Simulation and Analysis of Social Influence Network Models

Tools for specifying, analyzing and simulating models of social influence network theory based on the Friedkin-Johnsen model, Friedkin and Johnsen (1990) , which includes the consensus model of DeGroot (1974) as a special case. Equilibrium opinions, total influence matrices and convergence diagnostics are computed in closed form, also for signed networks with antagonistic ties, Altafini (2013) . Simulations allow influence weights and susceptibilities to depend on time and on the state of the system, and can couple latent opinions with manifest responses through logistic or threshold response functions, whose results are aggregated into collective outcomes by quota rules.

SINT

SINT provides tools for specifying, analyzing and simulating models of social influence network theory based on the Friedkin-Johnsen model. The latent dynamics

$$y(t+1) = \Lambda W y(t) + (I - \Lambda) y(0)$$

can be analyzed in closed form (equilibrium, total influence matrix, convergence diagnostics, also for signed networks) or simulated with influence weights and susceptibilities that depend on time and on the state of the system. An optional response stage maps latent opinions to manifest responses, which can then be aggregated into collective outcomes.

Installation

You can install the development version of SINT from GitHub with:

# install.packages("remotes")
remotes::install_github("Silvestro26/SINT")

Example

Three agents with influence matrix W, susceptibilities lambda and initial opinions y0:

library(SINT)

W <- matrix(c(0.5, 0.5, 0,
              0.2, 0.6, 0.2,
              0,   0.3, 0.7), nrow = 3, byrow = TRUE)
lambda <- c(0.8, 0.5, 0.9)
y0 <- c(0, 0.5, 1)

fj_check(W, lambda)$converges
#> [1] TRUE
fj_equilibrium(W, lambda, y0)
#> [1] 0.3295820 0.4943730 0.6310289

The total influence matrix gives the weight of each initial opinion in each equilibrium opinion:

round(fj_influence(W, lambda), 3)
#>       [,1]  [,2]  [,3]
#> [1,] 0.373 0.595 0.032
#> [2,] 0.059 0.892 0.048
#> [3,] 0.043 0.651 0.305

See vignette("SINT") for a complete guide to the package.