📊 Ando, H., Nishi, A., & Handcock, M. S. (2025). Statistical Modeling of Networked Evolutionary Public Goods Games.

---

This repository, developed by Hiroyasu Ando and Mark S. Handcock, provides all data and scripts used in the statistical analysis of dynamic network structures arising from repeated networked public goods games. It contains 20 independent longitudinal networks across eight time points, along with complete tools for conducting maximum likelihood estimation (MLE), robustness and sensitivity analyses, and goodness-of-fit evaluations. The repository enables full replication of the modeling framework and empirical results presented in the study.

---

📁 Data

pgg_data.RData

• A collection of 20 independent dynamic networks from the networked public goods game.
• Each network spans 8 time points (0 to 7).
• Stored as igraph objects.

pgg_adj.RData

• The same networks as above, represented as adjacency matrices.

pgg_plus_data.RData / pgg_plus_adj.RData

• All possible Y⁺ (formation) network data for each network from time 1 to 7.
• igraph objects (pgg_plus_data.RData) and adjacency matrices (pgg_plus_adj.RData).
• Can be regenerated using the plus_network.R script.

pgg_minus_data.RData / pgg_minus_adj.RData

• All possible Y⁻ (persistence) network data for each network from time 1 to 7.
• igraph objects (pgg_minus_data.RData) and adjacency matrices (pgg_minus_adj.RData).
• Can be regenerated using the minus_network.R script.

---

📜 R-Scripts

plus_network.R

Generates all possible Y⁺ (formation) networks.

Outputs:

• pgg_plus_data.RData
• pgg_plus_adj.RData

---

minus_network.R

Generates all possible Y⁻ (persistence) networks.

Outputs:

• pgg_minus_data.RData
• pgg_minus_adj.RData

---

plus_model.R / minus_model.R

Main model for Table 1.

Outputs:

• Maximum likelihood estimates (MLE)
• Standard errors
• Log-likelihood

---

plus_model_non_triangle.R / minus_model_non_triangle.R

Covariates-only model (without the triangle term) used for Table 2 and Figure 5.

Outputs:

• Maximum likelihood estimates (MLE)
• Standard errors
• Log-likelihood

---

plus_model_gender.R / minus_model_gender.R

Main model with the gender covariates for the sensitivity analysis.

Outputs:

• Maximum likelihood estimates (MLE)
• Standard errors
• Log-likelihood

---

plus_model_2_star.R / minus_model_2_star.R

Main model with an added 2-star term for the sensitivity analysis.

Outputs:

• Maximum likelihood estimates (MLE)
• Standard errors
• Log-likelihood

---

model_each_time.R

Models at each time step, used for Figures 7 & 8.

Outputs:

• Maximum likelihood estimates (MLE)
• Standard errors
• Log-likelihood

---

graph_model_each_time.R

Generates visualizations of time-specific model results, used for Figure 7 and Figure 8.

---

graph_dynamic_network.R

Visualizes the dynamic evolution of the network over time, used for Figure 4.

---

gof_triangle_formation.R

Generates triangle GoF plots for the formation networks, used for Figure 5.

---

gof_k_star.R

Generates k-stars GoF plots for the public goods game networks, used for Figure 6.

---

gof_degree.R

Produces k-degrees GoF plots for the public goods game networks.

---

📦 Requirements

• R (≥ 4.0.0)
• igraph
• tidyverse
• Matrix
• parallel
• latex2exp

---

📄 Citation

If you use this code or data, please cite the original paper:

Ando, H., Nishi, A., & Handcock, M. S. (2025). Statistical Modeling of Networked Evolutionary Public Goods Games.

---

📬 Contact

For questions or collaborations, please reach out to:

Hiroyasu Ando
📧 hiro1999@g.ucla.edu

---