NetBootstrap

This is the first version of the R package 'NetBootstrap'.

To install and use the package, we recommend installing the package by

install.packages("devtools")  # If not already installed
library(devtools)
install_github("Wei-M-Wei/NetBootstrap")

Once installed, load the package with

library(NetBootstrap)

Features

• Main functionality: Perform parametric bootstrap inference in the netwrok formulation models, see the paper ¹.
• Validation example: An example 'test_example.R' is included. 'network_bootstrap(y, X, N, bootstrap_time, data, index, link = 'probit')' is the main function.

• help(network_bootstrap) # check an example provided
  

Additional resources

• Replication code: The repository includes replication code for all simulations and empirical applications.
• Suggestions welcome: Further improvements are planned, and we encourage feedback and suggestions to enhance the package.

Example

rm(list = ls())
library(NetBootstrap)

# Generate the simulated data
N = 30
K = 1
beta = 1
alpha = rep(0, N)
gamma = rep(0, N)
dens_N_up = log(log(N))
dens_N_low = -log(log(N))
dens_T_up = log(log(N))
dens_T_low = -log(log(N))
for (i in seq(N)){
  alpha[i] = dens_N_low + ((i - 1) / ( N - 1)) * (dens_N_up - dens_N_low)
}
for (i in seq(N)){
  gamma[i] = dens_T_low + ((i - 1) / ( N - 1)) * (dens_T_up - dens_T_low)
}

Z = array(0, dim = c(N, N, K))
Y = matrix(0, nrow = N, ncol = N)
for (t in seq(N)) {
  for (i in seq(N)) {
    epsi_it = rnorm(1, 0, 1)
    if ( t %% 2 == 0 & i %% 2 == 0){
      Z[i, t, ] = (1 - 2 * 1*(0)) * (1 - 2 * 1*(0))
    } else if(t %% 2 == 0 & i %% 2 == 1){
      Z[i, t, ] = (1 - 2 * 1*(1)) * (1 - 2 * 1*(0))
    } else if(t %% 2 == 1 & i %% 2 == 0){
      Z[i, t, ] = (1 - 2 * 1*(0)) * (1 - 2 * 1*(1))
    } else{
      Z[i, t, ] = (1 - 2 * 1*(1)) * (1 - 2 * 1*(1))
    }
    Y[i, t] = (beta * Z[i, t, ] + alpha[i] + gamma[t] > epsi_it)

  }
}


# final data
y = c(Y[!row(Y) == col(Y)])
X_in = matrix(0, N * N, K )
index_matrix = matrix(0, N * N, 2)
for (t in seq(N)) {
  for (i in seq(N)) {
    alpha_in = rep(0, N)
    gamma_in = rep(0, N)
    alpha_in[i] = 1
    gamma_in[t] = 1
    X_in[i + (t - 1) * N,] = c(Z[i,t,])
    index_matrix[i + (t - 1) * N,] = c(i,t)
  }
}
drop_index = NULL
for (i in seq(N)){
  drop_index = cbind(drop_index, i + (i - 1) * N)
}
X_design = as.matrix(X_in[-drop_index,])
index_in = index_matrix[-drop_index,]

# estimation procedure
data_in = data.frame(y = y, X = X_design, index = index_in)
index_name = colnames(data_in)[(K+2):(K+3)]
fit = network_bootstrap(y = y, X = X_design, N = N, bootstrap_time = 599, index = c('index.1', 'index.2'), data = data_in, link = 'probit')

# get the results
est_MLE = fit$cof_MLE[1]

# corrected by the mean of the bootstrap estimates
est_corrected_mean = fit$cof_mean[1]

# corrected by the median of the bootstrap estimates
est_corrected_median = fit$cof_median[1]

sd = fit$sd

Another Example

rm(list = ls())
library(NetBootstrap)

# This file can be found in 'reproduce code'
source('simulation data.R')

#generate the simulated data
N = 30
K = 1

# a specific design for the simulation data, see our paper for more details
design = 1
beta = c(1)

# prepare the data
DGP = data_generation(N = N, beta = beta, design = design)
y = DGP$y
X_design = DGP$X
data_in = DGP$data
index_name = colnames(data_in)[(K+2):(K+3)]

# estimation
fit = network_bootstrap(y = y, X = X_design, N = N, bootstrap_time = bootstrap_time, index = index_name, data = data_in, link = 'probit')

# get the results
est_MLE = fit$cof_MLE[1]

# corrected by the mean of the bootstrap estimates
est_corrected_mean = fit$cof_mean[1]

# corrected by the median of the bootstrap estimates
est_corrected_median = fit$cof_median[1]

A CRAN release is coming soon.

Reference

Footnotes

1. Haoyaun, X., Wei, M., Dhaene, G., Beyhum, J. Parametric bootstrap inference in network formation models. ↩