Agent-based modelling for archaeologists. From concept to application and publication

22.1 Using NetLogo’s BehaviorSpace

22.2 Single simulation run

22.3 Repetitions under the same parameter configuration

22.4 Different parameter configurations

22.5 Alternative designs

22.6 Stochastic exploration for sensitivity analysis

To perform sensitivity analysis in a simulation model, we need to sample parameter values more efficiently than using regular intervals. There are three common sampling methods: Random Sampling, Latin Hypercube Sampling (LHS), and Sobol Sampling. Below is an explanation of how to obtain parameter samples using each method in R.

22.6.1 Random Sampling

Random sampling is the simplest method, where parameter values are drawn independently from a given probability distribution (e.g., uniform, normal). This method may not cover the parameter space as efficiently as structured sampling methods.

Implementation in R

set.seed(123)  # For reproducibility
n <- 100  # Number of samples
param1 <- runif(n, min = 0, max = 1)  # Uniform distribution
param2 <- rnorm(n, mean = 0, sd = 1)  # Normal distribution

# Combine into a data frame
samples_random <- data.frame(param1, param2)
head(samples_random)

📌 Pros: Simple and easy to implement
📌 Cons: Potential clustering of samples, leading to inefficient coverage of the parameter space.

22.6.2 Latin Hypercube Sampling (LHS)

Latin Hypercube Sampling ensures that each parameter is sampled more uniformly across its range. It divides the range of each parameter into equal intervals and ensures that each interval is sampled exactly once (Chalom and Prado 2015).

Implementation in R Using the lhs package:

library(lhs)
set.seed(123)
n <- 100  # Number of samples
k <- 2  # Number of parameters

# Generate LHS sample in [0,1] range
samples_lhs <- randomLHS(n, k)

# Transform to specific distributions
param1 <- qunif(samples_lhs[,1], min = 0, max = 1)  # Uniform
param2 <- qnorm(samples_lhs[,2], mean = 0, sd = 1)  # Normal

# Combine into a data frame
samples_lhs <- data.frame(param1, param2)
head(samples_lhs)

📌 Pros: More uniform coverage of the space than random sampling
📌 Cons: Does not account for interactions between parameters explicitly

22.6.3 Sobol Sampling

Sobol sampling is a quasi-random low-discrepancy sequence designed for global sensitivity analysis. It provides better uniformity across the space than both random and LHS methods (Renardy et al. 2021).

Implementation in R Using the randtoolbox package:

library(randtoolbox)
set.seed(123)
n <- 100  # Number of samples
k <- 2  # Number of parameters

# Generate Sobol sequence
samples_sobol <- sobol(n, dim = k, scrambling = 3)

# Transform to specific distributions
param1 <- qunif(samples_sobol[,1], min = 0, max = 1)  # Uniform
param2 <- qnorm(samples_sobol[,2], mean = 0, sd = 1)  # Normal

# Combine into a data frame
samples_sobol <- data.frame(param1, param2)
head(samples_sobol)

📌 Pros: Highly efficient, low-discrepancy sequence for sensitivity analysis
📌 Cons: Requires specialized libraries, and might not be ideal for small sample sizes

22.6.4 Comparison of Methods

Sampling Method	Uniform Coverage	Computational Efficiency	Best Use Case
Random	Poor	Fast	Basic sensitivity analysis
Latin Hypercube (LHS)	Good	Moderate	Optimized space-filling with no interaction control
Sobol	Excellent	Moderate	Global sensitivity analysis

22.6.5 Conclusion

Use random sampling when simplicity is preferred.
Use LHS when uniform coverage of individual parameters is important.
Use Sobol sampling for high-dimensional sensitivity analysis.