’ll use the exact approach, but note that `randomization_accept_prob` is set very low (0.0001) for demonstration, so that we can see some filtering in action.

    RunMainAnalysis <- (!is.null(check_jax_availability()) )
    # if FALSE, consider calling build_backend()

    if(RunMainAnalysis){
    CandRandomizations <- generate_randomizations(
      n_units = n_units,
      n_treated = n_treated,
      X = X,
      randomization_type = "monte_carlo",
      max_draws = 100000L,
      batch_size = 1000L,
      randomization_accept_prob = 0.0001
    )
    }

    ## Using monte carlo randomization

    ## Starting batch processing with 100 batches.

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    ## MC Loop Time (s): 1.0135

## 4. S3 Methods: Print, Summary, and Plot

`generate_randomizations()` returns an S3 object of class `fastrerandomize_randomizations`. We can use its associated print, summary, and plot methods to inspect the candidate randomizations.

    if(RunMainAnalysis){
    # 4a. Print the object
    print(CandRandomizations)

    # 4b. Summary
    summary(CandRandomizations)

    # 4c. Plot the balance distribution
    plot(CandRandomizations)
    }

    ## Object of class 'fastrerandomize_randomizations'
    ##
    ## Call:
    ##    generate_randomizations(n_units = n_units, n_treated = n_treated,
    ##       X = X, randomization_accept_prob = 1e-04, max_draws = 100000L,
    ##       batch_size = 1000L, randomization_type = "monte_carlo")
    ##
    ## Number of candidate randomizations: 10
    ## Number of units (columns): 302
    ## Balance statistics available for each randomization.
    ## Summary of 'fastrerandomize_randomizations' object:
    ##
    ## Balance statistics (summary):
    ##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.
    ## 0.00190 0.01989 0.02277 0.02136 0.02449 0.03175

## 3. Randomization Test

Next, we showcase a randomization-based inference procedure using fastrerandomize.

### 3a. Setup Simulated Outcomes

We simulate an outcome Y that depends on our covariates X, the chosen randomization, and some true treatment effect τ. Here, we pick the first acceptable randomization from our set as our “observed” assignment, Wobs.

    if(RunMainAnalysis){
    CoefY <- rnorm(ncol(X))          # Coefficients for outcome model
    Wobs  <- CandRandomizations$randomizations[1, ]  # use the 1st acceptable randomization
    tau_true <- 1                     # true treatment effect
    # Generate Y = X * Coef + W*tau + noise
    Yobs <- as.numeric( as.matrix(X) %*% as.matrix(CoefY) + Wobs * tau_true + rnorm(n_units, sd = 0.1))
    }

### 3b. Run the Randomization Test

We pass our observed treatment assignment (`obsW`), observed outcomes (`obsY`), and the full matrix of candidate randomizations (`candidate_randomizations`) to `randomization_test()`. This test:

- Computes the observed difference in means
- Permutes the treatment assignment across our candidate randomizations
- Estimates the p-value by comparing the observed statistic to its permutation distribution

    if(RunMainAnalysis){
    randomization_test_results <- randomization_test(
      obsW = Wobs,
      obsY = Yobs,
      candidate_randomizations = CandRandomizations$randomizations,
      findFI = TRUE
    )

    # Inspect results
    print(randomization_test_results)
    summary(randomization_test_results)
    plot(randomization_test_results)
    }

    ## Object of class 'fastrerandomize_test'
    ##
    ## Call:
    ##    randomization_test(obsW = Wobs, obsY = Yobs, candidate_randomizations = CandRandomizations$randomizations,
    ##       findFI = TRUE)
    ##
    ## P-value:  0.1
    ## Observed effect (tau_obs):  0.988699
    ## Fiducial interval: [-491.1697, 1015.033]
    ## Summary of 'fastrerandomize_test' object:
    ##
    ## Call:
    ##    randomization_test(obsW = Wobs, obsY = Yobs, candidate_randomizations = CandRandomizations$randomizations,
    ##       findFI = TRUE)
    ##
    ## P-value:
    ##    0.1
    ##
    ## Observed effect (tau_obs):
    ##    0.988699
    ##
    ## Fiducial Interval:
    ##   [-491.1697, 1015.033]

The `findFI = TRUE` flag further attempts to locate a fiducial interval (FI) for the treatment effect.

## Conclusion

This tutorial demonstrated a basic workflow with fastrerandomize:

- Generating synthetic or real covariate data
- Producing a set of acceptable treatment assignments via randomization
- Visualizing and summarizing these assignments
- Testing for treatment effects with a randomization-based approach

We encourage you to consult the package documentation for more advanced functionalities, including GPU-accelerated computations via JAX and flexible definitions of balance criteria in addition to what was shown here.