Understanding set.seed() in R: A Comprehensive Guide

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Table of Contents

Introduction

In R programming, reproducibility is crucial for scientific computing, data analysis, and machine learning. The set.seed() function is a fundamental tool that helps ensure your random operations produce the same results across different runs of your code. This tutorial will guide you through the basics of using set.seed(), explain its role in ensuring reproducibility, and explore advanced topics like controlling random number generator (RNG) algorithms and managing reproducibility in parallel computations.

The Basics of set.seed()

The set.seed() function initializes R’s random number generator to produce a reproducible sequence of random numbers. When you set a seed, any subsequent random operations will generate the same sequence of numbers.

Basic Usage of set.seed()
# Setting a seed
set.seed(123)
random_numbers1 <- rnorm(5)
print(random_numbers1)

# Setting the same seed again
set.seed(123)
random_numbers2 <- rnorm(5)
print(random_numbers2)

# The two sets of numbers will be identical
all.equal(random_numbers1, random_numbers2)
[1] -0.56047565 0.23017749 1.55870831 0.07050839 0.12928774 [1] -0.56047565 0.23017749 1.55870831 0.07050839 0.12928774 [1] TRUE

Why Use set.seed()?

Setting a seed is essential for several reasons:

  • Reproducibility: Others can replicate your exact results
  • Debugging: Makes it easier to track down issues in code involving random numbers
  • Consistency: Ensures consistent results across multiple runs
  • Teaching: Helps demonstrate concepts with predictable examples
Note: While set.seed() makes your random operations reproducible, you should still use different seeds when testing the robustness of your analyses.

Best Practices

Choosing a Seed Value

  • Use a memorable number (e.g., dates, project codes)
  • Document why you chose a particular seed
  • Avoid using common values like 1, 2, or 123 in production code

When to Set Seeds

Best Practices:
  • Set seeds at the beginning of your script
  • Set new seeds before each independent random operation
  • Document seed values in your code
  • Consider using different seeds for different parts of your analysis
Seed Selection Examples
# Using a date-based seed (e.g., Year-Month-Day for a specific analysis)
set.seed(20241120)
random_numbers_date <- rnorm(5)  # Generate 5 random numbers
print(random_numbers_date)

# Using a project-specific seed (e.g., a memorable number or project ID)
set.seed(8675309)
random_numbers_project <- rnorm(5)  # Generate 5 random numbers
print(random_numbers_project)

# Using multiple seeds for robustness testing across different configurations
seeds <- c(12345, 67890, 13579)  # Define multiple seeds
results <- lapply(seeds, function(seed) {
    set.seed(seed)  # Set the seed for each iteration
    analysis_result <- rnorm(5)  # Replace with your analysis or simulation
    list(seed = seed, result = analysis_result)
})

# Display results for each seed
print(results)

# Example: Running a simulation study with different seeds
simulation_results <- lapply(seeds, function(seed) {
    set.seed(seed)
    replicate(1000, mean(rnorm(30, mean = 0, sd = 1)))  # Simulate 1000 sample means
})

# Analyzing variability in results across seeds
mean_of_means <- sapply(simulation_results, mean)  # Calculate the overall mean for each seed
variance_of_means <- sapply(simulation_results, var)  # Calculate the variance for each seed

# Print the summary of variability
print(data.frame(Seed = seeds, Mean = mean_of_means, Variance = variance_of_means))

Explanation of the Additions

Date-Based Seed:

  • Generates reproducible random numbers using a seed derived from a specific date.
  • Useful for analyses conducted on a particular day.

Project-Specific Seed:

  • Demonstrates using a memorable or meaningful number as a seed (e.g., project ID, song lyrics).
  • Ensures reproducibility tied to a specific project.

Robustness Testing:

  • Uses multiple seeds to test the stability of results across different random number streams.
  • Shows how to loop through multiple seeds and collect results for comparison.

Simulation Study:

  • Simulates 1000 sample means for each seed to assess the impact of different seeds on variability.
  • Calculates and prints the mean and variance of the results to evaluate robustness.

Structured Output:

  • Organizes results into a data frame for clear presentation and analysis.

Output Examples

Date-Based Seed

[1] 0.3284625 1.0584871 0.9085288 1.7659220 0.2530814

Project-Specific Seed

[1] -0.9965824  0.7218241 -0.6172088  2.0293916  1.0654161

Robustness Testing

Results for each seed:

[[1]]
$seed
[1] 12345

$result
[1]  0.5855288  0.7094660 -0.1093033 -0.4534972  0.6058875

[[2]]
$seed
[1] 67890

$result
[1]  0.2606402 -1.8133921 -0.5776329  0.8837962  0.3280845

[[3]]
$seed
[1] 13579

$result
[1] -1.234715 -1.252834 -0.254778 -1.526647  1.097115

Simulation Study

Analyzing variability in results across seeds:

Seed Mean Variance
12345 0.002144093 0.03354847
67890 0.001990898 0.03424187
13579 -0.003285555 0.03057086

Simulation Study Analysis

The simulation study demonstrates the impact of using different seeds on variability in random number generation. Key observations include:

  • Stability of Means: The mean values across seeds are close to 0, reflecting the expected behavior when sampling from a normal distribution with mean = 0. This indicates that the choice of seed does not significantly influence the overall average.
  • Consistent Variance: Variances are similar across seeds (e.g., 0.0335, 0.0342, 0.0306), showing robust and stable random number generation.
  • Reproducibility: Using specific seeds ensures exact reproducibility of results, crucial for debugging, teaching, and sharing analyses.
  • Robustness: The results highlight that multiple seeds can be used for robustness testing without introducing bias or compromising statistical properties.

This study confirms that seeds control the sequence of random numbers but do not bias the outcomes, making them a reliable tool for reproducibility and robustness in simulations.

Common Use Cases

The set.seed() function is an essential tool in a variety of real-world applications where randomness is involved. Below are some common use cases where reproducibility and control over random number generation play a critical role. Each example is accompanied by a code snippet to illustrate its practical application.

1. Data Sampling

Random sampling is widely used in data analysis for tasks such as creating subsets of data, splitting datasets into training and testing sets, or selecting representative samples. Using set.seed(), you can ensure the results of your sampling are consistent across runs.

Random Sampling Example
# Create a reproducible random sample
set.seed(42)
data <- 1:100
sample_data <- sample(data, size = 10)
print(sample_data)

# Train-test split
set.seed(42)
n <- nrow(mtcars)
train_idx <- sample(1:n, size = 0.7 * n)
train_data <- mtcars[train_idx, ]
test_data <- mtcars[-train_idx, ]

2. Machine Learning

In machine learning workflows, reproducibility is critical for model evaluation and comparison. Setting a seed ensures that your random operations, such as k-means clustering initialization or cross-validation splits, produce consistent results every time. This is especially important for debugging and sharing analyses with collaborators.

Machine Learning Example
# Reproducible k-means clustering
set.seed(123)
kmeans_result <- kmeans(iris[, -5], centers = 3)

# Cross-validation using createFolds from caret package
# Ensure the caret package is installed and loaded
if (!requireNamespace("caret", quietly = TRUE)) {
  install.packages("caret")
}
library(caret)

set.seed(456)
cv_folds <- createFolds(iris$Species, k = 5)

3. Simulation Studies

Simulations, such as Monte Carlo studies, often involve generating large sets of random numbers to estimate probabilities, averages, or other statistical properties. Using set.seed() ensures that these simulations are reproducible, making it possible to debug results or verify findings across multiple runs.

Simulation Example
# Monte Carlo simulation
set.seed(789)
simulations <- replicate(1000, {
    sample_mean <- mean(rnorm(30, mean = 0, sd = 1))
    return(sample_mean)
})

Troubleshooting

While using set.seed() simplifies reproducibility, there are some common pitfalls and challenges to be aware of. Below are the most frequent issues users encounter and how to address them effectively.

Common Issues:
  1. Inconsistent Results: This typically happens when set.seed() is either forgotten or placed in the wrong part of the script. Always set the seed at the beginning of your workflow or immediately before any random operations.
  2. Package Conflicts: Some packages override or reset the random number generator, leading to unexpected results. For example, packages that parallelize computations may change the RNG state. Always check package documentation for compatibility with reproducibility.
  3. Parallel Processing: Random number generation in parallel workflows requires special handling to ensure reproducibility across threads or nodes. Use packages like doRNG to manage RNG states in parallel computations effectively.

How to Address These Issues

  • Always Set the Seed: Include set.seed() early in your script to establish a reproducible starting point.
  • Verify Package Behavior: When using external packages, ensure they respect the RNG state. If conflicts arise, consider resetting the RNG using set.seed() after package-specific operations.
  • Handle Parallel RNG Carefully: Use tools like doRNG or explicitly set seeds for each worker in a cluster to ensure consistent results across parallel tasks.

By proactively addressing these challenges, you can maximize the benefits of set.seed() and maintain reproducibility throughout your analyses.

Parallel Processing Considerations

Reproducibility in parallel processing requires special packages, such as doRNG:

Parallel Processing Example
# Ensure required packages are installed
if (!requireNamespace("doParallel", quietly = TRUE)) {
  install.packages("doParallel")
}
if (!requireNamespace("foreach", quietly = TRUE)) {
  install.packages("foreach")
}
if (!requireNamespace("doRNG", quietly = TRUE)) {
  install.packages("doRNG")
}

# Load necessary libraries
library(parallel)
library(doParallel)
library(foreach)
library(doRNG)

# Set up parallel processing with reproducible results
cl <- makeCluster(2)  # Create a cluster with 2 cores
registerDoParallel(cl)  # Register the parallel backend

# Perform reproducible parallel operations
set.seed(123)  # Set a seed for reproducibility
results <- foreach(i = 1:4, .options.RNG = 123) %dorng% {
    rnorm(5)  # Generate 5 random numbers
}

# Stop the cluster after use
stopCluster(cl)

# Print the results
print(results)

Clustering Results

The clustering results from the parallel operations using reproducible seeds are shown below. Each cluster result corresponds to a separate computation with its own random number generator (RNG) state.

Cluster Results
  • Cluster 1: 
    [1]  0.4254817  0.7639398  0.3574166 -0.1078357 -0.6753462
  • Cluster 2: 
    [1] -0.8817684  0.3062778  0.4202693 -0.2812589 -0.4360600
  • Cluster 3: 
    [1] -0.44483490  1.42473001 -0.57319258  1.25115168  0.04414866
  • Cluster 4: 
    [1] -1.77732677 -0.33801631  0.30183574 -0.03940505  2.22958331
RNG States

Each cluster computation also records the state of the RNG, which ensures reproducibility of results:

  • RNG State for Cluster 1: 
    [1] 10407 642048078 81368183 -2093158836 506506973 1421492218 -1906381517
  • RNG State for Cluster 2: 
    [1] 10407 1340772676 -1389246211 -999053355 -953732024 1888105061 2010658538
  • RNG State for Cluster 3: 
    [1] 10407 -1318496690 -948316584 683309249 -990823268 -1895972179 1275914972
  • RNG State for Cluster 4: 
    [1] 10407 524763474 1715794407 1887051490 -1833874283 494155061 -1221391662
Reproducibility Version

The clustering computations were conducted using doRNG version 1.7.4, ensuring consistent and reproducible results across runs.

Analysis

The results demonstrate how seeds control the RNG states, producing unique but reproducible outputs for each cluster. By recording RNG states, these computations can be reliably replicated, making this approach ideal for parallel reproducible analyses.

Advanced Usage: Random Number Generators (RNGs) in R

Random Number Generators (RNGs) in R are controlled by specific algorithms that determine the sequence of random numbers. These algorithms play a crucial role in ensuring reproducibility and efficiency in computations involving randomness. R provides several RNG algorithms, each suited for different use cases:

  • "Mersenne-Twister": The default RNG, known for its speed and large period, making it suitable for most applications.
  • "Knuth-TAOCP": An older algorithm, often used for specialized or legacy applications.
  • "Knuth-TAOCP-2002": An updated version of Knuth’s algorithm.
  • "L'Ecuyer-CMRG": Designed for reproducibility in parallel computations.

To control the RNG algorithm in R, you can use the RNGkind() function. This allows you to specify the RNG type for both random number generation and sampling, ensuring flexibility and compatibility with your specific needs.

Switching RNG Algorithms

Switching between RNG algorithms allows you to customize your random number generation process for specific tasks. Below are examples demonstrating how to use RNGkind() to select different algorithms:

Switching RNG Algorithms
# Default RNG: Mersenne-Twister
RNGkind("Mersenne-Twister")
set.seed(123)
rnorm(5)

# Switch to Inversion RNG
RNGkind("Inversion")
set.seed(123)
rnorm(5)

# Switch to L'Ecuyer-CMRG RNG
RNGkind("L'Ecuyer-CMRG")
set.seed(123)
rnorm(5)

Comparing RNGs

Different RNG algorithms can produce varying sequences of numbers even with the same seed. This is because the internal workings of each algorithm differ. Here is an example comparing "Mersenne-Twister" and "Inversion" algorithms:

Comparing RNG Algorithms
# Using Mersenne-Twister
RNGkind("Mersenne-Twister")
set.seed(42)
rnorm(3)

# Using Knuth-TAOCP
RNGkind("Knuth-TAOCP")
set.seed(42)
rnorm(3)

# Using L'Ecuyer-CMRG
RNGkind("L'Ecuyer-CMRG")
set.seed(42)
rnorm(3)

Output:

  • Mersenne-Twister: 
    [1]  1.3709584 -0.5646982  0.3631284
  • Knuth-TADCP: 
    [1] -2.1409071  0.1270539 -0.6542142
  • L'Ecuyer-CMRG: 
    [1] -0.93907708 -0.04167943  0.82941349

Using RNG for Sampling

In R 3.6.0, the sampling behavior was updated, introducing the sample.kind argument in RNGkind(). This argument allows you to select between "Rounding" (post-3.6.0) and "Rejection" (pre-3.6.0) methods for compatibility with older versions of R. Here’s how you can specify the sampling method:

Specifying Sampling Method
# Default sampling method (post R 3.6.0)
RNGkind(sample.kind = "Rounding")
set.seed(42)
sample(1:10, 5)

# Use the pre-3.6.0 sampling method for compatibility
RNGkind(sample.kind = "Rejection")
set.seed(42)
sample(1:10, 5)

Output:

  • Rounding (Default Post-3.6.0): 
    [1] 2 5 4 6 9
  • Rejection (Pre-3.6.0): 
    [1] 2 4 7 9 8

By controlling the RNG algorithm and sampling method, you can ensure consistency and compatibility across different versions of R, as well as adapt your workflow to specific computational requirements.

Here's a more accurate and modern overview of RNG choices:

Common Random Number Generators and Their Use Cases

  • xoshiro256**
    • Strengths: Excellent speed, strong statistical properties, small state size.
    • Weaknesses: Not cryptographically secure.
    • Best for: Modern general-purpose applications, scientific simulations, games.
  • PCG (Permuted Congruential Generator)
    • Strengths: Excellent statistical properties, good speed, small state.
    • Weaknesses: More complex implementation than simpler RNGs.
    • Best for: Applications requiring high-quality randomness with space constraints.
  • Mersenne Twister (MT19937)
    • Strengths: Very long period (2^19937-1), widely supported.
    • Weaknesses: Large state size (2.5KB), fails some statistical tests, not cryptographically secure.
    • Best for: Legacy applications, when compatibility is priority. While failing some statistical tests (like certain linearity tests), it remains sufficient for many applications where statistical rigour is not paramount.
  • L'Ecuyer-CMRG (MRG32k3a)
    • Strengths: Mathematically proven parallel streams, excellent statistical properties.
    • Weaknesses: Shorter period than MT (2^191), more complex implementation.
    • Best for: Parallel simulations requiring reproducible results.
  • ChaCha20/CSPRNG
    • Strengths: Cryptographically secure, good speed for a CSPRNG.
    • Weaknesses: Slower than non-cryptographic RNGs.
    • Best for: Security-critical applications, generating keys/tokens.

Most of these RNGs are available in common programming libraries (e.g., random module in Python and random in C++

Key Selection Criteria:

  • Security Requirements:
    • Use CSPRNGs (like ChaCha20) for any security-related applications.
    • Non-cryptographic RNGs are suitable for simulations/games.
  • Performance Considerations:
    • Consider both generation speed and state size.
    • Evaluate memory constraints of your platform.
  • Statistical Quality:
    • Modern RNGs (xoshiro256**, PCG) generally offer better statistical properties.
    • Test against relevant statistical test suites for your use case.
  • Implementation Factors:
    • Consider available library support and ease of integration.
    • Ensure proper seeding mechanisms are available.
    • Verify parallel generation capabilities if needed.

State Sizes of Common RNGs

The state size of a random number generator (RNG) determines the memory required to store its internal state. Smaller state sizes are ideal for memory-constrained environments, while larger states allow for longer periods. Below is a comparison of state sizes for popular RNGs:

RNG State Size Notes
xoshiro256** 256 bits (32 bytes) Memory efficient, excellent for general-purpose applications.
PCG 128 bits (16 bytes) Compact, suitable for embedded systems.
MT19937 (Mersenne Twister) 19937 bits (~2.5 KB) Large state, legacy use in simulations and games.
L'Ecuyer-CMRG 191 bits (~24 bytes) Designed for parallel streams and simulations.
ChaCha20 512 bits (64 bytes) Cryptographically secure, compact for a CSPRNG.

Key Insights:

  • Smaller state sizes (< 32 bytes) are ideal for constrained environments.
  • Larger state sizes (> 2 KB) enable longer periods but require more memory.
  • Modern RNGs like xoshiro256** and PCG offer an excellent balance between size and performance.

Additional Considerations:

  • Prioritize RNGs with strong statistical properties, especially uniformity and independence.
  • For parallel simulations, choose RNGs that can generate independent streams of random numbers.
  • The optimal RNG depends on the unique requirements of your application.
  • Always test your chosen RNG to ensure it meets your specific statistical needs.

Behavior Across R Versions

R 3.6.0 introduced changes to the RNG used for sampling. To maintain compatibility, specify sample.kind explicitly:

Specifying RNG for Sampling
set.seed(123, sample.kind = "Rounding")
Key Takeaways:
  • Always set seeds for reproducible results
  • Document your seed choices
  • Use different seeds for testing robustness
  • Consider parallel processing implications

Conclusion

Understanding and properly using set.seed() is essential for reproducible R programming. It ensures that random operations yield consistent results, making your analyses reliable, repeatable, and easy to debug. From simple data sampling to advanced simulation studies and machine learning workflows, setting a seed enhances reproducibility and enables robust testing across different scenarios.

This blog post covered the basics of set.seed(), advanced usage of RNG algorithms, best practices for setting seeds, and troubleshooting common issues. By leveraging tools like RNGkind() to control random number generation, and packages such as doRNG for parallel processing, you can maintain reproducibility even in complex workflows.

Further Reading

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Suf is a senior advisor in data science with deep expertise in Natural Language Processing, Complex Networks, and Anomaly Detection. Formerly a postdoctoral research fellow, he applied advanced physics techniques to tackle real-world, data-heavy industry challenges. Before that, he was a particle physicist at the ATLAS Experiment of the Large Hadron Collider. Now, he’s focused on bringing more fun and curiosity to the world of science and research online.

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