Background
Opinion diffusion models
Modeling considerations
Statistical physics
\(\text {SIR}\) model
Bayesian and naive learning
DeGroot model
Methods
Objective function
Genetic algorithm
Gene-swapping
Selection
Blending
Crossover
Mutation
-
If \(w^*<0\), \(w^*\) is set to 0
-
If \(w^*>1-w_{fixed}\), \(w^*\) is set to \(1-w_{fixed}\). All other non-zero weights in the row are then set to 0.
-
If the selected weight \(w=1-w_{fixed}\), the excess weight of \(1-w_{fixed}-w^*\) is evenly distributed between all other non-fixed weights within the row.
Survival
Other features
Hyperparameter | Value | Description |
---|---|---|
chromosomes | 21 | Number of chromosomes |
probb | 0.01 | Initial probability of blending (\(p_b\)) |
factorb | 2 | Multiplicative factor for modifying \(p_b\) |
maxb | 0.2 | Maximum value of \(p_b\) |
iterb | 1000 | Number of iterations with no improvement before modifying \(p_b\) |
probc | 0.2 | Initial probability of crossover (\(p_c\)) |
factorc | 0.5 | Multiplicative factor for modifying \(p_c\) |
minc | 0 | Minimum value of \(p_c\) |
iterc | 1000 | Number of iterations with no improvement before modifying \(p_c\) |
probm | 0.2 | Initial probability of blending (\(p_m\)) |
factorm | 0.5 | Multiplicative factor for modifying \(p_m\) |
minm | 0.01 | Minimum value of \(p_m\) |
iterm | 1000 | Number of iterations with no improvement before modifying \(p_m\) |
sigma | 1 | Initial value of standard deviation \(\sigma\) of error for mutation operator |
factors | 0.5 | Multiplicative factor for modifying \(\sigma\) |
mins | 0.001 | Minimum value of \(\sigma\) |
iters | 2000 | Number of iterations with no improvement before modifying \(\sigma\) |
max_iter | 1E6 | Maximum number of iterations to run algorithm |
min_improve | 0 | Minimum decrease in value of objective function considered an improvement |
min_dev | 0 | Acceptable value of objective function for stopping algorithm |
reintroduce | “elite” | type of chromosome to be reintroduced |
iterr | 2500 | Number of iterations with no improvement before reintroducing chromosome |
Simulation study
Input | Values | Notes |
---|---|---|
Network size | \(N=4,10,20,50\) | Reachability enforced |
Degree | \(d=2,5,9\) | Minimum degree \(d=1\) for all nodes |
Self-weight | \(w_{ii}=0.1,0.5,0.8\) | Beta distribution with \(\kappa =\alpha +\beta =10\) |
Time steps | \(T=2,3,6,11\) | Performance assessed on \(t=1,\ldots ,20\) |
Missingness | \(0\%,10\%,25\%,50\%\) | Minimum 2 observations per agent |
Target | Mean |
---|---|
\(d=2\) | \({\bar{d}}=2.47\) |
\(d=5\) | \({\bar{d}}=5.03\) |
\(d=9\) | \({\bar{d}}=9.01\) |
Results
Network size and degree
Size | Degree | ||
---|---|---|---|
2 | 5 | 9 | |
4 | 0.15 (0.23) | NA | NA |
10 | 0.17 (0.18) | 0.17 (0.14) | 0.15 (0.10) |
20 | 0.17 (0.17) | 0.18 (0.12) | 0.15 (0.10) |
50 | 0.17 (0.15) | 0.17 (0.12) | 0.15 (0.08) |
Size | Mean |
---|---|
4 | \({\bar{d}}=2.15\) |
10 | \({\bar{d}}=2.48\) |
20 | \({\bar{d}}=2.58\) |
50 | \({\bar{d}}=2.62\) |
Size | Degree | ||
---|---|---|---|
2 | 5 | 9 | |
4 | \(4.92\times 10^{-8}\) | NA | NA |
10 | \(3.89\times 10^{-4}\) | \(1.68\times 10^{-3}\) | \(1.05\times 10^{-2}\) |
20 | \(3.17\times 10^{-2}\) | \(2.75\times 10^{-2}\) | \(4.48\times 10^{-2}\) |
50 | \(4.77\times 10^{-2}\) | \(4.29\times 10^{-2}\) | \(5.00\times 10^{-2}\) |
Self-weight
Target self-weight | \({\mathbf{RMSE}}_{{{\mathbf{rec}}}}\) |
---|---|
0.1 | 0.18 (0.18) |
0.5 | 0.17 (0.12) |
0.8 | 0.14 (0.10) |
Missingness and time steps
Time steps | Missingness | |||
---|---|---|---|---|
0 | 0.1 | 0.25 | 0.5 | |
2 | 0.15 (0.07) | NA | NA | NA |
3 | 0.09 (0.04) | 0.15 (0.05) | 0.20 (0.06) | 0.28 (0.07) |
6 | 0.06 (0.04) | 0.14 (0.05) | 0.19 (0.08) | 0.25 (0.09) |
11 | 0.06 (0.04) | 0.14 (0.06) | 0.20 (0.10) | 0.24 (0.12) |
Observations | Missingness | |
---|---|---|
0 | 0.5 | |
2 | 0.15 (0.07) | 0.28 (0.07) |
6 | 0.06 (0.04) | 0.24 (0.12) |
Application: diffusion of willingness to use \(\text {PrEP}\) among \(\text {BMSM}\)
Study overview
Recruitment of social networks
Assessments
Methods
Forward transformation
Back transformation
Results
Network 1 (\(N=12\)) | ||
Agent 1 | Leader | Seed |
Agent 2 | Leader | |
Agent 3 | Leader | |
Agent 4 | Leader | |
Network 2 (\(N=11\)) | ||
Agent 1 | Leader | Seed |
Agent 2 | Leader | |
Agent 3 | Leader | |
Network 3 (\(N=8\)) | ||
Agent 1 | Leader | Seed |
Network 4 (\(N=5\)) | ||
Agent 1 | Seed | |
Agent 4 | Leader | |
Network 5 (\(N=4\)) | ||
Agent 1 | Leader | Seed |
Agent 2 | Leader |
Accuracy of predicted opinions
Willingness build | |||||||||||
0.22* (0.23) | 0.03* (0.03) | 0.15* (0.10) | 0.59* (0.12) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.06* (0.04) | 0.53* (0.10) | 0 | 0 | 0.05 (0.04) | 0.01 (0.00) | 0.25 (0.10) | 0.09 (0.06) | 0.01 (0.01) | 0 | 0 | 0 |
0.09* (0.14) | 0 | 0.74* (0.03) | 0 | 0 | 0 | 0 | 0 | 0 | 0.00 (0.00) | 0.17 (0.12) | 0 |
0.00* (0.00) | 0 | 0 | 0.50* (0.24) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.50 (0.24) |
0 | 0.24* (0.00) | 0 | 0 | 0.76 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0.12* (0.00) | 0 | 0 | 0 | 0.88 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0.00* (0.01) | 0 | 0 | 0 | 0 | 1.00 (0.01) | 0 | 0 | 0 | 0 | 0 |
0 | 1.00* (0.00) | 0 | 0 | 0 | 0 | 0 | 0.00 (0.00) | 0 | 0 | 0 | 0 |
0 | 0.22* (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0.78 (0.00) | 0 | 0 | 0 |
0 | 0 | 0.03* (0.01) | 0 | 0 | 0 | 0 | 0 | 0 | 0.97 (0.01) | 0 | 0 |
0 | 0 | 0.00* (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1.00 (0.00) | 0 |
0 | 0 | 0 | 0.44* (0.21) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.56 (0.21) |
Willingness remove | |||||||||||
0.10* (0.07) | 0.33* (0.08) | 0.22* (0.02) | 0.35* (0.07) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.00* (0.00) | 0.50* (0.42) | 0.00* (0.00) | 0.13* (0.25) | 0.00 (0.00) | 0.00 (0.00) | 0.12 (0.24) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.20 (0.35) | 0.05 (0.08) |
0.03* (0.03) | 0.02* (0.02) | 0.71* (0.04) | 0.02* (0.02) | 0.04 (0.05) | 0.00 (0.00) | 0.04 (0.05) | 0.02 (0.03) | 0.01 (0.02) | 0.01 (0.02) | 0.06 (0.07) | 0.04 (0.06) |
0.00* (0.00) | 0.18* (0.34) | 0.00* (0.00) | 0.28* (0.38) | 0.00 (0.00) | 0.00 (0.00) | 0.05 (0.06) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.25 (0.35) | 0.24 (0.36) |
0 | 0.08* (0.11) | 0.21* (0.09) | 0.18* (0.17) | 0.14 (0.18) | 0.00 (0.00) | 0.07 (0.06) | 0.03 (0.03) | 0.04 (0.04) | 0.00 (0.00) | 0.12 (0.09) | 0.13 (0.13) |
0 | 0.05* (0.04) | 0.22* (0.10) | 0.04* (0.02) | 0.08 (0.10) | 0.01 (0.01) | 0.10 (0.08) | 0.03 (0.03) | 0.36 (0.10) | 0.01 (0.01) | 0.05 (0.04) | 0.05 (0.03) |
0 | 0.06* (0.11) | 0.00* (0.00) | 0.25* (0.28) | 0.00 (0.00) | 0.00 (0.00) | 0.26 (0.29) | 0.20 (0.42) | 0.00 (0.00) | 0.00 (0.00) | 0.10 (0.10) | 0.14 (0.20) |
0 | 0.01* (0.01) | 0.00* (0.00) | 0.01* (0.02) | 0.00 (0.00) | 0.02 (0.02) | 0.15 (0.31) | 0.52 (0.43) | 0.00 (0.00) | 0.07 (0.05) | 0.02 (0.06) | 0.19 (0.33) |
0 | 0.00* (0.00) | 0.93* (0.10) | 0.00* (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.07 (0.11) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) |
0 | 0.01* (0.01) | 0.02* (0.02) | 0.01* (0.01) | 0.00 (0.01) | 0.07 (0.06) | 0.01 (0.01) | 0.02 (0.01) | 0.02 (0.02) | 0.80 (0.10) | 0.02 (0.02) | 0.01 (0.02) |
0 | 0.14* (0.27) | 0.00* (0.00) | 0.30* (0.34) | 0.00 (0.00) | 0.00 (0.00) | 0.12 (0.24) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.33 (0.41) | 0.11 (0.14) |
0 | 0.09* (0.18) | 0.00* (0.00) | 0.04* (0.05) | 0.00 (0.00) | 0.00 (0.00) | 0.17 (0.25) | 0.20 (0.42) | 0.00 (0.00) | 0.00 (0.00) | 0.19 (0.36) | 0.31 (0.42) |
Weight estimates and variability
Efficacy build | |||||||||||
0.79* (0.02) | 0.00* (0.00) | 0.20* (0.03) | 0.01* (0.04) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.16* (0.04) | 0.83* (0.02) | 0 | 0 | 0.00 (0.00) | 0.00 (0.00) | 0.01 (0.02) | 0.00 (0.00) | 0.00 (0.00) | 0 | 0 | 0 |
0.00* (0.00) | 0 | 0.92* (0.01) | 0 | 0 | 0 | 0 | 0 | 0 | 0.07 (0.02) | 0.01 (0.01) | 0 |
0.05* (0.05) | 0 | 0 | 0.51* (0.19) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.44 (0.14) |
0 | 0.00* (0.00) | 0 | 0 | 1.00 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0.04* (0.00) | 0 | 0 | 0 | 0.96 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0.00* (0.00) | 0 | 0 | 0 | 0 | 1.00 (0.00) | 0 | 0 | 0 | 0 | 0 |
0 | 0.00* (0.00) | 0 | 0 | 0 | 0 | 0 | 1.00 (0.00) | 0 | 0 | 0 | 0 |
0 | 0.05* (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0.95 (0.00) | 0 | 0 | 0 |
0 | 0 | 0.01* (0.01) | 0 | 0 | 0 | 0 | 0 | 0 | 0.99 (0.01) | 0 | 0 |
0 | 0 | 0.14* (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.86 (0.00) | 0 |
0 | 0 | 0 | 0.00* (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1.00 (0.00) |
Efficacy remove | |||||||||||
0.70* (0.14) | 0.02* (0.04) | 0.09* (0.10) | 0.19* (0.20) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.02* (0.03) | 0.69* (0.04) | 0.00* (0.00) | 0.01* (0.01) | 0.27 (0.09) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.01 (0.01) | 0.00 (0.00) |
0.00* (0.00) | 0.00* (0.00) | 0.36* (0.09) | 0.00* (0.00) | 0.00 (0.00) | 0.31 (0.08) | 0.31 (0.11) | 0.00 (0.00) | 0.00 (0.01) | 0.01 (0.01) | 0.00 (0.00) | 0.01 (0.01) |
0.12* (0.13) | 0.01* (0.01) | 0.05* (0.06) | 0.24* (0.28) | 0.03 (0.03) | 0.03 (0.03) | 0.23 (0.15) | 0.01 (0.01) | 0.00 (0.00) | 0.20 (0.33) | 0.03 (0.03) | 0.06 (0.05) |
0 | 0.03* (0.09) | 0.03* (0.02) | 0.11* (0.13) | 0.69 (0.14) | 0.02 (0.01) | 0.03 (0.02) | 0.00 (0.00) | 0.01 (0.01) | 0.03 (0.03) | 0.01 (0.03) | 0.06 (0.06) |
0 | 0.00* (0.01) | 0.00* (0.01) | 0.00* (0.00) | 0.00 (0.01) | 0.77 (0.07) | 0.00 (0.00) | 0.01 (0.02) | 0.20 (0.11) | 0.01 (0.02) | 0.00 (0.00) | 0.00 (0.00) |
0 | 0.00* (0.00) | 0.00* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0.01 (0.03) | 0.99 (0.03) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) |
0 | 0.05* (0.03) | 0.00* (0.01) | 0.00* (0.00) | 0.13 (0.06) | 0.00 (0.01) | 0.00 (0.00) | 0.8 (0.05) | 0.00 (0.01) | 0.00 (0.01) | 0.00 (0.01) | 0.00 (0.00) |
0 | 0.01* (0.02) | 0.00* (0.01) | 0.00* (0.00) | 0.00 (0.00) | 0.01 (0.04) | 0.00 (0.00) | 0.11 (0.02) | 0.86 (0.06) | 0.00 (0.00) | 0.00 (0.01) | 0.00 (0.00) |
0 | 0.00* (0.01) | 0.05* (0.07) | 0.02* (0.04) | 0.00 (0.01) | 0.05 (0.06) | 0.04 (0.04) | 0.01 (0.01) | 0.03 (0.06) | 0.04 (0.07) | 0.00 (0.00) | 0.74 (0.29) |
0 | 0.06* (0.05) | 0.05* (0.05) | 0.15* (0.11) | 0.41 (0.13) | 0.02 (0.03) | 0.10 (0.12) | 0.00 (0.00) | 0.00 (0.00) | 0.12 (0.09) | 0.05 (0.06) | 0.05 (0.05) |
0 | 0.01* (0.01) | 0.15* (0.10) | 0.05* (0.06) | 0.01 (0.01) | 0.08 (0.05) | 0.19 (0.14) | 0.01 (0.01) | 0.02 (0.02) | 0.27 (0.16) | 0.03 (0.04) | 0.17 (0.19) |
Willingness build | ||||||||||
0.99* (0.01) | 0.00* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.18* (0.07) | 0.82* (0.07) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.23* (0.12) | 0 | 0.02* (0.03) | 0 | 0.17 (0.17) | 0.11 (0.07) | 0.16 (0.14) | 0.07 (0.06) | 0.24 (0.19) | 0 | 0 |
0.50* (0.01) | 0 | 0 | 0.02 (0.02) | 0 | 0 | 0 | 0 | 0 | 0.00 (0.00) | 0.48 (0.01) |
0 | 0 | 0.18* (0.27) | 0 | 0.82 (0.27) | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0.00* (0.00) | 0 | 0 | 1.00 (0.00) | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0.24* (0.25) | 0 | 0 | 0 | 0.76 (0.25) | 0 | 0 | 0 | 0 |
0 | 0 | 0.23* (0.19) | 0 | 0 | 0 | 0 | 0.77 (0.19) | 0 | 0 | 0 |
0 | 0 | 0.10* (0.14) | 0 | 0 | 0 | 0 | 0 | 0.90 (0.14) | 0 | 0 |
0 | 0 | 0 | 1.00 (0.00) | 0 | 0 | 0 | 0 | 0 | 0.00 (0.00) | 0 |
0 | 0 | 0 | 0.00 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 1.00 (0.00) |
Willingness Remove | ||||||||||
1.00* (0.00) | 0.00* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.07* (0.08) | 0.06* (0.08) | 0.19* (0.31) | 0.03 (0.07) | 0.16 (0.26) | 0.03 (0.03) | 0.04 (0.08) | 0.19 (0.26) | 0.04 (0.05) | 0.03 (0.04) | 0.17 (0.29) |
0.11* (0.15) | 0.04* (0.06) | 0.05* (0.08) | 0.31 (0.36) | 0.06 (0.08) | 0.05 (0.07) | 0.10 (0.14) | 0.14 (0.21) | 0.09 (0.10) | 0.01 (0.02) | 0.03 (0.05) |
0.06* (0.08) | 0.13* (0.28) | 0.20* (0.38) | 0.06 (0.11) | 0.05 (0.07) | 0.04 (0.06) | 0.07 (0.15) | 0.15 (0.23) | 0.08 (0.18) | 0.13 (0.31) | 0.03 (0.04) |
0 | 0.12* (0.20) | 0.18* (0.27) | 0.17 (0.30) | 0.09 (0.24) | 0.02 (0.03) | 0.03 (0.04) | 0.06 (0.09) | 0.06 (0.13) | 0.18 (0.30) | 0.08 (0.15) |
0 | 0.00* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0.00 (0.00) | 1.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) |
0 | 0.13* (0.16) | 0.09* (0.10) | 0.19 (0.37) | 0.13 (0.19) | 0.04 (0.04) | 0.04 (0.04) | 0.06 (0.06) | 0.09 (0.16) | 0.05 (0.05) | 0.19 (0.30) |
0 | 0.07* (0.09) | 0.22* (0.38) | 0.14 (0.28) | 0.05 (0.10) | 0.02 (0.03) | 0.11 (0.25) | 0.05 (0.08) | 0.11 (0.16) | 0.17 (0.30) | 0.06 (0.07) |
0 | 0.11* (0.10) | 0.06* (0.07) | 0.14 (0.26) | 0.08 (0.10) | 0.04 (0.04) | 0.03 (0.04) | 0.17 (0.25) | 0.13 (0.19) | 0.14 (0.31) | 0.09 (0.17) |
0 | 0.01* (0.03) | 0.00* (0.01) | 0.02 (0.04) | 0.05 (0.09) | 0.45 (0.12) | 0.01 (0.01) | 0.08 (0.12) | 0.02 (0.05) | 0.35 (0.25) | 0.00 (0.01) |
0 | 0.14* (0.15) | 0.05* (0.06) | 0.17 (0.27) | 0.12 (0.27) | 0.03 (0.04) | 0.10 (0.18) | 0.08 (0.10) | 0.10 (0.11) | 0.05 (0.06) | 0.14 (0.26) |
Self-efficacy build | ||||||||||
0.80* (0.01) | 0.01* (0.01) | 0.18* (0.02) | 0.00 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.00* (0.00) | 1.00* (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.02* (0.02) | 0 | 0.00* (0.00) | 0 | 0.03 (0.05) | 0.61 (0.08) | 0.12 (0.13) | 0.15 (0.14) | 0.07 (0.08) | 0 | 0 |
0.01* (0.01) | 0 | 0 | 0.89 (0.02) | 0 | 0 | 0 | 0 | 0 | 0.06 (0.03) | 0.03 (0.02) |
0 | 0 | 0.31* (0.01) | 0 | 0.69 (0.01) | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1.00* (0.00) | 0 | 0 | 0.00 (0.00) | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0.02* (0.04) | 0 | 0 | 0 | 0.98 (0.04) | 0 | 0 | 0 | 0 |
0 | 0 | 0.11* (0.01) | 0 | 0 | 0 | 0 | 0.89 (0.01) | 0 | 0 | 0 |
0 | 0 | 0.29* (0.01) | 0 | 0 | 0 | 0 | 0 | 0.71 (0.01) | 0 | 0 |
0 | 0 | 0 | 0.35 (0.01) | 0 | 0 | 0 | 0 | 0 | 0.65 (0.01) | 0 |
0 | 0 | 0 | 0.04 (0.02) | 0 | 0 | 0 | 0 | 0 | 0 | 0.96 (0.02) |
Self-efficacy remove | ||||||||||
1.00* (0.00) | 0.00* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.07* (0.08) | 0.06* (0.08) | 0.19* (0.31) | 0.03 (0.07) | 0.16 (0.26) | 0.03 (0.03) | 0.04 (0.08) | 0.19 (0.26) | 0.04 (0.05) | 0.03 (0.04) | 0.17 (0.29) |
0.84* (0.00) | 0.16* (0.01) | 0.00* (0.00) | 0.00 (0.01) | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0.02* (0.04) | 0.01* (0.04) | 0.00* (0.00) | 0.09 (0.11) | 0.01 (0.02) | 0.02 (0.02) | 0.03 (0.02) | 0.14 (0.13) | 0.02 (0.02) | 0.64 (0.31) | 0.01 (0.02) |
0.09* (0.03) | 0.06* (0.04) | 0.20* (0.17) | 0.06 (0.06) | 0.10 (0.03) | 0.08 (0.10) | 0.04 (0.04) | 0.03 (0.02) | 0.05 (0.02) | 0.03 (0.02) | 0.27 (0.14) |
0.01* (0.01) | 0.02* (0.04) | 0.01* (0.02) | 0.02 (0.04) | 0.01 (0.01) | 0.00 (0.01) | 0.03 (0.06) | 0.45 (0.32) | 0.40 (0.31) | 0.02 (0.03) | 0.02 (0.02) |
0 | 0.00* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0.50 (0.01) | 0.50 (0.01) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) |
0 | 0.10* (0.13) | 0.00* (0.00) | 0.08 (0.10) | 0.02 (0.04) | 0.63 (0.09) | 0.09 (0.07) | 0.02 (0.02) | 0.01 (0.02) | 0.06 (0.05) | 0.00 (0.00) |
0 | 0.00* (0.00) | 0.00* (0.00) | 0.22 (0.41) | 0.00 (0.00) | 0.00 (0.00) | 0.06 (0.19) | 0.67 (0.47) | 0.05 (0.12) | 0.00 (0.01) | 0.00 (0.00) |
0 | 0.03* (0.06) | 0.05* (0.05) | 0.10 (0.16) | 0.02 (0.02) | 0.02 (0.03) | 0.02 (0.04) | 0.02 (0.06) | 0.68 (0.23) | 0.01 (0.02) | 0.04 (0.05) |
0 | 0.00* (0.00) | 0.07* (0.08) | 0.00 (0.00) | 0.02 (0.03) | 0.01 (0.02) | 0.00 (0.00) | 0.08 (0.26) | 0.71 (0.25) | 0.00 (0.00) | 0.11 (0.06) |
0 | 0.21* (0.12) | 0.02* (0.02) | 0.16 (0.12) | 0.02 (0.02) | 0.03 (0.03) | 0.21 (0.09) | 0.14 (0.14) | 0.06 (0.04) | 0.11 (0.07) | 0.02 (0.02) |
Willingness build | |||||||
0.05* (0.08) | 0.00 (0.00) | 0.49 (0.01) | 0.46 (0.07) | 0 | 0 | 0 | 0 |
1.00* (0.00) | 0.00 (0.00) | 0 | 0 | 0.00 (0.00) | 0 | 0 | 0 |
0.04* (0.06) | 0 | 0.96 (0.06) | 0 | 0 | 0 | 0 | 0 |
0.00* (0.00) | 0 | 0 | 0.15 (0.13) | 0 | 0.51 (0.24) | 0.34 (0.21) | 0.00 (0.00) |
0 | 0.51 (0.15) | 0 | 0 | 0.49 (0.15) | 0 | 0 | 0 |
0 | 0 | 0 | 0.53 (0.05) | 0 | 0.47 (0.05) | 0 | 0 |
0 | 0 | 0 | 0.49 (0.05) | 0 | 0 | 0.51 (0.05) | 0 |
0 | 0 | 0 | 0.24 (0.00) | 0 | 0 | 0 | 0.76 (0.00) |
Willingness remove | |||||||
0.02* (0.03) | 0.94 (0.15) | 0.01 (0.02) | 0.03 (0.09) | 0 | 0 | 0 | 0 |
0.25* (0.24) | 0.44 (0.34) | 0.04 (0.05) | 0.11 (0.31) | 0.03 (0.03) | 0.06 (0.10) | 0.03 (0.03) | 0.03 (0.01) |
0.30* (0.10) | 0.05 (0.06) | 0.10 (0.11) | 0.17 (0.15) | 0.13 (0.07) | 0.12 (0.08) | 0.07 (0.05) | 0.07 (0.01) |
0.20* (0.27) | 0.01 (0.02) | 0.00 (0.00) | 0.28 (0.29) | 0.16 (0.30) | 0.13 (0.16) | 0.22 (0.31) | 0.00 (0.00) |
0 | 0.26 (0.41) | 0.00 (0.00) | 0.04 (0.06) | 0.12 (0.16) | 0.30 (0.32) | 0.29 (0.33) | 0.01 (0.02) |
0 | 0.00 (0.00) | 0.00 (0.00) | 0.44 (0.39) | 0.08 (0.20) | 0.20 (0.29) | 0.28 (0.36) | 0.00 (0.00) |
0 | 0.03 (0.07) | 0.00 (0.00) | 0.15 (0.24) | 0.10 (0.17) | 0.40 (0.33) | 0.32 (0.32) | 0.00 (0.00) |
0 | 0.00 (0.00) | 0.20 (0.07) | 0.02 (0.02) | 0.01 (0.04) | 0.01 (0.01) | 0.02 (0.06) | 0.74 (0.01) |
Self-efficacy build | |||||||
0.96* (0.04) | 0.03 (0.03) | 0.00 (0.00) | 0.01 (0.02) | 0 | 0 | 0 | 0 |
0.00* (0.00) | 0.94 (0.01) | 0 | 0 | 0.06 (0.01) | 0 | 0 | 0 |
0.14* (0.00) | 0 | 0.86 (0.00) | 0 | 0 | 0 | 0 | 0 |
0.00* (0.00) | 0 | 0 | 0.93 (0.10) | 0 | 0.06 (0.10) | 0.00 (0.01) | 0.01 (0.01) |
0 | 0.01 (0.02) | 0 | 0 | 0.99 (0.02) | 0 | 0 | 0 |
0 | 0 | 0 | 0.31 (0.03) | 0 | 0.69 (0.03) | 0 | 0 |
0 | 0 | 0 | 0.00 (0.00) | 0 | 0 | 1.00 (0.00) | 0 |
0 | 0 | 0 | 0.14 (0.00) | 0 | 0 | 0 | 0.86 (0.00) |
Self-efficacy remove | |||||||
0.91* (0.02) | 0.05 (0.02) | 0.00 (0.00) | 0.03 (0.03) | 0 | 0 | 0 | 0 |
0.02* (0.01) | 0.67 (0.24) | 0.06 (0.01) | 0.14 (0.25) | 0.03 (0.03) | 0.05 (0.06) | 0.02 (0.01) | 0.02 (0.01) |
0.00* (0.01) | 0.00 (0.00) | 0.85 (0.01) | 0.03 (0.06) | 0.01 (0.01) | 0.00 (0.00) | 0.10 (0.06) | 0.00 (0.01) |
0.03* (0.05) | 0.26 (0.35) | 0.02 (0.03) | 0.04 (0.09) | 0.48 (0.38) | 0.06 (0.07) | 0.08 (0.12) | 0.02 (0.01) |
0 | 0.04 (0.02) | 0.03 (0.03) | 0.13 (0.12) | 0.34 (0.15) | 0.13 (0.13) | 0.18 (0.10) | 0.15 (0.15) |
0 | 0.18 (0.06) | 0.01 (0.01) | 0.08 (0.05) | 0.04 (0.03) | 0.52 (0.15) | 0.06 (0.04) | 0.12 (0.04) |
0 | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.01) | 0.00 (0.00) | 0.64 (0.02) | 0.35 (0.01) |
0 | 0.02 (0.01) | 0.00 (0.00) | 0.01 (0.01) | 0.01 (0.01) | 0.07 (0.04) | 0.02 (0.03) | 0.87 (0.03) |
Build | Remove | ||||||||
---|---|---|---|---|---|---|---|---|---|
Willingness | |||||||||
0.63 (0.05) | 0.01 (0.01) | 0.36 (0.05) | 0.00* (0.00) | 0 | 0.4 (0.21) | 0.01 (0.01) | 0.57 (0.20) | 0.02* (0.02) | 0 |
0.28 (0.00) | 0.72 (0.00) | 0 | 0 | 0 | 0.18 (0.08) | 0.70 (0.04) | 0.06 (0.06) | 0.01* (0.02) | 0.04 (0.06) |
0.00 (0.00) | 0 | 1.00 (0.00) | 0 | 0 | 0.00 (0.01) | 0.00 (0.00) | 0.99 (0.02) | 0.00* (0.00) | 0.00 (0.01) |
0.17 (0.00) | 0 | 0 | 0.83* (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.32 (0.00) | 0.00 (0.00) | 0.68* (0.00) | 0.00 (0.00) |
0 | 0 | 0 | 0.00* (0.01) | 1.00 (0.01) | 0 | 0.01 (0.01) | 0.61 (0.28) | 0.03* (0.02) | 0.35 (0.31) |
Self-efficacy | |||||||||
0.00 (0.00) | 0.87 (0.00) | 0.00 (0.00) | 0.13* (0.00) | 0 | 0.72 (0.06) | 0.08 (0.02) | 0.15 (0.04) | 0.04* (0.03) | 0 |
1.00 (0.00) | 0.00 (0.00) | 0 | 0 | 0 | 0.00 (0.00) | 0.70 (0.01) | 0.00 (0.00) | 0.25* (0.04) | 0.05 (0.05) |
0.03 (0.02) | 0 | 0.97 (0.02) | 0 | 0 | 0.01 (0.01) | 0.00 (0.00) | 0.99 (0.01) | 0.00* (0.00) | 0.00 (0.00) |
0.00 (0.00) | 0 | 0 | 1.00* (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 0.00 (0.00) | 1.00* (0.00) | 0.00 (0.00) |
0 | 0 | 0 | 0.10* (0.04) | 0.90 (0.04) | 0 | 0.00 (0.00) | 0.07 (0.00) | 0.91* (0.03) | 0.02 (0.03) |
Build | Remove | ||||||
---|---|---|---|---|---|---|---|
Willingness | |||||||
0.50* (0.09) | 0.50* (0.09) | 0.00 (0.00) | 0.00 (0.00) | 0.48* (0.06) | 0.52* (0.06) | 0.00 (0.00) | 0.00 (0.00) |
0.49* (0.06) | 0.51* (0.06) | 0 | 0 | 0.53* (0.14) | 0.47* (0.14) | 0.00 (0.00) | 0.00 (0.00) |
0.04* (0.00) | 0 | 0.96 (0.00) | 0 | 0.00* (0.00) | 0.00* (0.00) | 0.68 (0.01) | 0.32 (0.01) |
0.21* (0.00) | 0 | 0 | 0.79 (0.00) | 0.12* (0.07) | 0.09* (0.07) | 0.00 (0.00) | 0.79 (0.00) |
Self-efficacy | |||||||
0.71* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0.29 (0.00) | 0.71* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 0.29 (0.00) |
0.12* (0.00) | 0.88* (0.00) | 0 | 0 | 0.10* (0.03) | 0.88* (0.01) | 0.00 (0.01) | 0.02 (0.03) |
0.00* (0.00) | 0 | 1.00 (0.00) | 0 | 0.00* (0.00) | 0.00* (0.00) | 1.00 (0.00) | 0.00 (0.00) |
0.00* (0.00) | 0 | 0 | 1.00 (0.00) | 0.00* (0.00) | 0.00* (0.00) | 0.00 (0.00) | 1.00 (0.00) |
Network | Measure | Adjacency | \({\mathbf{RMSE}}_{{{\mathbf{alg}}}}\) | \({\mathbf{RMSE}}_{{{\mathbf{fit}}}}\) |
---|---|---|---|---|
1 (\(N=12\)) | Willingness | Build | 0.09 | 0.36 (0.01) |
Remove | 0.16 | 0.37 (0.02) | ||
Self-efficacy | Build | 0.04 | 0.51 (0.00) | |
Remove | 0.00 | 0.28 (0.02) | ||
2 (\(N=11\)) | Willingness | Build | 0.12 | 0.45 (0.00) |
Remove | 0.19 | 0.42 (0.01) | ||
Self-efficacy | Build | 0.04 | 0.23 (0.00) | |
Remove | 0.00 | 0.23 (0.01) | ||
3 (\(N=8\)) | Willingness | Build | 0.09 | 0.33 (0.01) |
Remove | 0.20 | 0.33 (0.00) | ||
Self-efficacy | Build | 0.03 | 0.21 (0.01) | |
Remove | 0.00 | 0.15 (0.00) | ||
4 (\(N=5\)) | Willingness | Build | 0.02 | 0.71 (0.00) |
Remove | 0.11 | 0.70 (0.03) | ||
Self-efficacy | Build | 0.02 | 0.54 (0.00) | |
Remove | 0.00 | 0.42 (0.00) | ||
5 (\(N=4\)) | Willingness | Build | 0.05 | 0.32 (0.00) |
Remove | 0.06 | 0.29 (0.00) | ||
Self-efficacy | Build | 0.00 | 0.38 (0.00) | |
Remove | 0.00 | 0.38 (0.00) |
Comparison of leaders to other agents
Network | Adjacency | Leader | Self-weight | Weight | Proportion | Number |
---|---|---|---|---|---|---|
1 (\(N=12\)) | Build | Leader | 0.50 (0.21) | 0.21 (0.29) | 0.79 | 11 |
Non-leader | 0.74 (0.34) | 0.14 (0.17) | 0.88 | 7 | ||
Remove | Leader | 0.40 (0.26) | 0.11 (0.18) | 0.72 | 26 | |
Non-leader | 0.30 (0.26) | 0.05 (0.08) | 0.55 | 44 | ||
2 (\(N=11\)) | Build | Leader | 0.61 (0.52) | 0.17 (0.15) | 0.70 | 7 |
Non-leader | 0.66 (0.41) | 0.15 (0.16) | 0.75 | 6 | ||
Remove | Leader | 0.37 (0.55) | 0.09 (0.07) | 0.78 | 18 | |
Non-leader | 0.23 (0.33) | 0.08 (0.08) | 0.88 | 64 | ||
3 (\(N=8\)) | Build | Leader | 0.05 (NA) | 0.35 (0.57) | 0.67 | 2 |
Non-leader | 0.48 (0.33) | 0.26 (0.25) | 0.57 | 4 | ||
Remove | Leader | 0.02 (NA) | 0.25 (0.05) | 1.00 | 3 | |
Non-leader | 0.31 (0.22) | 0.11 (0.17) | 0.80 | 36 | ||
4 (\(N=5\)) | Build | Leader | 0.83 (NA) | 0.00 (0.00) | 0.00 | 0 |
Non-leader | 0.84 (0.19) | 0.14 (0.16) | 0.67 | 4 | ||
Remove | Leader | 0.68 (NA) | 0.02 (0.01) | 0.75 | 3 | |
Non-leader | 0.61 (0.30) | 0.13 (0.21) | 0.57 | 8 | ||
5 (\(N=4\)) | Build | Leader | 0.50 (0.01) | 0.31 (0.23) | 1.00 | 4 |
Non-leader | 0.88 (0.12) | 0.00 (0.00) | 0.00 | 0 | ||
Remove | Leader | 0.48 (0.01) | 0.21 (0.25) | 0.67 | 4 | |
Non-leader | 0.74 (0.08) | 0.05 (0.13) | 0.17 | 1 |
Network | Adjacency | Leader | Self-Weight | Weight | Proportion | Number |
---|---|---|---|---|---|---|
1 (\(N=12\)) | Build | Leader | 0.76 (0.18) | 0.05 (0.07) | 0.57 | 8 |
Non-leader | 0.97 (0.05) | 0.07 (0.15) | 0.50 | 4 | ||
Remove | Leader | 0.50 (0.23) | 0.04 (0.05) | 0.58 | 21 | |
Non-leader | 0.55 (0.39) | 0.05 (0.12) | 0.54 | 43 | ||
2 (\(N=11\)) | Build | Leader | 0.60 (0.53) | 0.20 (0.31) | 0.90 | 9 |
Non-leader | 0.72 (0.32) | 0.13 (0.20) | 0.88 | 7 | ||
Remove | Leader | 0.35 (0.43) | 0.04 (0.06) | 0.57 | 13 | |
Non-leader | 0.32 (0.29) | 0.09 (0.16) | 0.70 | 51 | ||
3 (\(N=8\)) | Build | Leader | 0.96 (NA) | 0.05 (0.08) | 0.33 | 1 |
Non-leader | 0.90 (0.11) | 0.02 (0.03) | 0.71 | 5 | ||
Remove | Leader | 0.91 (NA) | 0.02 (0.01) | 0.67 | 2 | |
Non-leader | 0.56 (0.29) | 0.07 (0.10) | 0.78 | 35 | ||
4 (\(N=5\)) | Build | Leader | 1.00 (NA) | 0.12 (0.02) | 1.0 | 2 |
Non-leader | 0.47 (0.54) | 0.22 (0.44) | 0.25 | 1 | ||
Remove | Leader | 1.00 (NA) | 0.30 (0.42) | 0.75 | 3 | |
Non-leader | 0.61 (0.41) | 0.03 (0.05) | 0.36 | 5 | ||
5 (\(N=4\)) | Build | Leader | 0.80 (0.12) | 0.03 (0.06) | 0.25 | 1 |
Non-leader | 1.00 (0.00) | 0.14 (0.21) | 0.5 | 1 | ||
Remove | Leader | 0.80 (0.12) | 0.02 (0.04) | 0.17 | 1 | |
Non-leader | 1.00 (0.00) | 0.05 (0.12) | 0.33 | 2 |