27/replication_package/Network-sample-calculations_script.R

#package installation
# install.packages('plyr')
# install.packages('dplyr')
# install.packages('tidyr')
# install.packages('igraph')
# install.packages('geosphere')
# install.packages('ggplot2')
# install.packages('tictoc')

rm(list=ls())
library(plyr);library(dplyr, warn.conflicts = F)
library(tidyr)
library(igraph)
library(geosphere)
library(ggplot2, warn.conflicts = F)
library(tictoc)

#setwd() #set working directory
dir.create(paste0(getwd(), '/Output/'))
dir.create(paste0(getwd(), '/Output/Network-sample-calculations/'))
path0 = paste0(getwd(), '/Output/Network-sample-calculations/', Sys.Date(),'/') #Directory for output files
dir.create(path0)

s = function(x){summary(factor(x))}

dat = readRDS('4-20-20_Network-KNearest_DeID_demed.RDS')
################################################################################################

tic()
out_sim_list = readRDS('4-21-20_1000x_sample_nearest.RDS')
toc() #

cor_df = data.frame(Nearest5_SameRel_samp_AllLinksSameRelig = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig = rep(NA, length(out_sim_list)),
                    
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh1 = rep(NA, length(out_sim_list)),
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh2 = rep(NA, length(out_sim_list)),
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh3 = rep(NA, length(out_sim_list)),
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh4 = rep(NA, length(out_sim_list)),
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh5 = rep(NA, length(out_sim_list)),
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh6 = rep(NA, length(out_sim_list)),
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh7 = rep(NA, length(out_sim_list)),
                    Nearest5_SameRel_samp_AllLinksSameRelig_Neigh8 = rep(NA, length(out_sim_list)),
                    
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh1 = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh2 = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh3 = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh4 = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh5 = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh6 = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh7 = rep(NA, length(out_sim_list)),
                    Nearest10_SameRel_samp_AllLinksSameRelig_Neigh8 = rep(NA, length(out_sim_list)),
                    
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh1 = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh2 = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh3 = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh4 = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh5 = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh6 = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh7 = rep(NA, length(out_sim_list)),
                    Nearest15_SameRel_samp_AllLinksSameRelig_Neigh8 = rep(NA, length(out_sim_list))
                    )

tic()
for(i in 1:length(out_sim_list)){
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig[i] =  #nearest 5 religion correlation
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp, out_sim_list[[i]]$AllLinksSameRelig, use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig[i] =  #nearest 10 religion correlation
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp, out_sim_list[[i]]$AllLinksSameRelig, use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig[i] =  #nearest 5 religion correlation
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp, out_sim_list[[i]]$AllLinksSameRelig, use = 'pairwise.complete.obs')
  
  
  #nearest-5
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh1[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 1")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 1")], use = 'pairwise.complete.obs')
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh2[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 145")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 145")], use = 'pairwise.complete.obs')
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh3[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 30")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 30")], use = 'pairwise.complete.obs')
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh4[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 68")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 68")], use = 'pairwise.complete.obs')
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh5[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 42")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 42")], use = 'pairwise.complete.obs')
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh6[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 51")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 51")], use = 'pairwise.complete.obs')
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh7[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 82")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 82")], use = 'pairwise.complete.obs')
  cor_df$Nearest5_SameRel_samp_AllLinksSameRelig_Neigh8[i] = 
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 93")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 93")], use = 'pairwise.complete.obs')
  
  #nearest-10
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh1[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 1")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 1")], use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh2[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 145")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 145")], use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh3[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 30")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 30")], use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh4[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 68")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 68")], use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh5[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 42")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 42")], use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh6[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 51")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 51")], use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh7[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 82")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 82")], use = 'pairwise.complete.obs')
  cor_df$Nearest10_SameRel_samp_AllLinksSameRelig_Neigh8[i] = 
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 93")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 93")], use = 'pairwise.complete.obs')
  
  #nearest-15
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh1[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 1")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 1")], use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh2[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 145")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 145")], use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh3[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 30")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 30")], use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh4[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 68")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Jaipur 68")], use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh5[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 42")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 42")], use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh6[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 51")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 51")], use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh7[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 82")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 82")], use = 'pairwise.complete.obs')
  cor_df$Nearest15_SameRel_samp_AllLinksSameRelig_Neigh8[i] = 
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp[which(out_sim_list[[i]]$A.A7 ==  "Patna 93")],
        out_sim_list[[i]]$AllLinksSameRelig[which(out_sim_list[[i]]$A.A7 ==  "Patna 93")], use = 'pairwise.complete.obs')
  
} #throws a warning about "standard deviation is 0", because sometimes by chance everyone has the same Nearest10 score
toc() #2.5 sec


#histograms for nearest-k vs contact correlations from neighborhood samples
#FIGURE A3
ggplot(data = cor_df, aes(cor_df$Nearest10_SameRel_samp_AllLinksSameRelig)) + geom_histogram(aes(y = (..count..)/sum(..count..)  ), bins = 50) +
  theme_bw() + labs(x = 'Correlation, Nearest-k vs Outgroup Contacts', y = 'Proportion') + 
  ggtitle('Nearest-10 Same Religion vs. Outgroup Contacts\nSample of 60 per neighborhood\nAll neighborhoods together') + 
  theme(plot.title = element_text(hjust = 0.5, size = 14))
ggsave(filename = paste0(path0, 'k_contact_networksamp_histogram.png'), height = 150, width = 150, units = 'mm'); rm(path0)

#*******RESULT******#
#Correlations over 1k iterations between k-nearest score calculated for random sam- ple of 60 individuals from each neighborhood, versus contact with individuals from another religion.
#TABLE A2
mean(cor_df$Nearest5_SameRel_samp_AllLinksSameRelig) #0.4181599 
sd(cor_df$Nearest5_SameRel_samp_AllLinksSameRelig) #0.05066349 
mean(cor_df$Nearest10_SameRel_samp_AllLinksSameRelig) #0.4312065 
sd(cor_df$Nearest10_SameRel_samp_AllLinksSameRelig) #0.0466517 
mean(cor_df$Nearest15_SameRel_samp_AllLinksSameRelig) #0.4375551 
sd(cor_df$Nearest15_SameRel_samp_AllLinksSameRelig) #0.04528044 
###############################################################################################################################################


################################################################################################################################################

#*******RESULT******#
#Relationship between proportion of the 10 nearest neighbors of another religion, and proportion who have any contacts with members of another religion.
#TABLE A3

sum(dat$AllLinksSameRelig < 1, na.rm = T) / sum(dat$Nearest10_SameRel <= 10, na.rm = T) # 15% of whole sample have non-homogeneous contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel == 10, na.rm = T) / sum(dat$Nearest10_SameRel == 10, na.rm = T) #1% of samerel = 10 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 10, na.rm = T) / sum(dat$Nearest10_SameRel < 10, na.rm = T) #26% of samerel < 10 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 9, na.rm = T) / sum(dat$Nearest10_SameRel < 9, na.rm = T) #30% of samerel < 9 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 8, na.rm = T) / sum(dat$Nearest10_SameRel < 8, na.rm = T) #33% of samerel < 8 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 7, na.rm = T) / sum(dat$Nearest10_SameRel < 7, na.rm = T) #37% of samerel < 7 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 6, na.rm = T) / sum(dat$Nearest10_SameRel < 6, na.rm = T) #38% of samerel < 6 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 5, na.rm = T) / sum(dat$Nearest10_SameRel < 5, na.rm = T) #41% of samerel < 5 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 4, na.rm = T) / sum(dat$Nearest10_SameRel < 4, na.rm = T) #46% of samerel < 4 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 3, na.rm = T) / sum(dat$Nearest10_SameRel < 3, na.rm = T) #54% of samerel < 3 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 2, na.rm = T) / sum(dat$Nearest10_SameRel < 2, na.rm = T) #66% of samerel < 2 have hetero contacts
sum(dat$AllLinksSameRelig < 1 & dat$Nearest10_SameRel < 1, na.rm = T) / sum(dat$Nearest10_SameRel < 1, na.rm = T) #75% of samerel < 1 have hetero contacts
s(dat$Nearest10_SameRel)

sum(dat$Nearest10_SameRel == 10, na.rm = T) #1159
sum(dat$Nearest10_SameRel < 10, na.rm = T) #1422
sum(dat$Nearest10_SameRel < 9, na.rm = T) #1134
sum(dat$Nearest10_SameRel < 8, na.rm = T) #909
sum(dat$Nearest10_SameRel < 7, na.rm = T) #734
sum(dat$Nearest10_SameRel < 6, na.rm = T) #539
sum(dat$Nearest10_SameRel < 5, na.rm = T) #378
sum(dat$Nearest10_SameRel < 4, na.rm = T) #240
sum(dat$Nearest10_SameRel < 3, na.rm = T) #135
sum(dat$Nearest10_SameRel < 2, na.rm = T) #68
sum(dat$Nearest10_SameRel < 1, na.rm = T) #28

################################################################################################################################################
#What is relationship between census-nearest-K and sample-nearest-K?

k_cor_df = data.frame(SameRel_5_cor = rep(NA, length(out_sim_list)),
                      SameRel_10_cor = rep(NA, length(out_sim_list)),
                      SameRel_15_cor = rep(NA, length(out_sim_list)),
                      
                      SameRel_10_cor_neigh1 = rep(NA, length(out_sim_list)),
                      SameRel_10_cor_neigh2 = rep(NA, length(out_sim_list)),
                      SameRel_10_cor_neigh3 = rep(NA, length(out_sim_list)),
                      SameRel_10_cor_neigh4 = rep(NA, length(out_sim_list)),
                      SameRel_10_cor_neigh5 = rep(NA, length(out_sim_list)),
                      SameRel_10_cor_neigh6 = rep(NA, length(out_sim_list)),
                      SameRel_10_cor_neigh7 = rep(NA, length(out_sim_list)),
                      SameRel_10_cor_neigh8 = rep(NA, length(out_sim_list))
                      
                      )
for(i in 1:length(out_sim_list)){
  k_cor_df$SameRel_5_cor[i] =  #nearest 5 religion correlation
    cor(out_sim_list[[i]]$Nearest5_SameRel_samp, out_sim_list[[i]]$Nearest5_SameRel, use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor[i] =  #nearest 10 religion correlation
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp, out_sim_list[[i]]$Nearest10_SameRel, use = 'pairwise.complete.obs')
  k_cor_df$SameRel_15_cor[i] =  #nearest 15 religion correlation
    cor(out_sim_list[[i]]$Nearest15_SameRel_samp, out_sim_list[[i]]$Nearest15_SameRel, use = 'pairwise.complete.obs')
  
  
  k_cor_df$SameRel_10_cor_neigh1  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Jaipur 1')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Jaipur 1')], use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor_neigh2  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Jaipur 145')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Jaipur 145')], use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor_neigh3  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Jaipur 30')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Jaipur 30')], use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor_neigh4  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Jaipur 68')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Jaipur 68')], use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor_neigh5  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Patna 42')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Patna 42')], use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor_neigh6  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Patna 51')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Patna 51')], use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor_neigh7  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Patna 82')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Patna 82')], use = 'pairwise.complete.obs')
  k_cor_df$SameRel_10_cor_neigh8  =  #nearest 10 religion correlation, neigh x
    cor(out_sim_list[[i]]$Nearest10_SameRel_samp[which(out_sim_list[[i]]$A.A7 == 'Patna 93')], 
        out_sim_list[[i]]$Nearest10_SameRel[which(out_sim_list[[i]]$A.A7 == 'Patna 93')], use = 'pairwise.complete.obs')

}#throws a warning about "standard deviation is 0", because sometimes by chance everyone in random sample has the same Nearest10 score

#*******RESULT******#
#Correlation between k-nearest score calculated for random sample of 60 individuals from each neighborhood, versus the same metric calculated for the entire neighborhood. The reported means and standard deviations of the correlations are for 500 random samples of 60 individuals from each neighborhood.
#TABLE A1
mean(k_cor_df$SameRel_5_cor) # 0.7706546 
sd(k_cor_df$SameRel_5_cor) # 0.02571546 
mean(k_cor_df$SameRel_10_cor) # 0.8508894
sd(k_cor_df$SameRel_10_cor) # 0.01996775 
mean(k_cor_df$SameRel_15_cor) #  0.8735986 
sd(k_cor_df$SameRel_15_cor) # 0.01815468 
################################################################################################################################################