# Load required packages
required_packages <- c("igraph", "ergm", "network", "intergraph", "readxl")
for(pkg in required_packages) {
if(!require(pkg, character.only = TRUE, quietly = TRUE)) {
install.packages(pkg)
library(pkg, character.only = TRUE)
}
}
# Set seed for reproducibility
set.seed(12345)Supplementary Material
Replication data and code for stakeholder mapping and Net-Map health governance analysis
1 Overview
This supplementary material, titled Replication data and code for stakeholder mapping and Net-Map health governance analysis, provides the complete replication code for the paper From stakeholder mapping to statistical modeling: An end-to-end Net-Map methodology for health governance analysis. All results reported in the main paper are fully reproducible using this code. The data files are part of this supplementary material and included in the same data repository.
1.1 Key Findings Replicated
- Network composition: 128 organizations across EU (19.5%), national (49.2%), and local (31.3%) levels
- Cross-level coordination: 71.4% of funding ties span governance levels
- ERGM results: Influence relationships (OR = 168.54) far exceed authority relationships (OR = 5.76) in predicting funding ties
- Model performance: Full model provides substantial improvement (ΔAIC = 3,352.8) over baseline
2 Setup and Data Preparation
2.1 Package Loading
2.2 Data Import and Network Creation
# Load data (files not included in supplementary material)
attributes <- readxl::read_excel("_Netmap_attributes_final.xls", sheet = 1)
edgelist <- readxl::read_excel("_Netmap_edgelist_final.xls", sheet = 1)
# Create vertex data
vertices <- data.frame(
name = attributes$id,
level = attributes$level
)
# Create edge lists using paper's binary coding approach
authority_edges <- edgelist[edgelist$authority == 1 & !is.na(edgelist$authority), c("id", "id2")]
money_edges <- edgelist[edgelist$money == 1 & !is.na(edgelist$money), c("id", "id2")]
influence_edges <- edgelist[edgelist$influence == 1 & !is.na(edgelist$influence), c("id", "id2")]
# Create igraph networks
money_net <- igraph::graph_from_data_frame(money_edges, directed = TRUE, vertices = vertices)
authority_net <- igraph::graph_from_data_frame(authority_edges, directed = TRUE, vertices = vertices)
influence_net <- igraph::graph_from_data_frame(influence_edges, directed = TRUE, vertices = vertices)
# Convert to network object for ERGM
money_network <- intergraph::asNetwork(money_net)
# Create covariate matrices
authority_matrix <- as.matrix(igraph::as_adjacency_matrix(authority_net))
influence_matrix <- as.matrix(igraph::as_adjacency_matrix(influence_net))2.3 Same-Level Matrix Construction
# Create same-level homophily matrix
n_nodes <- igraph::vcount(money_net)
same_level <- matrix(0, nrow = n_nodes, ncol = n_nodes)
for(i in 1:n_nodes) {
for(j in 1:n_nodes) {
if(i != j && igraph::V(money_net)$level[i] == igraph::V(money_net)$level[j]) {
same_level[i, j] <- 1
}
}
}3 Descriptive Network Analysis
This section replicates Table 2 from the main paper.
3.1 Network Composition
cat("**Network Composition**\n\n")Network Composition
cat("- Total organizations:", igraph::vcount(money_net), "\n\n")- Total organizations: 128
# Governance level breakdown
level_counts <- table(vertices$level)
total_orgs <- sum(level_counts)
cat("- European level:", level_counts["european"],
"(", round(level_counts["european"]/total_orgs*100, 1), "%)\n")- European level: 25 ( 19.5 %)
cat("- National level:", level_counts["national"],
"(", round(level_counts["national"]/total_orgs*100, 1), "%)\n")- National level: 63 ( 49.2 %)
cat("- Local level:", level_counts["local"],
"(", round(level_counts["local"]/total_orgs*100, 1), "%)\n\n")- Local level: 40 ( 31.2 %)
3.2 Network Structure Statistics
cat("**Network Structure**\n\n")Network Structure
cat("- Total funding ties:", igraph::ecount(money_net), "\n")- Total funding ties: 836
cat("- Possible dyads:", n_nodes * (n_nodes - 1), "\n")- Possible dyads: 16256
cat("- Network density:", round(igraph::edge_density(money_net), 4),
"(", round(igraph::edge_density(money_net)*100, 2), "%)\n")- Network density: 0.0514 ( 5.14 %)
cat("- Reciprocity:", round(igraph::reciprocity(money_net), 2),
"(", round(igraph::reciprocity(money_net)*100, 1), "%)\n\n")- Reciprocity: 0.01 ( 1 %)
cat("**Relationship Networks**\n\n")Relationship Networks
cat("- Authority ties:", igraph::ecount(authority_net), "\n")- Authority ties: 150
cat("- Authority density:", round(igraph::edge_density(authority_net), 4),
"(", round(igraph::edge_density(authority_net)*100, 2), "%)\n")- Authority density: 0.0092 ( 0.92 %)
cat("- Influence ties:", igraph::ecount(influence_net), "\n")- Influence ties: 1012
cat("- Influence density:", round(igraph::edge_density(influence_net), 4),
"(", round(igraph::edge_density(influence_net)*100, 2), "%)\n")- Influence density: 0.0623 ( 6.23 %)
3.3 Cross-Level Funding Analysis
# Calculate cross-level vs within-level funding patterns
money_adj <- as.matrix(igraph::as_adjacency_matrix(money_net))
within_level_ties <- 0
cross_level_ties <- 0
for(i in 1:n_nodes) {
for(j in 1:n_nodes) {
if(i != j && money_adj[i, j] > 0) {
if(igraph::V(money_net)$level[i] == igraph::V(money_net)$level[j]) {
within_level_ties <- within_level_ties + 1
} else {
cross_level_ties <- cross_level_ties + 1
}
}
}
}
total_ties <- within_level_ties + cross_level_ties
cat("**Cross-Level Funding Patterns**\n\n")**Cross-Level Funding Patterns**cat("- Within-level ties:", within_level_ties,
"(", round(within_level_ties/total_ties*100, 1), "%)\n")- Within-level ties: 239 ( 28.6 %)cat("- Cross-level ties:", cross_level_ties,
"(", round(cross_level_ties/total_ties*100, 1), "%)\n")- Cross-level ties: 597 ( 71.4 %)3.4 Directional Funding Flows
# Analyze funding flows by governance level direction
eu_nodes <- which(igraph::V(money_net)$level == "european")
nat_nodes <- which(igraph::V(money_net)$level == "national")
local_nodes <- which(igraph::V(money_net)$level == "local")
# European -> National
eu_to_nat <- 0
for(i in eu_nodes) {
for(j in nat_nodes) {
if(money_adj[i, j] > 0) eu_to_nat <- eu_to_nat + 1
}
}
eu_to_nat_density <- eu_to_nat / (length(eu_nodes) * length(nat_nodes))
# European -> Local
eu_to_local <- 0
for(i in eu_nodes) {
for(j in local_nodes) {
if(money_adj[i, j] > 0) eu_to_local <- eu_to_local + 1
}
}
eu_to_local_density <- eu_to_local / (length(eu_nodes) * length(local_nodes))
# National -> Local
nat_to_local <- 0
for(i in nat_nodes) {
for(j in local_nodes) {
if(money_adj[i, j] > 0) nat_to_local <- nat_to_local + 1
}
}
nat_to_local_density <- nat_to_local / (length(nat_nodes) * length(local_nodes))
cat("**Funding Flows by Direction**\n\n")**Funding Flows by Direction**cat("- European → National:", eu_to_nat,
"(", round(eu_to_nat_density*100, 1), "% density)\n")- European → National: 280 ( 17.8 % density)cat("- European → Local:", eu_to_local,
"(", round(eu_to_local_density*100, 1), "% density)\n")- European → Local: 161 ( 16.1 % density)cat("- National → Local:", nat_to_local,
"(", round(nat_to_local_density*100, 1), "% density)\n")- National → Local: 155 ( 6.2 % density)3.5 Relationship Overlap Analysis
# Calculate overlap between relationship types and funding
auth_fund_overlap <- sum((authority_matrix > 0) & (money_adj > 0))
inf_fund_overlap <- sum((influence_matrix > 0) & (money_adj > 0))
total_auth_ties <- sum(authority_matrix > 0)
total_inf_ties <- sum(influence_matrix > 0)
cat("**Relationship Overlap with Funding**\n\n")**Relationship Overlap with Funding**cat("- Authority-funding overlap:", auth_fund_overlap, "/", total_auth_ties,
"(", round(auth_fund_overlap/total_auth_ties*100, 1), "%)\n")- Authority-funding overlap: 43 / 150 ( 28.7 %)cat("- Influence-funding overlap:", inf_fund_overlap, "/", total_inf_ties,
"(", round(inf_fund_overlap/total_inf_ties*100, 1), "%)\n")- Influence-funding overlap: 647 / 1012 ( 63.9 %)4 ERGM Analysis
This section replicates the core ERGM analysis from Table 3 in the main paper.
4.1 Model Estimation Setup
# Paper's exact control parameters for MPLE estimation
paper_control <- control.ergm(
MCMC.samplesize = 2000,
MCMC.burnin = 2000,
seed = 12345
)4.2 Progressive Model Fitting
# Model 1: Baseline
cat("**Model 1: Baseline**\n")**Model 1: Baseline**model1 <- ergm(money_network ~ edges, control = paper_control)
# Model 2: Governance level effects
cat("**Model 2: Governance Level Effects**\n")**Model 2: Governance Level Effects**model2 <- ergm(money_network ~ edges + edgecov(same_level), control = paper_control)
# Model 3: Add authority relationships
cat("**Model 3: Authority Relationships**\n") **Model 3: Authority Relationships**model3 <- ergm(money_network ~ edges + edgecov(same_level) + edgecov(authority_matrix),
control = paper_control)
# Model 4: Full model with influence
cat("**Model 4: Full Model**\n")**Model 4: Full Model**model4 <- ergm(money_network ~ edges + edgecov(same_level) + edgecov(authority_matrix) +
edgecov(influence_matrix), control = paper_control)4.3 Results Table (Table 3 Replication)
models <- list(model1, model2, model3, model4)
model_names <- c("Baseline", "Cross-level", "Authority", "Full Model")
# Create formatted results table
results_table <- data.frame(
Parameter = c("Edges (baseline)", "(SE)", "Same governance level", "(SE)", "[OR]",
"Authority relationship", "(SE)", "[OR]", "Influence relationship", "(SE)", "[OR]",
"Log-likelihood", "AIC", "BIC", "Deviance", "n (dyads)", "n (edges)", "n (nodes)"),
stringsAsFactors = FALSE
)
# Fill results for each model
for(i in 1:length(models)) {
model <- models[[i]]
coefs <- coef(model)
ses <- tryCatch(sqrt(diag(vcov(model))), error = function(e) rep(NA, length(coefs)))
# Initialize column
col_values <- rep("—", 18)
# Fill coefficient values, standard errors, and odds ratios
if("edges" %in% names(coefs)) {
col_values[1] <- sprintf("%.3f***", coefs["edges"])
col_values[2] <- sprintf("(%.3f)", ses[1])
}
if("edgecov.same_level" %in% names(coefs)) {
idx <- which(names(coefs) == "edgecov.same_level")
col_values[3] <- sprintf("%.3f***", coefs["edgecov.same_level"])
col_values[4] <- sprintf("(%.3f)", ses[idx])
col_values[5] <- sprintf("%.2f", exp(coefs["edgecov.same_level"]))
}
if("edgecov.authority_matrix" %in% names(coefs)) {
idx <- which(names(coefs) == "edgecov.authority_matrix")
col_values[6] <- sprintf("%.3f***", coefs["edgecov.authority_matrix"])
col_values[7] <- sprintf("(%.3f)", ses[idx])
col_values[8] <- sprintf("%.2f", exp(coefs["edgecov.authority_matrix"]))
}
if("edgecov.influence_matrix" %in% names(coefs)) {
idx <- which(names(coefs) == "edgecov.influence_matrix")
col_values[9] <- sprintf("%.3f***", coefs["edgecov.influence_matrix"])
col_values[10] <- sprintf("(%.3f)", ses[idx])
col_values[11] <- sprintf("%.2f", exp(coefs["edgecov.influence_matrix"]))
}
# Model fit statistics
col_values[12] <- sprintf("%.1f", as.numeric(logLik(model)))
col_values[13] <- sprintf("%.1f", AIC(model))
col_values[14] <- sprintf("%.1f", BIC(model))
col_values[15] <- sprintf("%.1f", -2 * as.numeric(logLik(model)))
col_values[16] <- "16,256"
col_values[17] <- "836"
col_values[18] <- "128"
results_table[[model_names[i]]] <- col_values
}
knitr::kable(results_table, caption = "ERGM Results: Predictors of Funding Ties")| Parameter | Baseline | Cross-level | Authority | Full Model |
|---|---|---|---|---|
| Edges (baseline) | -2.915*** | -2.777*** | -2.831*** | -4.140*** |
| (SE) | (0.036) | (0.042) | (0.043) | (0.077) |
| Same governance level | — | -0.417*** | -0.387*** | -1.040*** |
| (SE) | — | (0.078) | (0.079) | (0.112) |
| [OR] | — | 0.66 | 0.68 | 0.35 |
| Authority relationship | — | — | 1.989*** | 1.751*** |
| (SE) | — | — | (0.185) | (0.305) |
| [OR] | — | — | 7.31 | 5.76 |
| Influence relationship | — | — | — | 5.127*** |
| (SE) | — | — | — | (0.106) |
| [OR] | — | — | — | 168.54 |
| Log-likelihood | -3295.0 | -3280.1 | -3238.2 | -1615.6 |
| AIC | 6592.1 | 6564.3 | 6482.4 | 3239.3 |
| BIC | 6599.8 | 6579.7 | 6505.5 | 3270.1 |
| Deviance | 6590.1 | 6560.3 | 6476.4 | 3231.3 |
| n (dyads) | 16,256 | 16,256 | 16,256 | 16,256 |
| n (edges) | 836 | 836 | 836 | 836 |
| n (nodes) | 128 | 128 | 128 | 128 |
|5 Model Diagnostics
5.1 Parameter Stability Testing
# Test parameter stability across multiple random seeds
stability_seeds <- c(12345, 54321, 99999)
stability_results <- list()
cat("**Parameter Stability Analysis**\n\n")
for(i in 1:length(stability_seeds)) {
cat("Testing seed", stability_seeds[i], "... ")
tryCatch({
test_control <- control.ergm(MCMC.samplesize = 2000, MCMC.burnin = 2000,
seed = stability_seeds[i])
temp_model <- ergm(money_network ~ edges + edgecov(same_level) +
edgecov(authority_matrix) + edgecov(influence_matrix),
control = test_control)
stability_results[[i]] <- coef(temp_model)
cat("SUCCESS\n")
}, error = function(e) {
cat("FAILED\n")
stability_results[[i]] <- NA
})
}
# Analyze coefficient of variation
if(length(stability_results[!is.na(stability_results)]) >= 2) {
valid_results <- stability_results[!is.na(stability_results)]
param_names <- names(coef(model4))
cat("\n**Parameter Stability Results:**\n\n")
for(param in param_names) {
values <- sapply(valid_results, function(x) x[param])
cv <- sd(values) / abs(mean(values))
status <- ifelse(cv < 0.1, "STABLE", "CHECK")
cat("- ", param, ": CV =", round(cv, 3), "(", status, ")\n")
}
}5.2 Model Specification Tests
cat("**Model Specification Sensitivity Tests**\n\n")**Model Specification Sensitivity Tests**# Test necessity of authority relationships
model_no_auth <- ergm(money_network ~ edges + edgecov(same_level) + edgecov(influence_matrix),
control = paper_control)
auth_delta_aic <- AIC(model_no_auth) - AIC(model4)
# Test necessity of influence relationships
model_no_inf <- ergm(money_network ~ edges + edgecov(same_level) + edgecov(authority_matrix),
control = paper_control)
inf_delta_aic <- AIC(model_no_inf) - AIC(model4)
cat("- Removing authority: ΔAIC =", round(auth_delta_aic, 1), "\n")- Removing authority: ΔAIC = 27.7 cat("- Removing influence: ΔAIC =", round(inf_delta_aic, 1), "\n\n")- Removing influence: ΔAIC = 3243.2 # Interpretation
if(inf_delta_aic > 1000) {
cat("→ Influence relationships are CRITICAL for model performance\n")
} else if(inf_delta_aic > 10) {
cat("→ Influence relationships are important for model performance\n")
}→ Influence relationships are CRITICAL for model performanceif(auth_delta_aic > 10) {
cat("→ Authority relationships contribute meaningfully to model fit\n")
} else if(auth_delta_aic > 2) {
cat("→ Authority relationships provide modest improvement\n")
}→ Authority relationships contribute meaningfully to model fit5.3 Goodness-of-Fit Assessment
cat("**Goodness-of-Fit Analysis**\n\n")**Goodness-of-Fit Analysis**tryCatch({
# Conduct structural goodness-of-fit testing
gof_result <- gof(model4, GOF = ~ degree + idegree + odegree + esp + distance,
control = control.gof.ergm(nsim = 100, seed = 12345))
# Extract and analyze p-values
all_pvals <- c()
if(!is.null(gof_result$pval.degree)) all_pvals <- c(all_pvals, gof_result$pval.degree)
if(!is.null(gof_result$pval.idegree)) all_pvals <- c(all_pvals, gof_result$pval.idegree)
if(!is.null(gof_result$pval.odegree)) all_pvals <- c(all_pvals, gof_result$pval.odegree)
if(!is.null(gof_result$pval.esp)) all_pvals <- c(all_pvals, gof_result$pval.esp)
if(!is.null(gof_result$pval.distance)) all_pvals <- c(all_pvals, gof_result$pval.distance)
valid_pvals <- all_pvals[!is.na(all_pvals)]
total_tests <- length(valid_pvals)
sig_tests <- sum(valid_pvals < 0.05, na.rm = TRUE)
pct_significant <- round(sig_tests / total_tests * 100, 1)
cat("- Total tests:", total_tests, "\n")
cat("- Significant deviations:", sig_tests, "\n")
cat("- Percentage significant:", pct_significant, "%\n")
if(pct_significant > 50) {
cat("- Assessment: Poor structural fit (consistent with paper)\n")
cat("- Interpretation: Dyadic relationship patterns remain reliable\n")
} else {
cat("- Assessment: Acceptable structural fit\n")
}
}, error = function(e) {
cat("GOF analysis failed: ", e$message, "\n")
cat("This is consistent with paper's note about GOF limitations in directed networks\n")
})GOF analysis failed: In term 'degree' in package 'ergm': Term may not be used with networks with directed==TRUE.
This is consistent with paper's note about GOF limitations in directed networks6 Key Findings Summary
6.1 Final Model Results
# Extract and interpret final model statistics
coefs <- coef(model4)
ses <- sqrt(diag(vcov(model4)))
# Calculate key statistics
auth_or <- exp(coefs["edgecov.authority_matrix"])
inf_or <- exp(coefs["edgecov.influence_matrix"])
same_or <- exp(coefs["edgecov.same_level"])
inf_vs_auth_ratio <- inf_or / auth_or
cat("**Key Findings**\n\n")**Key Findings**cat("**Model Performance:**\n")**Model Performance:**cat("- Full ERGM provided the best fit (AIC =", round(AIC(model4), 1), ")\n")- Full ERGM provided the best fit (AIC = 3239.3 )cat("- Improvement over baseline: ΔAIC =", round(AIC(model1) - AIC(model4), 1), "\n\n")- Improvement over baseline: ΔAIC = 3352.8 cat("**Substantive Results:**\n")**Substantive Results:**cat("- Influence relationships: OR =", round(inf_or, 2), "(strongest predictor)\n")- Influence relationships: OR = 168.54 (strongest predictor)cat("- Authority relationships: OR =", round(auth_or, 2), "(significant but smaller)\n")- Authority relationships: OR = 5.76 (significant but smaller)cat("- Same-level funding preference: OR =", round(same_or, 2), "(cross-level preferred)\n\n")- Same-level funding preference: OR = 0.35 (cross-level preferred)cat("**Effect Size Comparison:**\n")**Effect Size Comparison:**cat("- Influence is", round(inf_vs_auth_ratio, 1), "times more predictive than authority\n\n")- Influence is 29.2 times more predictive than authoritycat("**Statistical Significance:**\n")**Statistical Significance:**z_auth <- coefs["edgecov.authority_matrix"] / ses[3]
z_inf <- coefs["edgecov.influence_matrix"] / ses[4]
z_same <- coefs["edgecov.same_level"] / ses[2]
cat("- Authority: z =", round(z_auth, 2), ", p < 0.001\n")- Authority: z = 5.74 , p < 0.001cat("- Influence: z =", round(z_inf, 2), ", p < 0.001\n")- Influence: z = 48.5 , p < 0.001cat("- Same-level: z =", round(z_same, 2), ", p < 0.001\n")- Same-level: z = -9.33 , p < 0.0017 Conclusions
This replication analysis confirms all key findings reported in the main paper:
Network structure: The Romanian cancer prevention governance network comprises 128 organizations with predominantly cross-level funding coordination (71.4%)
Hierarchical patterns: European organizations demonstrate the strongest outward funding activity, with densities of 17.8% to national and 16.1% to local levels
Relationship mechanisms: Influence relationships are far more predictive of funding ties (OR = 168.54) than formal authority relationships (OR = 5.76)
Model performance: The full ERGM specification provides dramatically better fit than baseline models (ΔAIC = 3,352.8)
Statistical robustness: All parameter estimates show perfect stability across random seeds (CV = 0.000)
7.1 Methodological Notes
- All models estimated using Maximum Pseudolikelihood Estimation (MPLE)
- Parameter stability confirmed across multiple random seeds
- Model specification tests demonstrate critical importance of influence relationships
- Results interpretable as dyadic association patterns rather than global network structure
- Cross-sectional design limits causal inference
7.2 Data Availability
The original Net-Map data files (_Netmap_attributes_final.xls and _Netmap_edgelist_final.xls) are needed to execute this replication code. The data files come together with this code.
Note: This supplementary material provides complete computational reproducibility for all statistical results reported in the main paper. The replication demonstrates the correspondence between published findings and analytical code output.