README.md

In insongkim/polnet: Mapping Political Communities: A Statistical Analysis of Lobbying Networks in Legislative Politics

polnet: A Statistical Analysis of Political Networks

This R package provides a computationally efficient way of fitting the Latent Space Network Model (LSM) and bipartite Link Community Model (biLCM) developed by Kim and Kunisky (2018).

Authors

In Song Kim, Dmitriy Kunisky, Sean (Shiyao) Liu, Sooahn Shin

Paper

Mapping Political Communities: A Statistical Analysis of Lobbying Networks in Legislative Politics

Installation

There is currently no package available for the LNSM or biLCM models on CRAN. It is possible to download the package through GitHub instead.

First, make sure the devtools package is installed.

if(!require(devtools)) install.packages("devtools")

This only has to be done if devtools is not already installed and only has to be done once.

Then, use the install_github() function from devtools to install the package.

library(devtools)
install_github("insongkim/polnet", dependencies = TRUE, ref = "master")

Note on 64-bit Windows Compatibility

This package depends on RStan and further on RCpp and C++ compilers. Please make sure in your system environment the path to a 64-bit C++ compiler has been correctly specified and prioritized.

Further, if your R console is not up to the latest version, run the following code before installing the package from github to suppress the warning message indicating packages are built on an R console later than your version.

Sys.setenv(R_REMOTES_NO_ERRORS_FROM_WARNINGS="true")

Examples

biLCM

The example of biLCM using synthetic data is as follows.

library(polnet)
set.seed(11)
# Generate Synthetic Data
sim.data <- random_biLCM_data(m = 100, n = 50, k = 4, kappa_weight = NULL, a = 10000, b = 1, 
                              alpha_membership = NULL, alpha_c = rep(0.5, 100), 
                              beta_membership = NULL, beta_c = rep(0.5, 50), non_zero = TRUE)
res <- biLCM(edges = sim.data$A, group1.id = NULL, group2.id = NULL, count.id = NULL, k = 4,
             tolerance = 1e-6, max.iter = 200)
plot.compare.biLCM(res, sim.data, group1 = TRUE, nth = 10)

The following plot compares true and estimated community distribution of the 10th actor in the first group (i.e., (α10,1,α10,2,α10,3,α10,4)). Note that the order of communities is permutation-invariant.

LSM with variational inference

The example of LSM (with variational inference) using synthetic data is as follows. The largest advantage for running a variational inference version of the LSM model is its speed. As a result, this becomes useful in the case where the researcher is interested in identifying the 'clusters' of the units.

library("polnet")
set.seed(11)
# Generate Synthetic Data
sim.data <- random_LSM_data_cluster(n.cluster=4, 
                                     group1.center=rbind(c(-0.5,-1), c(-1, 0.3), c(0.4, 1), c(0.2, -0.2))*5,    
                                     group2.center=rbind(c(-0.5,-1), c(-1, 0.3), c(0.4, 1), c(0.2, -0.2))*5, 
                                     v=3, sigma_sq_L = 0.5, sigma_sq_P = 0.7, tau=c(0.5, 0.8))
res <- LSM(sim.data$LSM_data$A, D=2, method = "vi", iter=50000)
plot.compare.LSM(res, sim.data$LSM_data$Theta, sim.data$LSM_data$Psi, sim.data$group1.popularity, 
                  sim.data$group2.popularity, sim.data$group1.cluster, sim.data$group2.cluster, 
                  legend_position = "center")

LSM with MCMC

If a researcher wants to do a full MCMC procedure with her data. We recommend the following procedure:

1. Run a variational inference version of the LSM model.

2. Fix the coordinates of 2 * d actors and run the full MCMC model.

The reason to fix 2 * d actors is to achieve identification by removing rotational/flipping/reflectional invariance, where d is the dimension of the model. If 2 * d cannot achieve identification for your data, you may increase the number of fixed actors until identification has been achieved.

We now illustrate this procedure with a synthetic data. We first run a variational inference version of LSM on the synthetic dataset.

library("polnet")
set.seed(11)
# Generate Synthetic Data
sim.data <- random_LSM_data_cluster(n.cluster=4, 
                                     group1.center=rbind(c(-0.5,-1), c(-1, 0.3), c(0.4, 1), c(0.2, -0.2))*5, 
                                     group2.center=rbind(c(-0.5,-1), c(-1, 0.3), c(0.4, 1), c(0.2, -0.2))*5, 
                                     v=3, sigma_sq_L = 0.5, sigma_sq_P = 0.7, tau=c(0.5, 0.8))

# Quick Estimation with Variational Inference 
res.vb <- LSM(sim.data$LSM_data$A, D=2, method = "vi", iter=50000)
plot.compare.LSM(res.vb, sim.data$LSM_data$Theta, 
                  sim.data$LSM_data$Psi, sim.data$group1.popularity, 
                  sim.data$group2.popularity, sim.data$group1.cluster, 
                  sim.data$group2.cluster, legend_position = "center")

We then choose the wildest row and column actors from the posterior estimates from the LSM model (vi version). There are different ways to do this choice. We have embedded two algorithms in our choose.fix function. Here we use the o

fix.actors <- choose.fix(res.vb, choose.method="axis")

We then run the full MCMC model with the coordinates of these chosen actors fixed.

res.mcmc <- LSM(sim.data$LSM_data$A, D=2, 
          method = "mcmc", iter=2000, 
          fixed.actor.object = fix.actors, 
          cores=4, control = list(max_treedepth = 20))

The following plot compares the MCMC posterior coordinates of actors with their true coordinates.

plot.compare.LSM(res.mcmc, sim.data$LSM_data$Theta, sim.data$LSM_data$Psi, sim.data$group1.popularity, 
                  sim.data$group2.popularity, sim.data$group1.cluster, sim.data$group2.cluster, 
                  legend_position = "center")

biLCM with latent position

The pie charts of biLCM can be combined with the latent position of members as shown in figure 8 of the paper. plot.biLCM.position plots legislation community distributions estimated by biLCM at their corresponding latent position. The following plot combines the result of biLCM with the latent position estimated by LSM.

library(polnet)
set.seed(11)
# Generate Synthetic Data
sim.data <- random_biLCM_data(m = 20, n = 10, k = 4, kappa_weight = NULL, a = 10000, b = 1,
                              alpha_membership = NULL, alpha_c = rep(0.5, 100),
                              beta_membership = NULL, beta_c = rep(0.5, 50), non_zero = TRUE)
LSM_res <- LSM(sim.data$A, D=2, method = "vi", iter=50000)
bilcm_res <- biLCM(edges = sim.data$A, group1.id = NULL, group2.id = NULL, count.id = NULL, k = 4,
                   tolerance = 1e-6, max.iter = 200)
plot.biLCM.position(biLCM_Object = bilcm_res, LSM_Object = LSM_res, legend_position = "none")

insongkim/polnet documentation built on March 3, 2020, 11:55 p.m.