1 Overview

This script analyzes virtual team networks across three time points using Exponential Random Graph Models (ERGMs). The analysis examines how individual attributes (Big Five personality traits, demographics) influence network tie formation within teams.

Key Features:

Analyzes leadership granting networks at three time points
Tests effects of the Big Five personality traits and control variables
Uses block-diagonal constraints to analyze teams separately
Compares models with and without control variables

2 Setup

2.1 Load Required Packages

# Load necessary library for network analysis
library(statnet)      # Suite of packages for statistical network analysis

2.2 Import Data

Before running this script, please ensure you have the following files in your working directory:

T1_AttributeData.csv - Individual attributes at Time 1
T1_VoteMatrix.csv - Voting adjacency matrix at Time 1
T2_AttributeData.csv - Individual attributes at Time 2
T2_VoteMatrix.csv - Voting adjacency matrix at Time 2
T3_AttributeData.csv - Individual attributes at Time 3
T3_VoteMatrix.csv - Voting adjacency matrix at Time 3

You can set your working directory using setwd("your/path/here") or through RStudio’s Session menu.

3 Define Functions

3.1 Data Preparation Function

This function loads and preprocesses data for a given time point.

# Function to load and prepare network data for a specific time point
prepare_network_data <- function(n) {
  
  # Load attribute and matrix files
  attribute_file <- paste0("T", n, "_AttributeData.csv")
  matrix_file <- paste0("T", n, "_VoteMatrix.csv")
  
  attribute <- read.csv(attribute_file)
  vote_matrix <- read.csv(matrix_file)
  
  # Calculate matrix dimensions
  endnum <- nrow(vote_matrix)
  
  # Recode voting data: Convert to binary network
  # Only rating 5 (strongest endorsement) becomes 1, all others become 0
  vote_matrix[is.na(vote_matrix)] <- 0
  vote_matrix[vote_matrix == "1"] <- 0
  vote_matrix[vote_matrix == "2"] <- 0
  vote_matrix[vote_matrix == "3"] <- 0
  vote_matrix[vote_matrix == "4"] <- 0
  vote_matrix[vote_matrix == "5"] <- 1
  
  # Extract adjacency matrix (excluding header row/column)
  network_matrix <- vote_matrix[2:endnum, 2:endnum]
  network_matrix <- as.network.matrix(sapply(network_matrix, as.numeric))
  
  # Create network object
  # - directed = TRUE: votes have direction (A voting for B ≠ B voting for A)
  # - loops = FALSE: people cannot vote for themselves
  network_obj <- as.network(x = network_matrix, 
                           directed = TRUE, 
                           loops = FALSE, 
                           matrix.type = "adjacency")
  
  # Attach individual attributes as vertex attributes
  for (i in 1:ncol(attribute)) {
    set.vertex.attribute(network_obj, colnames(attribute)[i], attribute[, i])
  }
  
  return(network_obj)
}

3.2 ERGM Modeling Functions

3.2.1 Full Model with Control Variables

# Function to run ERGM model with control variables
run_ergm_full <- function(network_obj, time_label) {
  
  cat("\n========================================\n")
  cat(paste("Time", time_label, "- ERGM with Controls\n"))
  cat("========================================\n")
  
  # Run ERGM with full set of predictors
  ergm_model <- ergm(network_obj ~ 
                      # Structural effects
                      edges +              # Baseline tie probability
                      mutual +             # Reciprocity (A→B and B→A)
                      transitiveties +     # Transitive closure (A→B→C implies A→C)
                      cyclicalties +       # Cyclical patterns (A→B→C→A)
                      
                      # Control variables (centered)
                      nodeicov("age.c") +       # Age effect on receiving ties
                      nodeicov("tech.c") +      # Technical skill effect
                      nodeicov("eng.c") +       # English proficiency effect
                      nodeicov("self_ef.c") +   # Self-efficacy effect
                      nodeicov("gender.c") +    # Gender effect (receiver)
                      
                      # Big Five personality traits (centered, receiver)
                      nodeicov("B5_a.c") +      # Agreeableness
                      nodeicov("B5_c.c") +      # Conscientiousness
                      nodeicov("B5_e.c") +      # Extraversion
                      nodeicov("B5_o.c") +      # Openness
                      nodeicov("B5_n.c") +      # Neuroticism
                       
                      # Big Five personality traits (centered, sender)
                      nodeocov("B5_a.c") +      # Agreeableness
                      nodeocov("B5_c.c") +      # Conscientiousness
                      nodeocov("B5_e.c") +      # Extraversion
                      nodeocov("B5_o.c") +      # Openness
                      nodeocov("B5_n.c"),       # Neuroticism
                    
                    # Model specifications
                    eval.loglik = TRUE,
                    constraints = ~blockdiag("team_id"),  # Analyze teams separately
                    control = control.ergm(MCMLE.maxit = 10000))
  
  cat("\nModel estimation complete!\n")
  print(summary(ergm_model))
  
  return(ergm_model)
}

3.2.2 Reduced Model without Control Variables

# Function to run ERGM model without control variables
run_ergm_reduced <- function(network_obj, time_label) {
  
  cat("\n========================================\n")
  cat(paste("Time", time_label, "- ERGM without Controls\n"))
  cat("========================================\n")
  
  # Run ERGM with only structural effects and personality traits
  ergm_model <- ergm(network_obj ~ 
                      # Structural effects
                      edges +              # Baseline tie probability
                      mutual +             # Reciprocity (A→B and B→A)
                      transitiveties +     # Transitive closure (A→B→C implies A→C)
                      cyclicalties +       # Cyclical patterns (A→B→C→A)
                      
                      # Big Five personality traits (centered, receiver)
                      nodeicov("B5_a.c") +      # Agreeableness
                      nodeicov("B5_c.c") +      # Conscientiousness
                      nodeicov("B5_e.c") +      # Extraversion
                      nodeicov("B5_o.c") +      # Openness
                      nodeicov("B5_n.c") +      # Neuroticism
                       
                      # Big Five personality traits (centered, sender)
                      nodeocov("B5_a.c") +      # Agreeableness
                      nodeocov("B5_c.c") +      # Conscientiousness
                      nodeocov("B5_e.c") +      # Extraversion
                      nodeocov("B5_o.c") +      # Openness
                      nodeocov("B5_n.c"),       # Neuroticism
                    
                    # Model specifications
                    eval.loglik = TRUE,
                    constraints = ~blockdiag("team_id"),  # Analyze teams separately
                    control = control.ergm(MCMLE.maxit = 10000))
  
  cat("\nModel estimation complete!\n")
  print(summary(ergm_model))
  
  return(ergm_model)
}

4 Run Analysis for All Time Points

Each time point is analyzed with both full and reduced models.

4.1 Time 1 Analysis

# Prepare Time 1 network data
t1.network <- prepare_network_data(1)

4.1.1 Full Model with Controls

# Run ERGM with control variables for Time 1
t1.model.full <- run_ergm_full(t1.network, 1)

## 
## ========================================
## Time 1 - ERGM with Controls
## ========================================

## 
## Model estimation complete!
## Call:
## ergm(formula = network_obj ~ edges + mutual + transitiveties + 
##     cyclicalties + nodeicov("age.c") + nodeicov("tech.c") + nodeicov("eng.c") + 
##     nodeicov("self_ef.c") + nodeicov("gender.c") + nodeicov("B5_a.c") + 
##     nodeicov("B5_c.c") + nodeicov("B5_e.c") + nodeicov("B5_o.c") + 
##     nodeicov("B5_n.c") + nodeocov("B5_a.c") + nodeocov("B5_c.c") + 
##     nodeocov("B5_e.c") + nodeocov("B5_o.c") + nodeocov("B5_n.c"), 
##     constraints = ~blockdiag("team_id"), eval.loglik = TRUE, 
##     control = control.ergm(MCMLE.maxit = 10000))
## 
## Monte Carlo Maximum Likelihood Results:
## 
##                     Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges              -1.669395   0.107558      0 -15.521  < 1e-04 ***
## mutual             -0.089673   0.232290      0  -0.386 0.699467    
## transitiveties      1.073365   0.115442      0   9.298  < 1e-04 ***
## cyclicalties       -0.365351   0.096541      0  -3.784 0.000154 ***
## nodeicov.age.c      0.008905   0.011223      0   0.793 0.427509    
## nodeicov.tech.c     0.043826   0.058304      0   0.752 0.452239    
## nodeicov.eng.c      0.339905   0.109381      0   3.108 0.001887 ** 
## nodeicov.self_ef.c  0.158277   0.104636      0   1.513 0.130371    
## nodeicov.gender.c   0.375557   0.125848      0   2.984 0.002843 ** 
## nodeicov.B5_a.c    -0.113183   0.131595      0  -0.860 0.389741    
## nodeicov.B5_c.c     0.005798   0.137424      0   0.042 0.966350    
## nodeicov.B5_e.c     0.174147   0.100186      0   1.738 0.082170 .  
## nodeicov.B5_o.c     0.006029   0.123968      0   0.049 0.961214    
## nodeicov.B5_n.c     0.157087   0.113014      0   1.390 0.164534    
## nodeocov.B5_a.c     0.263125   0.120565      0   2.182 0.029077 *  
## nodeocov.B5_c.c    -0.232142   0.128767      0  -1.803 0.071419 .  
## nodeocov.B5_e.c    -0.007466   0.097938      0  -0.076 0.939230    
## nodeocov.B5_o.c    -0.089711   0.118843      0  -0.755 0.450327    
## nodeocov.B5_n.c    -0.028471   0.106729      0  -0.267 0.789656    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 1791  on 1292  degrees of freedom
##  Residual Deviance: 1409  on 1273  degrees of freedom
##  
## AIC: 1447  BIC: 1545  (Smaller is better. MC Std. Err. = 0.5818)

4.1.2 Reduced Model without Controls

# Run ERGM without control variables for Time 1
t1.model.reduced <- run_ergm_reduced(t1.network, 1)

## 
## ========================================
## Time 1 - ERGM without Controls
## ========================================

## 
## Model estimation complete!
## Call:
## ergm(formula = network_obj ~ edges + mutual + transitiveties + 
##     cyclicalties + nodeicov("B5_a.c") + nodeicov("B5_c.c") + 
##     nodeicov("B5_e.c") + nodeicov("B5_o.c") + nodeicov("B5_n.c") + 
##     nodeocov("B5_a.c") + nodeocov("B5_c.c") + nodeocov("B5_e.c") + 
##     nodeocov("B5_o.c") + nodeocov("B5_n.c"), constraints = ~blockdiag("team_id"), 
##     eval.loglik = TRUE, control = control.ergm(MCMLE.maxit = 10000))
## 
## Monte Carlo Maximum Likelihood Results:
## 
##                  Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges           -1.642664   0.110879      0 -14.815  < 1e-04 ***
## mutual          -0.092612   0.233523      0  -0.397 0.691671    
## transitiveties   1.076075   0.115265      0   9.336  < 1e-04 ***
## cyclicalties    -0.357424   0.095141      0  -3.757 0.000172 ***
## nodeicov.B5_a.c  0.004165   0.123640      0   0.034 0.973128    
## nodeicov.B5_c.c  0.144598   0.132438      0   1.092 0.274915    
## nodeicov.B5_e.c  0.213883   0.096600      0   2.214 0.026822 *  
## nodeicov.B5_o.c  0.027963   0.122254      0   0.229 0.819081    
## nodeicov.B5_n.c  0.211147   0.109768      0   1.924 0.054407 .  
## nodeocov.B5_a.c  0.292294   0.123013      0   2.376 0.017495 *  
## nodeocov.B5_c.c -0.239938   0.131141      0  -1.830 0.067307 .  
## nodeocov.B5_e.c  0.001956   0.096246      0   0.020 0.983782    
## nodeocov.B5_o.c -0.111475   0.120292      0  -0.927 0.354083    
## nodeocov.B5_n.c -0.022895   0.104692      0  -0.219 0.826888    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 1791  on 1292  degrees of freedom
##  Residual Deviance: 1429  on 1278  degrees of freedom
##  
## AIC: 1457  BIC: 1530  (Smaller is better. MC Std. Err. = 0.7134)

4.2 Time 2 Analysis

# Prepare Time 2 network data
t2.network <- prepare_network_data(2)

4.2.1 Full Model with Controls

# Run ERGM with control variables for Time 2
t2.model.full <- run_ergm_full(t2.network, 2)

## 
## ========================================
## Time 2 - ERGM with Controls
## ========================================

## 
## Model estimation complete!
## Call:
## ergm(formula = network_obj ~ edges + mutual + transitiveties + 
##     cyclicalties + nodeicov("age.c") + nodeicov("tech.c") + nodeicov("eng.c") + 
##     nodeicov("self_ef.c") + nodeicov("gender.c") + nodeicov("B5_a.c") + 
##     nodeicov("B5_c.c") + nodeicov("B5_e.c") + nodeicov("B5_o.c") + 
##     nodeicov("B5_n.c") + nodeocov("B5_a.c") + nodeocov("B5_c.c") + 
##     nodeocov("B5_e.c") + nodeocov("B5_o.c") + nodeocov("B5_n.c"), 
##     constraints = ~blockdiag("team_id"), eval.loglik = TRUE, 
##     control = control.ergm(MCMLE.maxit = 10000))
## 
## Monte Carlo Maximum Likelihood Results:
## 
##                     Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges              -1.641354   0.111739      0 -14.689   <1e-04 ***
## mutual             -0.184742   0.231605      0  -0.798   0.4251    
## transitiveties      1.162945   0.114327      0  10.172   <1e-04 ***
## cyclicalties       -0.348292   0.087140      0  -3.997   <1e-04 ***
## nodeicov.age.c      0.009710   0.010382      0   0.935   0.3496    
## nodeicov.tech.c     0.102645   0.059092      0   1.737   0.0824 .  
## nodeicov.eng.c      0.229688   0.097951      0   2.345   0.0190 *  
## nodeicov.self_ef.c  0.075468   0.098079      0   0.769   0.4416    
## nodeicov.gender.c   0.291963   0.121520      0   2.403   0.0163 *  
## nodeicov.B5_a.c    -0.283977   0.128837      0  -2.204   0.0275 *  
## nodeicov.B5_c.c     0.266630   0.133818      0   1.992   0.0463 *  
## nodeicov.B5_e.c     0.228668   0.095357      0   2.398   0.0165 *  
## nodeicov.B5_o.c     0.003181   0.124229      0   0.026   0.9796    
## nodeicov.B5_n.c     0.134621   0.112971      0   1.192   0.2334    
## nodeocov.B5_a.c     0.204907   0.120027      0   1.707   0.0878 .  
## nodeocov.B5_c.c    -0.094626   0.126723      0  -0.747   0.4552    
## nodeocov.B5_e.c    -0.068456   0.090733      0  -0.754   0.4506    
## nodeocov.B5_o.c    -0.105812   0.114665      0  -0.923   0.3561    
## nodeocov.B5_n.c    -0.116907   0.108461      0  -1.078   0.2811    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 1791  on 1292  degrees of freedom
##  Residual Deviance: 1443  on 1273  degrees of freedom
##  
## AIC: 1481  BIC: 1579  (Smaller is better. MC Std. Err. = 0.5463)

4.2.2 Reduced Model without Controls

# Run ERGM without control variables for Time 2
t2.model.reduced <- run_ergm_reduced(t2.network, 2)

## 
## ========================================
## Time 2 - ERGM without Controls
## ========================================

## 
## Model estimation complete!
## Call:
## ergm(formula = network_obj ~ edges + mutual + transitiveties + 
##     cyclicalties + nodeicov("B5_a.c") + nodeicov("B5_c.c") + 
##     nodeicov("B5_e.c") + nodeicov("B5_o.c") + nodeicov("B5_n.c") + 
##     nodeocov("B5_a.c") + nodeocov("B5_c.c") + nodeocov("B5_e.c") + 
##     nodeocov("B5_o.c") + nodeocov("B5_n.c"), constraints = ~blockdiag("team_id"), 
##     eval.loglik = TRUE, control = control.ergm(MCMLE.maxit = 10000))
## 
## Monte Carlo Maximum Likelihood Results:
## 
##                  Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges           -1.656278   0.109462      0 -15.131  < 1e-04 ***
## mutual          -0.187132   0.231672      0  -0.808  0.41924    
## transitiveties   1.186599   0.110260      0  10.762  < 1e-04 ***
## cyclicalties    -0.344754   0.086204      0  -3.999  < 1e-04 ***
## nodeicov.B5_a.c -0.172197   0.126503      0  -1.361  0.17345    
## nodeicov.B5_c.c  0.360679   0.128303      0   2.811  0.00494 ** 
## nodeicov.B5_e.c  0.243426   0.092492      0   2.632  0.00849 ** 
## nodeicov.B5_o.c -0.002519   0.117531      0  -0.021  0.98290    
## nodeicov.B5_n.c  0.180333   0.108313      0   1.665  0.09593 .  
## nodeocov.B5_a.c  0.233952   0.117515      0   1.991  0.04650 *  
## nodeocov.B5_c.c -0.103335   0.119687      0  -0.863  0.38793    
## nodeocov.B5_e.c -0.067927   0.093532      0  -0.726  0.46769    
## nodeocov.B5_o.c -0.105904   0.117847      0  -0.899  0.36884    
## nodeocov.B5_n.c -0.102215   0.103513      0  -0.987  0.32342    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 1791  on 1292  degrees of freedom
##  Residual Deviance: 1459  on 1278  degrees of freedom
##  
## AIC: 1487  BIC: 1559  (Smaller is better. MC Std. Err. = 0.6546)

4.3 Time 3 Analysis

# Prepare Time 3 network data
t3.network <- prepare_network_data(3)

4.3.1 Full Model with Controls

# Run ERGM with control variables for Time 3
t3.model.full <- run_ergm_full(t3.network, 3)

## 
## ========================================
## Time 3 - ERGM with Controls
## ========================================

## 
## Model estimation complete!
## Call:
## ergm(formula = network_obj ~ edges + mutual + transitiveties + 
##     cyclicalties + nodeicov("age.c") + nodeicov("tech.c") + nodeicov("eng.c") + 
##     nodeicov("self_ef.c") + nodeicov("gender.c") + nodeicov("B5_a.c") + 
##     nodeicov("B5_c.c") + nodeicov("B5_e.c") + nodeicov("B5_o.c") + 
##     nodeicov("B5_n.c") + nodeocov("B5_a.c") + nodeocov("B5_c.c") + 
##     nodeocov("B5_e.c") + nodeocov("B5_o.c") + nodeocov("B5_n.c"), 
##     constraints = ~blockdiag("team_id"), eval.loglik = TRUE, 
##     control = control.ergm(MCMLE.maxit = 10000))
## 
## Monte Carlo Maximum Likelihood Results:
## 
##                      Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges              -1.7014811  0.1074582      0 -15.834  < 1e-04 ***
## mutual             -0.3840270  0.2510451      0  -1.530 0.126088    
## transitiveties      1.1920625  0.1186028      0  10.051  < 1e-04 ***
## cyclicalties       -0.3538807  0.0945406      0  -3.743 0.000182 ***
## nodeicov.age.c     -0.0007457  0.0114700      0  -0.065 0.948161    
## nodeicov.tech.c     0.0783091  0.0601161      0   1.303 0.192701    
## nodeicov.eng.c      0.2516402  0.1009584      0   2.493 0.012684 *  
## nodeicov.self_ef.c  0.0811618  0.1037539      0   0.782 0.434066    
## nodeicov.gender.c   0.3163355  0.1260173      0   2.510 0.012064 *  
## nodeicov.B5_a.c    -0.3153922  0.1315448      0  -2.398 0.016503 *  
## nodeicov.B5_c.c     0.3546105  0.1362886      0   2.602 0.009271 ** 
## nodeicov.B5_e.c     0.2066197  0.1012866      0   2.040 0.041355 *  
## nodeicov.B5_o.c     0.0060494  0.1206428      0   0.050 0.960008    
## nodeicov.B5_n.c     0.2303910  0.1163301      0   1.980 0.047648 *  
## nodeocov.B5_a.c     0.3245078  0.1215940      0   2.669 0.007613 ** 
## nodeocov.B5_c.c    -0.0663821  0.1349470      0  -0.492 0.622781    
## nodeocov.B5_e.c    -0.0557252  0.0944489      0  -0.590 0.555188    
## nodeocov.B5_o.c    -0.0516858  0.1201025      0  -0.430 0.666943    
## nodeocov.B5_n.c     0.0103972  0.1092962      0   0.095 0.924212    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 1791  on 1292  degrees of freedom
##  Residual Deviance: 1375  on 1273  degrees of freedom
##  
## AIC: 1413  BIC: 1511  (Smaller is better. MC Std. Err. = 0.6968)

4.3.2 Reduced Model without Controls

# Run ERGM without control variables for Time 3
t3.model.reduced <- run_ergm_reduced(t3.network, 3)

## 
## ========================================
## Time 3 - ERGM without Controls
## ========================================

## 
## Model estimation complete!
## Call:
## ergm(formula = network_obj ~ edges + mutual + transitiveties + 
##     cyclicalties + nodeicov("B5_a.c") + nodeicov("B5_c.c") + 
##     nodeicov("B5_e.c") + nodeicov("B5_o.c") + nodeicov("B5_n.c") + 
##     nodeocov("B5_a.c") + nodeocov("B5_c.c") + nodeocov("B5_e.c") + 
##     nodeocov("B5_o.c") + nodeocov("B5_n.c"), constraints = ~blockdiag("team_id"), 
##     eval.loglik = TRUE, control = control.ergm(MCMLE.maxit = 10000))
## 
## Monte Carlo Maximum Likelihood Results:
## 
##                 Estimate Std. Error MCMC % z value Pr(>|z|)    
## edges           -1.70705    0.10963      0 -15.570  < 1e-04 ***
## mutual          -0.40725    0.25337      0  -1.607  0.10798    
## transitiveties   1.22031    0.11988      0  10.179  < 1e-04 ***
## cyclicalties    -0.35087    0.09814      0  -3.575  0.00035 ***
## nodeicov.B5_a.c -0.19394    0.13275      0  -1.461  0.14402    
## nodeicov.B5_c.c  0.44712    0.13745      0   3.253  0.00114 ** 
## nodeicov.B5_e.c  0.24089    0.09697      0   2.484  0.01299 *  
## nodeicov.B5_o.c -0.01998    0.12103      0  -0.165  0.86889    
## nodeicov.B5_n.c  0.27939    0.11674      0   2.393  0.01670 *  
## nodeocov.B5_a.c  0.33847    0.12108      0   2.795  0.00518 ** 
## nodeocov.B5_c.c -0.06903    0.13183      0  -0.524  0.60050    
## nodeocov.B5_e.c -0.05132    0.09758      0  -0.526  0.59890    
## nodeocov.B5_o.c -0.07305    0.11770      0  -0.621  0.53485    
## nodeocov.B5_n.c  0.02567    0.11032      0   0.233  0.81599    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
##      Null Deviance: 1791  on 1292  degrees of freedom
##  Residual Deviance: 1389  on 1278  degrees of freedom
##  
## AIC: 1417  BIC: 1490  (Smaller is better. MC Std. Err. = 0.8349)

5 Session Information

# Document R version and package versions for reproducibility
sessionInfo()

## R version 4.5.1 (2025-06-13)
## Platform: aarch64-apple-darwin20
## Running under: macOS Tahoe 26.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/Chicago
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
## [1] statnet_2019.6        tsna_0.3.6            sna_2.8              
## [4] statnet.common_4.12.0 ergm.count_4.1.3      tergm_4.2.2          
## [7] networkDynamic_0.11.5 ergm_4.10.1           network_1.19.0       
## 
## loaded via a namespace (and not attached):
##  [1] sass_0.4.10              generics_0.1.4           robustbase_0.99-6       
##  [4] stringi_1.8.7            lattice_0.22-7           digest_0.6.37           
##  [7] magrittr_2.0.4           evaluate_1.0.5           lpSolveAPI_5.5.2.0-17.14
## [10] grid_4.5.1               networkLite_1.1.0        fastmap_1.2.0           
## [13] jsonlite_2.0.0           Matrix_1.7-3             rle_0.10.0              
## [16] purrr_1.1.0              jquerylib_0.1.4          Rdpack_2.6.4            
## [19] cli_3.6.5                rlang_1.1.6              rbibutils_2.3           
## [22] cachem_1.1.0             yaml_2.3.10              tools_4.5.1             
## [25] parallel_4.5.1           memoise_2.0.1            coda_0.19-4.1           
## [28] dplyr_1.1.4              vctrs_0.6.5              R6_2.6.1                
## [31] lifecycle_1.0.4          stringr_1.5.2            MASS_7.3-65             
## [34] trust_0.1-8              pkgconfig_2.0.3          pillar_1.11.1           
## [37] bslib_0.9.0              ergm.multi_0.3.0         glue_1.8.0              
## [40] DEoptimR_1.1-4           xfun_0.53                tibble_3.3.0            
## [43] tidyselect_1.2.1         rstudioapi_0.17.1        knitr_1.50              
## [46] htmltools_0.5.8.1        nlme_3.1-168             rmarkdown_2.29          
## [49] compiler_4.5.1

6 Notes

ERGM Terms Explained:

edges: Overall density of the network (baseline probability of tie formation)
mutual: Tendency for reciprocal ties (if A votes for B, does B vote for A?)
transitiveties: Tendency for transitive closure (if A→B and B→C, then A→C)
cyclicalties: Tendency for cyclical patterns (A→B→C→A)
nodeicov: Effect of a node attribute on receiving ties (in-degree)
nodeocov: Effect of a node attribute on sending ties (out-degree)

Variables:

B5_a: Agreeableness (Big Five personality trait)
B5_c: Conscientiousness
B5_e: Extraversion
B5_o: Openness to Experience
B5_n: Neuroticism
.c suffix: Indicates centered variables (mean-centered for interpretability)
age.c: Centered age
tech.c: Centered technical skills
eng.c: Centered English proficiency
self_ef.c: Centered self-efficacy
gender.c: Centered gender

Constraints:

blockdiag(“team_id”): Analyzes each team separately while estimating a single set of parameters

Model Comparison:

Full Model: Includes structural effects, control variables, and Big Five personality traits
Reduced Model: Includes only structural effects and Big Five personality traits (no demographic controls)

Code Structure:

This script uses functional programming to reduce repetition: - prepare_network_data(n): Loads and prepares data for time point n - run_ergm_full(): Runs ERGM model with all control variables - run_ergm_reduced(): Runs ERGM model without control variables - Each time point is analyzed with both model types - Models stored as t1.model.full, t1.model.reduced, etc.

R script for Personality and leader emergence in virtual teams: A temporal and interactive perspective

Biying Yang

2025-11-15