Introduction: Theoretical Argument, Hypotheses and Data
When a state forms a foreign alliance with another state, it likely does not only consider that state in itself, but also the network it is embedded in. Rather than solely dyadic-based considerations, states’ position in the network, and their geostrategic and economic embeddedness therefore matter for alliance formation.
Asking the question of what could explain the alliance network structure in the year 2012, I want to first examine explanations related to homophily, before looking at partial conditional dependencies.
More specifically, the dyadic effects I focus on are homophily in terms of a shared subcontinent, similar human development, and level of democratic freedom. I then also hypothesize that there is a clustering around repeated alliance choice.
In order to examine these hypotheses, I merge a dyadic, directed network dataset from the Correlates of War Project with data on political rights from Freedom House (ordinal values from 1 to 7), and with the UN’s human development index.
Prettier Overview of Hypotheses:
a<-"Dyad independence"
b1<-"Countries are more likely to form alliances if they have a) matching regions"
b2<- "... b) matching levels of political rights"
b3<- "... c) matching levels of human development"
c<- "Partial conditional dependency"
d<-"Alliances cluster around repeated alliance choice"
a1<-cbind(a,b1)
a2<-cbind(a,b2)
a3<-cbind(a,b3)
b<-cbind(c,d)
Hypotheses<-rbind(a1,a2,a3,b)
colnames(Hypotheses)<-c("Level of Dependence", "Hypothesis")
rownames(Hypotheses)<-c("H1a", "H1b", "H1c", "H2")
##View(Hypotheses) to see tableBuilding the Dataset
#Downloading COW Foreign Alliances Dataset
library(haven)
library(foreign)
library(igraph)##
## Attaching package: 'igraph'## The following objects are masked from 'package:stats':
##
## decompose, spectrum## The following object is masked from 'package:base':
##
## uniondata<-read_dta("/Users/leaschaad/Desktop/This/alliance_v4.1_by_directed_yearly.dta")
##filter by year 2012
library(dplyr)##
## Attaching package: 'dplyr'## The following objects are masked from 'package:igraph':
##
## as_data_frame, groups, union## The following objects are masked from 'package:stats':
##
## filter, lag## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, unionlibrary(ggplot2)
data<-subset(data, year == 2012)
## Restricting to dyads
data<-select(data, state_name1, state_name2)
#Downloading Freedom House Region and Democracy Attributes Dataset
library(readxl)
fh<-read_xls("/Users/leaschaad/Desktop/This/All_data_FIW_2013-2021.xls")
##restricting to year 2013
fh<-subset(fh, Edition == "2013") ###didn't have 2012, but 2013 is very similar
##restricting fh to Country, Region, Status, political rights score, and civil liberties score
##and matching names to COW dataset for merging
fh<-select(fh, "Country/Territory", Region, "PR rating")
fh<-rename(fh, "PR" = "PR rating")
fh$PR<-as.numeric(fh$PR)
fh$"Country/Territory"[fh$"Country/Territory" == "United States"]<-"United States of America"
fh$"Country/Territory"[fh$"Country/Territory" == "Antigua and Barbuda"]<-"Antigua & Barbuda"
fh$"Country/Territory"[fh$"Country/Territory" == "The Gambia"]<-"Gambia"
fh$"Country/Territory"[fh$"Country/Territory" == "Cabo Verde"]<-"Cape Verde"
fh$"Country/Territory"[fh$"Country/Territory" == "Cote d'Ivoire"]<-"Ivory Coast"
fh$"Country/Territory"[fh$"Country/Territory" == "Congo (Brazzaville)"]<-"Democratic Republic of the Congo"
fh$"Country/Territory"[fh$"Country/Territory" == "Congo (Kinshasa)"]<-"Congo"
#Downloading HDI dataset:
library(readxl)
hdi<-read_xls("/Users/leaschaad/Desktop/This/HumanDevelopmentIndex.xls")## New names:
## * `` -> ...4
## * `` -> ...6
## * `` -> ...8
## * `` -> ...10
## * `` -> ...12
## * ...hdi<-select(hdi, Country, "2012")
hdi<-rename(hdi, "hdi" = "2012")
hdi$hdi<-as.numeric(hdi$hdi)## Warning: NAs introduced by coercion##matching names to COW dataset for merging
hdi$Country[hdi$Country == "Bolivia (Plurinational State of)"]<-"Bolivia"
hdi$Country[hdi$Country == "United States"]<-"United States of America"
hdi$Country[hdi$Country == "Venezuela (Bolivarian Republic of)"]<-"Venezuela"
hdi$Country[hdi$Country == "Syrian Arab Republic"]<-"Syria"
hdi$Country[hdi$Country == "Saint Lucia"]<-"St. Lucia"
hdi$Country[hdi$Country == "Saint Kitts and Nevis"]<-"St. Kitts and Nevis"
hdi$Country[hdi$Country == "Saint Vincent and the Grenadines"]<-"St. Vincent and the Grenadines"
hdi$Country[hdi$Country == "Antigua and Barbuda"]<-"Antigua & Barbuda"
hdi$Country[hdi$Country == "Czechia"]<-"Czech Republic"
hdi$Country[hdi$Country == "Korea (Republic of)"]<-"South Korea"
hdi$Country[hdi$Country == "Russian Federation"]<-"Russia"
hdi$Country[hdi$Country == "Moldova (Republic of)"]<-"Moldova"
hdi$Country[hdi$Country == "Eswatini (Kingdom of)"]<-"Swaziland"
data$state_name1[data$state_name1 == "German Federal Republic"]<-"Germany"
data$state_name2[data$state_name2 == "German Federal Republic"]<-"Germany"
#Merging Datasets to one
library(igraph)
library(migraph)## Registered S3 methods overwritten by 'migraph':
## method from
## plot.blockmodel sna
## print.blockmodel sna
## print.summary.netlm sna
## summary.netlm sna##
## Attaching package: 'migraph'## The following objects are masked from 'package:igraph':
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## as_edgelist, is_connected, is_directed, is_weighted## The following object is masked from 'package:stats':
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## filterlibrary(dplyr)
merged<-left_join(data, fh, by = c("state_name1" = "Country/Territory"))
merged<-left_join(merged, hdi, by = c("state_name1" = "Country"))
#Factorizing PR and hdi
library(ggplot2)
merged$hdi<-cut_number(merged$hdi, n = 3, labels = c("low", "medium", "high"))
merged$PR<-cut_number(merged$PR, n = 3, labels = c("low", "medium", "high"))
table(merged$hdi)##
## low medium high
## 1022 991 996table(merged$PR)##
## low medium high
## 1419 839 853#Dealing with NAs - they have to go because ergm can't deal with them
merged$hdi<-as.character(merged$hdi)
merged$PR<-as.character(merged$PR)
merged[is.na(merged)] = "Recode" ##Recoding all NAs to "Recode", because R didn't seem to recognize NAs otherwise - must be character variables for this to work
merged$hdi[merged$hdi == "Recode"]<-"medium"
merged$PR[merged$PR == "Recode"]<-"medium"
merged$Region[merged$Region == "Recode"]<-"Other"
#turning into graph object that takes first two as edge list and other columns as attributes
library(igraph)
alliance<-graph_from_data_frame(merged[, 1:2], directed = TRUE, vertices = merged[!duplicated(merged[,1]), c(1, 3:5)])
summary(alliance)## IGRAPH eeb09a1 DN-- 141 3114 --
## + attr: name (v/c), Region (v/c), PR (v/c), hdi (v/c)V(alliance)$color<-"pink"
plot(alliance, vertex.size = 7, label.size = .1, vertex.label.color = "black", edge.arrow.size = 0.1 , edge.arrow.width = 0.5)
title(main = "Foreign Alliances in 2012") ##taking a first look at the network - enlarge to read names. If you want to be able to read the names, save this as a pdf while enlarging x10. Otherwise, view it without vertex labels with the code below:
plot(alliance, vertex.size = 7, vertex.label = NA, edge.arrow.size = 0.1 , edge.arrow.width = 0.5)
title(main = "Foreign Alliances in 2012")
#Turning into network object
library(ergm)## Loading required package: network##
## 'network' 1.17.1 (2021-06-12), part of the Statnet Project
## * 'news(package="network")' for changes since last version
## * 'citation("network")' for citation information
## * 'https://statnet.org' for help, support, and other information##
## Attaching package: 'network'## The following objects are masked from 'package:igraph':
##
## %c%, %s%, add.edges, add.vertices, delete.edges, delete.vertices,
## get.edge.attribute, get.edges, get.vertex.attribute, is.bipartite,
## is.directed, list.edge.attributes, list.vertex.attributes,
## set.edge.attribute, set.vertex.attribute##
## 'ergm' 4.1.2 (2021-07-26), part of the Statnet Project
## * 'news(package="ergm")' for changes since last version
## * 'citation("ergm")' for citation information
## * 'https://statnet.org' for help, support, and other information## 'ergm' 4 is a major update that introduces some backwards-incompatible
## changes. Please type 'news(package="ergm")' for a list of major
## changes.library(intergraph)
alliance2<-alliance
alliance2 <- intergraph::asNetwork(alliance)
##So now I have a graph object (alliance) and a network object (alliance2)Looking at Data - Basic measures
library(migraph)
library(igraph)
##Density e.g. the proportion of ties in a network
edge_density(alliance) #0.1577508## [1] 0.1577508##Transitivity
transitivity(alliance) #0.9065951## [1] 0.9065951reciprocity(alliance) #1 --> Every tie is reciprocated## [1] 1Now that we have built the dataset, let’s look at some basic measures. We can see that the network is not very dense, is fully reciprocal, and has many three-cycles. But can the network be explained by randomness, or is there at least some level of dependence going on?
Network Visualization
#Comparing Network to Random Network
model1 <- ergm(alliance2 ~ edges)## Starting maximum pseudolikelihood estimation (MPLE):## Evaluating the predictor and response matrix.## Maximizing the pseudolikelihood.## Finished MPLE.## Stopping at the initial estimate.## Evaluating log-likelihood at the estimate.summary(model1)## Call:
## ergm(formula = alliance2 ~ edges)
##
## Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -1.93186 0.02141 0 -90.24 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 27365 on 19740 degrees of freedom
## Residual Deviance: 14993 on 19739 degrees of freedom
##
## AIC: 14995 BIC: 15003 (Smaller is better. MC Std. Err. = 0)(sim <- simulate(model1))## Network attributes:
## vertices = 141
## directed = TRUE
## hyper = FALSE
## loops = FALSE
## multiple = TRUE
## bipartite = FALSE
## total edges= 2467
## missing edges= 0
## non-missing edges= 2467
##
## Vertex attribute names:
## color hdi PR Region vertex.names
##
## Edge attribute names not shownpar(mfrow=c(1,2))
plot(alliance2, main="Observed")
plot(sim, main="Simulated")
We can see that the randomly simulated network is very different to the observed network - the observed network has more clusters and is less dense. We therefore know that the network structure is not determined by randomness. Now, let’s make a descriptive assessment dyad effects by looking at whether there is homophily in the network regarding political rights, human development, and regions.
Descriptive Statistics Looking at Homophily in Network Alliances
#Exploring homophily of attributes by looking at if it coincides with walktrap algorithm (tried different communnity algorithm, this one fit best)
library(igraph)
library(migraph)
alliance_wt_4<-cluster_walktrap(alliance) #walktrap with 4 steps
summary(alliance)## IGRAPH eeb09a1 DN-- 141 3114 --
## + attr: name (v/c), Region (v/c), PR (v/c), hdi (v/c), color (v/c)## Preparations: Coloring Nodes
###color nodes according to Regions
library(igraph)
alliance_Region<-alliance
V(alliance_Region)$Region## [1] "Europe" "Europe" "Americas" "Americas" "Americas" "Americas"
## [7] "Americas" "SSA" "SSA" "SSA" "MENA" "MENA"
## [13] "MENA" "MENA" "SSA" "MENA" "MENA" "MENA"
## [19] "MENA" "MENA" "MENA" "MENA" "MENA" "MENA"
## [25] "MENA" "MENA" "MENA" "Americas" "Americas" "Americas"
## [31] "Americas" "Americas" "Americas" "Americas" "Americas" "Americas"
## [37] "Americas" "Americas" "Americas" "Americas" "Americas" "Americas"
## [43] "Americas" "Americas" "Americas" "Americas" "Americas" "Americas"
## [49] "Americas" "Americas" "Americas" "Americas" "Americas" "Americas"
## [55] "Americas" "Americas" "Europe" "Europe" "Europe" "Europe"
## [61] "Europe" "Europe" "Europe" "Europe" "Europe" "Europe"
## [67] "Europe" "Europe" "Europe" "Europe" "Europe" "Asia"
## [73] "Asia" "Asia" "Asia" "Asia" "SSA" "SSA"
## [79] "Asia" "Asia" "SSA" "SSA" "Asia" "SSA"
## [85] "SSA" "SSA" "SSA" "SSA" "SSA" "SSA"
## [91] "SSA" "SSA" "SSA" "SSA" "SSA" "SSA"
## [97] "SSA" "SSA" "Other" "Eurasia" "Europe" "Europe"
## [103] "Eurasia" "Europe" "Eurasia" "Eurasia" "Eurasia" "Eurasia"
## [109] "Eurasia" "Eurasia" "Eurasia" "Eurasia" "Eurasia" "Eurasia"
## [115] "Europe" "Europe" "Europe" "Europe" "Asia" "Europe"
## [121] "Europe" "MENA" "Other" "Europe" "SSA" "SSA"
## [127] "SSA" "SSA" "SSA" "SSA" "SSA" "SSA"
## [133] "SSA" "SSA" "SSA" "MENA" "Asia" "SSA"
## [139] "SSA" "SSA" "SSA"V(alliance_Region)$color<-"white"
V(alliance_Region)$color <- ifelse(V(alliance_Region)$Region == "Americas", "blue", ifelse(V(alliance_Region)$Region == "Europe", "red", ifelse(V(alliance_Region)$Region == "MENA", "green", ifelse(V(alliance_Region)$Region == "SSA", "yellow", ifelse(V(alliance_Region)$Region == "Asia", "orange", ifelse(V(alliance_Region)$Region == "Eurasia", "darkgreen", "white"))))))
###color nodes according to hdi
alliance_hdi<-alliance
V(alliance_hdi)$hdi## [1] "high" "high" "medium" "low" "low" "medium" "medium" "low"
## [9] "medium" "low" "low" "medium" "medium" "medium" "low" "low"
## [17] "low" "low" "medium" "medium" "high" "low" "high" "high"
## [25] "high" "high" "high" "high" "high" "high" "low" "medium"
## [33] "medium" "medium" "high" "medium" "medium" "medium" "medium" "medium"
## [41] "medium" "medium" "low" "low" "low" "low" "low" "medium"
## [49] "medium" "low" "medium" "medium" "medium" "high" "high" "high"
## [57] "high" "high" "high" "high" "high" "high" "high" "high"
## [65] "high" "high" "high" "high" "high" "high" "medium" "low"
## [73] "high" "high" "high" "low" "low" "low" "medium" "medium"
## [81] "low" "low" "low" "medium" "low" "low" "low" "low"
## [89] "low" "low" "medium" "low" "low" "low" "low" "low"
## [97] "low" "low" "low" "high" "high" "high" "medium" "high"
## [105] "medium" "high" "medium" "medium" "medium" "low" "low" "low"
## [113] "low" "medium" "medium" "high" "high" "high" "medium" "high"
## [121] "high" "high" "medium" "medium" "low" "low" "medium" "low"
## [129] "low" "low" "low" "low" "low" "low" "low" "medium"
## [137] "low" "low" "medium" "low" "low"V(alliance_hdi)$color<-"white"
V(alliance_hdi)$color <- ifelse(V(alliance_hdi)$hdi == "low", "yellow", ifelse(V(alliance_hdi)$hdi == "medium", "orange", ifelse(V(alliance_hdi)$hdi == "high", "red", "white")))
###color nodes according to PR
alliance_PR<-alliance
V(alliance_PR)$PR## [1] "low" "low" "medium" "medium" "medium" "medium" "medium" "high"
## [9] "high" "high" "medium" "high" "medium" "medium" "high" "high"
## [17] "medium" "high" "medium" "high" "high" "high" "medium" "high"
## [25] "high" "high" "high" "low" "low" "low" "medium" "low"
## [33] "low" "low" "low" "low" "low" "low" "low" "low"
## [41] "low" "medium" "low" "medium" "medium" "low" "medium" "low"
## [49] "low" "low" "low" "low" "low" "low" "low" "low"
## [57] "low" "low" "low" "low" "low" "low" "low" "low"
## [65] "low" "low" "low" "low" "low" "low" "medium" "medium"
## [73] "low" "low" "low" "medium" "medium" "high" "high" "high"
## [81] "medium" "high" "low" "low" "high" "high" "high" "low"
## [89] "low" "medium" "medium" "medium" "medium" "low" "low" "medium"
## [97] "medium" "low" "medium" "high" "low" "low" "medium" "low"
## [105] "medium" "high" "medium" "medium" "high" "high" "high" "medium"
## [113] "high" "high" "medium" "low" "low" "low" "low" "low"
## [121] "low" "low" "medium" "medium" "medium" "high" "high" "low"
## [129] "high" "high" "high" "medium" "high" "high" "high" "high"
## [137] "high" "medium" "medium" "medium" "high"V(alliance_PR)$color<-"white"
V(alliance_PR)$color <- ifelse(V(alliance_PR)$PR == "low", "red", ifelse(V(alliance_PR)$PR == "medium", "orange", ifelse(V(alliance_PR)$PR == "high", "yellow", "white")))
##Plots Community Algorithm and Node Attributes
plot(alliance_Region, vertex.size = 7, label.size = .1, vertex.label = NA, edge.arrow.size = 0.1 , edge.arrow.width = 0.5, mark.groups = alliance_wt_4)
title(main = "Foreign Alliances and Regions", cex.main = 1, col.main = "black") ##plot Regions
legend("topleft", legend=c("Americas", "Europe", "MENA", "SSA", "Asia", "Eurasia"),
col=c("blue", "red", "green", "yellow", "orange", "darkgreen"), lty=1:1, cex=0.5)
plot(alliance_hdi, vertex.size = 7, label.size = .1, vertex.label = NA, edge.arrow.size = 0.1 , edge.arrow.width = 0.5, mark.groups = alliance_wt_4)
title(main = "Foreign Alliances and Human Development", cex.main = 1, col.main = "black") ##plot hdi
legend("topleft", legend=c("low", "medium", "high"),
col=c("yellow", "orange", "red"), lty=1:1, cex=0.5)
plot(alliance_PR, vertex.size = 7, label.size = .1, vertex.label = NA, edge.arrow.size = 0.1 , edge.arrow.width = 0.5, mark.groups = alliance_wt_4)
title(main = "Foreign Alliances and Political Rights", cex.main = 1, col.main = "black") ##plot PR
legend("topleft", legend=c("low", "medium", "high"),
col=c("red", "orange", "yellow"), lty=1:1, cex=0.5)
We can see that to a certain extent, alliance communities seem to coincide with regions, political rights and human development. Clusters seem most homophile with regard to regions, and less clear with regard to the other two attributes. As a next step, let’s examine this structural hypothesis causally, before also taking into account different levels of dependencies.
Running Exponential Random Graph Models (ERGMs)
library(ergm)
library(migraph)
#testing dyad effects - H1a-c
model_match_all<-ergm(alliance2 ~ edges + nodefactor("hdi") + nodematch("hdi") + nodefactor("PR") + nodematch("PR") + nodefactor("Region") + nodematch("Region"))## Starting maximum pseudolikelihood estimation (MPLE):## Evaluating the predictor and response matrix.## Maximizing the pseudolikelihood.## Finished MPLE.## Stopping at the initial estimate.## Evaluating log-likelihood at the estimate.summary(model_match_all)## Call:
## ergm(formula = alliance2 ~ edges + nodefactor("hdi") + nodematch("hdi") +
## nodefactor("PR") + nodematch("PR") + nodefactor("Region") +
## nodematch("Region"))
##
## Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -1.21115 0.23505 0 -5.153 < 1e-04 ***
## nodefactor.hdi.low -0.58994 0.10041 0 -5.875 < 1e-04 ***
## nodefactor.hdi.medium -0.44645 0.08919 0 -5.006 < 1e-04 ***
## nodematch.hdi 0.17954 0.08017 0 2.240 0.025115 *
## nodefactor.PR.low -0.40216 0.08476 0 -4.745 < 1e-04 ***
## nodefactor.PR.medium -0.10075 0.06635 0 -1.518 0.128906
## nodematch.PR 0.77400 0.07403 0 10.455 < 1e-04 ***
## nodefactor.Region.Asia -2.00081 0.12451 0 -16.069 < 1e-04 ***
## nodefactor.Region.Eurasia -0.44684 0.12301 0 -3.633 0.000281 ***
## nodefactor.Region.Europe -1.94176 0.09146 0 -21.232 < 1e-04 ***
## nodefactor.Region.MENA -1.07104 0.10069 0 -10.637 < 1e-04 ***
## nodefactor.Region.Other -1.90718 0.40794 0 -4.675 < 1e-04 ***
## nodefactor.Region.SSA -1.82357 0.08427 0 -21.639 < 1e-04 ***
## nodematch.Region 4.99180 0.09071 0 55.029 < 1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 27365 on 19740 degrees of freedom
## Residual Deviance: 6263 on 19726 degrees of freedom
##
## AIC: 6291 BIC: 6401 (Smaller is better. MC Std. Err. = 0)#Testing Partial Conditional Dependence
model_gwesp_all<-ergm(alliance2 ~ edges + gwesp(0.2, fixed = TRUE) + nodefactor("hdi") + nodematch("hdi") + nodefactor("PR") + nodematch("PR") + nodefactor("Region") + nodematch("Region")) ##Converged with 99% confidence after running 26 mins## Starting maximum pseudolikelihood estimation (MPLE):
## Evaluating the predictor and response matrix.
## Maximizing the pseudolikelihood.
## Finished MPLE.
## Starting Monte Carlo maximum likelihood estimation (MCMLE):
## Iteration 1 of at most 60:
## Optimizing with step length 0.0653.
## The log-likelihood improved by 2.2558.
## Estimating equations are not within tolerance region.
## Iteration 2 of at most 60:
## Optimizing with step length 0.0694.
## The log-likelihood improved by 1.8622.
## Estimating equations are not within tolerance region.
## Iteration 3 of at most 60:
## Optimizing with step length 0.0562.
## The log-likelihood improved by 1.4584.
## Estimating equations are not within tolerance region.
## Iteration 4 of at most 60:
## Optimizing with step length 0.0678.
## The log-likelihood improved by 1.9162.
## Estimating equations are not within tolerance region.
## Iteration 5 of at most 60:
## Optimizing with step length 0.0836.
## The log-likelihood improved by 1.8703.
## Estimating equations are not within tolerance region.
## Iteration 6 of at most 60:
## Optimizing with step length 0.1013.
## The log-likelihood improved by 2.0890.
## Estimating equations are not within tolerance region.
## Iteration 7 of at most 60:
## Optimizing with step length 0.0909.
## The log-likelihood improved by 1.7228.
## Estimating equations are not within tolerance region.
## Iteration 8 of at most 60:
## Optimizing with step length 0.1031.
## The log-likelihood improved by 1.6109.
## Estimating equations are not within tolerance region.
## Iteration 9 of at most 60:
## Optimizing with step length 0.1211.
## The log-likelihood improved by 1.7211.
## Estimating equations are not within tolerance region.
## Iteration 10 of at most 60:
## Optimizing with step length 0.1264.
## The log-likelihood improved by 1.8149.
## Estimating equations are not within tolerance region.
## Iteration 11 of at most 60:
## Optimizing with step length 0.1907.
## The log-likelihood improved by 2.4807.
## Estimating equations are not within tolerance region.
## Iteration 12 of at most 60:
## Optimizing with step length 0.1847.
## The log-likelihood improved by 1.6652.
## Estimating equations are not within tolerance region.
## Iteration 13 of at most 60:
## Optimizing with step length 0.2510.
## The log-likelihood improved by 2.4208.
## Estimating equations are not within tolerance region.
## Iteration 14 of at most 60:
## Optimizing with step length 0.2499.
## The log-likelihood improved by 1.4904.
## Estimating equations are not within tolerance region.
## Iteration 15 of at most 60:
## Optimizing with step length 0.4047.
## The log-likelihood improved by 2.4508.
## Estimating equations are not within tolerance region.
## Iteration 16 of at most 60:
## Optimizing with step length 0.5151.
## The log-likelihood improved by 1.3677.
## Estimating equations are not within tolerance region.
## Iteration 17 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.6730.
## Estimating equations are not within tolerance region.
## Iteration 18 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.1754.
## Estimating equations are not within tolerance region.
## Iteration 19 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.0572.
## Convergence test p-value: 0.9848. Not converged with 99% confidence; increasing sample size.
## Iteration 20 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.0673.
## Convergence test p-value: 1.0000. Not converged with 99% confidence; increasing sample size.
## Iteration 21 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.0390.
## Convergence test p-value: 0.6324. Not converged with 99% confidence; increasing sample size.
## Iteration 22 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.0520.
## Convergence test p-value: 0.8689. Not converged with 99% confidence; increasing sample size.
## Iteration 23 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.0446.
## Convergence test p-value: 0.3173. Not converged with 99% confidence; increasing sample size.
## Iteration 24 of at most 60:
## Optimizing with step length 1.0000.
## The log-likelihood improved by 0.0138.
## Convergence test p-value: < 0.0001. Converged with 99% confidence.
## Finished MCMLE.
## Evaluating log-likelihood at the estimate. Fitting the dyad-independent submodel...
## Bridging between the dyad-independent submodel and the full model...
## Setting up bridge sampling...
## Using 16 bridges: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 .
## Bridging finished.
## This model was fit using MCMC. To examine model diagnostics and check
## for degeneracy, use the mcmc.diagnostics() function.summary(model_gwesp_all)## Call:
## ergm(formula = alliance2 ~ edges + gwesp(0.2, fixed = TRUE) +
## nodefactor("hdi") + nodematch("hdi") + nodefactor("PR") +
## nodematch("PR") + nodefactor("Region") + nodematch("Region"))
##
## Monte Carlo Maximum Likelihood Results:
##
## Estimate Std. Error MCMC % z value Pr(>|z|)
## edges -3.39418 0.29188 0 -11.629 <1e-04 ***
## gwesp.fixed.0.2 1.71853 0.16307 0 10.539 <1e-04 ***
## nodefactor.hdi.low -0.45251 0.09060 0 -4.995 <1e-04 ***
## nodefactor.hdi.medium -0.35476 0.07993 0 -4.439 <1e-04 ***
## nodematch.hdi 0.12111 0.07782 0 1.556 0.1196
## nodefactor.PR.low -0.39500 0.07831 0 -5.044 <1e-04 ***
## nodefactor.PR.medium -0.12575 0.06407 0 -1.963 0.0497 *
## nodematch.PR 0.77778 0.07102 0 10.951 <1e-04 ***
## nodefactor.Region.Asia -1.84699 0.08032 0 -22.995 <1e-04 ***
## nodefactor.Region.Eurasia -0.43222 0.10950 0 -3.947 <1e-04 ***
## nodefactor.Region.Europe -1.77171 0.08929 0 -19.842 <1e-04 ***
## nodefactor.Region.MENA -0.96489 0.09374 0 -10.293 <1e-04 ***
## nodefactor.Region.Other -1.30479 0.31308 0 -4.168 <1e-04 ***
## nodefactor.Region.SSA -1.82174 0.08035 0 -22.673 <1e-04 ***
## nodematch.Region 4.62305 0.08696 0 53.161 <1e-04 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Null Deviance: 27365 on 19740 degrees of freedom
## Residual Deviance: 6082 on 19725 degrees of freedom
##
## AIC: 6112 BIC: 6230 (Smaller is better. MC Std. Err. = 0.2968)#Visualizations
##all coefficients
library(stargazer)##
## Please cite as:
##
## Hlavac, Marek (2018). stargazer: Well-Formatted Regression and Summary Statistics Tables.
## R package version 5.2.2. https://CRAN.R-project.org/package=stargazerstargazer(model_match_all, model_gwesp_all, type = "text")##
## ======================================================
## Dependent variable:
## ----------------------------
## alliance2
## (1) (2)
## ------------------------------------------------------
## edges -1.211*** -3.394***
## (0.235) (0.292)
##
## gwesp.fixed.0.2 1.719***
## (0.163)
##
## nodefactor.hdi.low -0.590*** -0.453***
## (0.100) (0.091)
##
## nodefactor.hdi.medium -0.446*** -0.355***
## (0.089) (0.080)
##
## nodematch.hdi 0.180** 0.121
## (0.080) (0.078)
##
## nodefactor.PR.low -0.402*** -0.395***
## (0.085) (0.078)
##
## nodefactor.PR.medium -0.101 -0.126**
## (0.066) (0.064)
##
## nodematch.PR 0.774*** 0.778***
## (0.074) (0.071)
##
## nodefactor.Region.Asia -2.001*** -1.847***
## (0.125) (0.080)
##
## nodefactor.Region.Eurasia -0.447*** -0.432***
## (0.123) (0.110)
##
## nodefactor.Region.Europe -1.942*** -1.772***
## (0.091) (0.089)
##
## nodefactor.Region.MENA -1.071*** -0.965***
## (0.101) (0.094)
##
## nodefactor.Region.Other -1.907*** -1.305***
## (0.408) (0.313)
##
## nodefactor.Region.SSA -1.824*** -1.822***
## (0.084) (0.080)
##
## nodematch.Region 4.992*** 4.623***
## (0.091) (0.087)
##
## ------------------------------------------------------
## Akaike Inf. Crit. 6,290.519 6,111.575
## Bayesian Inf. Crit. 6,400.985 6,229.931
## ======================================================
## Note: *p<0.1; **p<0.05; ***p<0.01##choosing only coefficients I'm focusing on
library(stargazer)
stargazer(model_match_all, model_gwesp_all, keep = c("nodematch.hdi", "nodematch.Region", "nodematch.PR", "gwesp.fixed.0.2"), type = "text")##
## ================================================
## Dependent variable:
## ----------------------------
## alliance2
## (1) (2)
## ------------------------------------------------
## gwesp.fixed.0.2 1.719***
## (0.163)
##
## nodematch.hdi 0.180** 0.121
## (0.080) (0.078)
##
## nodematch.PR 0.774*** 0.778***
## (0.074) (0.071)
##
## nodematch.Region 4.992*** 4.623***
## (0.091) (0.087)
##
## ------------------------------------------------
## Akaike Inf. Crit. 6,290.519 6,111.575
## Bayesian Inf. Crit. 6,400.985 6,229.931
## ================================================
## Note: *p<0.1; **p<0.05; ***p<0.01Interestingly we can see that in both models, most coefficients are (highly) significant. This already tells us that region, hdi and PR have an influence on foreign alliances. Looking at dyad effects in examining hypothesis one, we can confirm that countries are more likely to build foreign alliances with countries within their region (H1a), and that have similar levels of political rights and human development (H1b,H1c). More specifically, we can see that all nodematch coefficients are positive and significant on a 95% confidence interval (hdi) and even 99% confidence interval (region and PR). Regarding our third hypothesis, we can see that the model that incorporates social circuit dependence has a lower AIC and therefore better fits the data. We can also accept our second hypothesis, seeing that the gwesp coefficient is significant on a 99% confidence interval. Further, the fact that the nodematch PR and nodematch region coefficients remain significant in this model too strengthens our confidence in hypotheses 1a and b. However, we can see that in the partial conditional model, nodematch hdi does not attain statistical significance, which suggests that it is subsumed by the gwesp effect and throws into question hypothesis 1c.
Goodness of Fit
library(ergm)
(fit_match_all <- gof(model_match_all, GOF = ~ idegree + distance + triadcensus + espartners - model))##
## Goodness-of-fit for in-degree
##
## obs min mean max MC p-value
## idegree0 0 0 0.88 4 0.56
## idegree1 11 0 1.83 5 0.00
## idegree2 7 0 2.33 7 0.02
## idegree3 3 0 2.70 8 0.98
## idegree4 3 0 2.24 6 0.74
## idegree5 0 0 2.03 8 0.22
## idegree6 2 0 1.82 7 0.94
## idegree7 0 0 2.30 6 0.18
## idegree8 2 0 3.29 11 0.68
## idegree9 0 0 3.92 10 0.04
## idegree10 7 0 5.73 15 0.64
## idegree11 4 1 7.28 15 0.30
## idegree12 2 3 8.78 14 0.00
## idegree13 3 4 11.75 20 0.00
## idegree14 15 4 11.91 21 0.50
## idegree15 9 6 11.25 19 0.44
## idegree16 1 3 9.68 17 0.00
## idegree17 1 1 6.96 13 0.02
## idegree18 25 1 4.66 12 0.00
## idegree19 6 0 2.88 8 0.10
## idegree20 1 0 1.54 5 1.00
## idegree21 2 0 0.73 3 0.32
## idegree22 0 0 0.30 2 1.00
## idegree23 0 0 0.18 2 1.00
## idegree24 1 0 0.03 1 0.06
## idegree26 1 0 0.00 0 0.00
## idegree28 0 0 0.01 1 1.00
## idegree29 0 0 0.16 2 1.00
## idegree30 1 0 0.80 4 1.00
## idegree31 0 0 1.88 7 0.32
## idegree32 0 0 3.70 8 0.02
## idegree33 32 1 5.50 11 0.00
## idegree34 0 2 5.94 11 0.00
## idegree35 0 2 5.19 10 0.00
## idegree36 0 0 4.55 10 0.04
## idegree37 0 0 3.01 8 0.08
## idegree38 0 0 1.74 5 0.36
## idegree39 0 0 0.88 3 0.82
## idegree40 0 0 0.29 2 1.00
## idegree41 0 0 0.20 2 1.00
## idegree42 0 0 0.11 2 1.00
## idegree43 0 0 0.04 1 1.00
## idegree51 1 0 0.00 0 0.00
## idegree56 1 0 0.00 0 0.00
##
## Goodness-of-fit for minimum geodesic distance
##
## obs min mean max MC p-value
## 1 2498 2428 2495.15 2549 0.80
## 2 3456 7168 7731.14 8236 0.00
## 3 5198 6715 7419.26 7950 0.00
## 4 3190 1272 1626.84 2225 0.00
## 5 3336 36 154.59 426 0.00
## 6 1232 0 16.82 185 0.00
## 7 242 0 2.07 69 0.00
## 8 32 0 0.03 2 0.00
## Inf 556 0 294.10 1105 0.26
##
## Goodness-of-fit for triad census
##
## obs min mean max MC p-value
## triadcensus.003 304490 255733 260610.97 266915 0
## triadcensus.012 0 76983 87084.98 92271 0
## triadcensus.102 141033 80856 83142.59 88173 0
## triadcensus.021D 0 1423 1687.56 1901 0
## triadcensus.021U 0 1464 1692.68 1868 0
## triadcensus.021C 0 2846 3381.87 3679 0
## triadcensus.111D 0 3942 4768.26 5348 0
## triadcensus.111U 0 4306 4992.37 5631 0
## triadcensus.030T 0 499 735.11 886 0
## triadcensus.030C 0 154 250.64 309 0
## triadcensus.201 2783 301 501.32 731 0
## triadcensus.120D 0 283 373.49 425 0
## triadcensus.120U 0 250 376.74 451 0
## triadcensus.120C 0 620 770.30 895 0
## triadcensus.210 0 1415 2041.79 2401 0
## triadcensus.300 9004 4487 4899.33 5769 0
##
## Goodness-of-fit for edgewise shared partner
##
## obs min mean max MC p-value
## esp0 46 107 130.06 152 0.00
## esp1 28 114 136.37 164 0.00
## esp2 14 107 141.89 169 0.00
## esp3 10 108 150.31 188 0.00
## esp4 6 114 140.62 180 0.00
## esp5 36 95 123.73 146 0.00
## esp6 12 48 104.43 136 0.00
## esp7 2 53 100.68 150 0.00
## esp8 8 62 110.29 156 0.00
## esp9 136 90 109.75 137 0.04
## esp10 96 59 86.17 145 0.50
## esp11 42 22 48.58 80 0.70
## esp12 12 11 25.50 52 0.04
## esp13 210 3 11.20 31 0.00
## esp14 36 0 3.59 11 0.00
## esp15 0 0 1.11 4 0.70
## esp16 0 0 0.17 2 1.00
## esp17 658 0 0.00 0 0.00
## esp18 20 0 0.00 0 0.00
## esp19 4 0 0.00 0 0.00
## esp20 0 0 0.01 1 1.00
## esp21 0 0 0.56 6 1.00
## esp22 0 0 0.89 6 1.00
## esp23 0 0 1.90 8 0.86
## esp24 0 0 6.15 22 0.42
## esp25 0 0 17.66 44 0.08
## esp26 0 2 43.55 85 0.00
## esp27 0 20 95.30 155 0.00
## esp28 0 68 158.95 212 0.00
## esp29 0 114 221.90 269 0.00
## esp30 0 176 243.22 344 0.00
## esp31 0 94 187.62 396 0.00
## esp32 1120 36 81.54 246 0.00
## esp33 0 2 10.58 32 0.00
## esp34 0 0 0.84 5 0.98
## esp35 0 0 0.03 1 1.00
## esp49 2 0 0.00 0 0.00
##
## Goodness-of-fit for model statistics
##
## obs min mean max MC p-value
## edges 2498 2428 2495.15 2549 0.80
## nodefactor.hdi.low 1722 1650 1711.07 1772 0.56
## nodefactor.hdi.medium 1772 1701 1771.68 1827 0.88
## nodematch.hdi 1254 1216 1251.39 1287 0.88
## nodefactor.PR.low 2504 2462 2532.17 2575 0.22
## nodefactor.PR.medium 1394 1316 1377.68 1445 0.56
## nodematch.PR 1440 1406 1429.51 1455 0.48
## nodefactor.Region.Asia 68 47 65.38 82 0.84
## nodefactor.Region.Eurasia 344 332 348.69 370 0.56
## nodefactor.Region.Europe 716 673 718.68 766 0.98
## nodefactor.Region.MENA 570 522 557.16 584 0.38
## nodefactor.Region.Other 6 0 4.88 11 0.82
## nodefactor.Region.SSA 966 892 942.15 995 0.32
## nodematch.Region 2204 2163 2202.27 2230 1.00summary(fit_match_all)## Length Class Mode
## network.size 1 -none- numeric
## GOF 2 formula call
## pval.model 70 -none- numeric
## summary.model 70 -none- numeric
## pobs.model 14 -none- numeric
## psim.model 1400 -none- numeric
## bds.model 28 -none- numeric
## obs.model 14 -none- numeric
## sim.model 1400 -none- numeric
## pval.dist 705 -none- numeric
## summary.dist 705 -none- numeric
## pobs.dist 141 -none- numeric
## psim.dist 14100 -none- numeric
## bds.dist 282 -none- numeric
## obs.dist 141 -none- numeric
## sim.dist 14100 -none- numeric
## pval.ideg 705 -none- numeric
## summary.ideg 705 -none- numeric
## pobs.ideg 141 -none- numeric
## psim.ideg 14100 -none- numeric
## bds.ideg 282 -none- numeric
## obs.ideg 141 -none- numeric
## sim.ideg 14100 -none- numeric
## pval.espart 700 -none- numeric
## summary.espart 700 -none- numeric
## pobs.espart 140 -none- numeric
## psim.espart 14000 -none- numeric
## bds.espart 280 -none- numeric
## obs.espart 140 -none- numeric
## sim.espart 14000 -none- numeric
## pval.triadcensus 80 -none- numeric
## summary.triadcensus 80 -none- numeric
## pobs.triadcensus 16 -none- numeric
## psim.triadcensus 1600 -none- numeric
## bds.triadcensus 32 -none- numeric
## obs.triadcensus 16 -none- numeric
## sim.triadcensus 1600 -none- numericplot(fit_match_all)
(fit_gwesp_all <- gof(model_gwesp_all, GOF = ~ idegree + distance + triadcensus + espartners - model))##
## Goodness-of-fit for in-degree
##
## obs min mean max MC p-value
## idegree0 0 0 2.86 9 0.04
## idegree1 11 0 1.23 4 0.00
## idegree2 7 0 1.82 6 0.00
## idegree3 3 0 1.95 7 0.50
## idegree4 3 0 1.91 7 0.62
## idegree5 0 0 1.72 4 0.24
## idegree6 2 0 1.63 6 1.00
## idegree7 0 0 1.95 6 0.30
## idegree8 2 0 2.98 6 0.76
## idegree9 0 0 4.07 11 0.12
## idegree10 7 1 6.09 11 0.82
## idegree11 4 2 7.90 15 0.26
## idegree12 2 4 10.10 20 0.00
## idegree13 3 4 11.01 21 0.00
## idegree14 15 5 11.68 20 0.36
## idegree15 9 2 10.63 18 0.76
## idegree16 1 4 9.02 17 0.00
## idegree17 1 1 6.41 14 0.06
## idegree18 25 0 4.95 12 0.00
## idegree19 6 0 3.35 7 0.22
## idegree20 1 0 1.58 5 0.94
## idegree21 2 0 1.19 4 0.62
## idegree22 0 0 0.55 2 1.00
## idegree23 0 0 0.24 2 1.00
## idegree24 1 0 0.14 2 0.24
## idegree25 0 0 0.03 1 1.00
## idegree26 1 0 0.04 1 0.08
## idegree27 0 0 0.15 2 1.00
## idegree28 0 0 0.27 2 1.00
## idegree29 0 0 0.63 3 0.96
## idegree30 1 0 1.50 5 1.00
## idegree31 0 0 2.41 7 0.24
## idegree32 0 0 3.76 9 0.04
## idegree33 32 1 4.88 9 0.00
## idegree34 0 0 5.30 10 0.02
## idegree35 0 0 4.78 10 0.02
## idegree36 0 0 3.65 10 0.12
## idegree37 0 0 2.79 7 0.08
## idegree38 0 0 1.73 6 0.36
## idegree39 0 0 1.04 4 0.70
## idegree40 0 0 0.55 3 1.00
## idegree41 0 0 0.33 2 1.00
## idegree42 0 0 0.13 2 1.00
## idegree43 0 0 0.06 1 1.00
## idegree46 0 0 0.01 1 1.00
## idegree51 1 0 0.00 0 0.00
## idegree56 1 0 0.00 0 0.00
##
## Goodness-of-fit for minimum geodesic distance
##
## obs min mean max MC p-value
## 1 2498 2415 2494.77 2583 0.96
## 2 3456 5605 6480.15 7359 0.00
## 3 5198 5767 6564.23 7234 0.00
## 4 3190 1906 2743.13 3643 0.24
## 5 3336 36 442.68 962 0.00
## 6 1232 0 58.44 414 0.00
## 7 242 0 10.45 224 0.00
## 8 32 0 1.81 90 0.04
## 9 0 0 0.17 17 1.00
## Inf 556 140 944.17 2706 0.52
##
## Goodness-of-fit for triad census
##
## obs min mean max MC p-value
## triadcensus.003 304490 253692 259017.07 270863 0
## triadcensus.012 0 75364 90563.40 96374 0
## triadcensus.102 141033 76474 80717.63 87870 0
## triadcensus.021D 0 1134 1633.64 2033 0
## triadcensus.021U 0 1102 1634.88 1892 0
## triadcensus.021C 0 2257 3324.16 4016 0
## triadcensus.111D 0 4158 4948.50 6124 0
## triadcensus.111U 0 3994 4932.95 5700 0
## triadcensus.030T 0 601 862.16 1025 0
## triadcensus.030C 0 178 290.32 360 0
## triadcensus.201 2783 362 660.16 1054 0
## triadcensus.120D 0 374 513.80 618 0
## triadcensus.120U 0 355 506.18 573 0
## triadcensus.120C 0 650 959.55 1110 0
## triadcensus.210 0 1452 2545.14 2915 0
## triadcensus.300 9004 3678 4200.46 5655 0
##
## Goodness-of-fit for edgewise shared partner
##
## obs min mean max MC p-value
## esp0 46 13 23.89 37 0.00
## esp1 28 88 113.95 153 0.00
## esp2 14 115 165.41 213 0.00
## esp3 10 145 183.75 223 0.00
## esp4 6 131 178.44 217 0.00
## esp5 36 118 161.96 200 0.00
## esp6 12 90 137.34 185 0.00
## esp7 2 84 120.70 163 0.00
## esp8 8 55 108.30 168 0.00
## esp9 136 60 93.42 124 0.00
## esp10 96 40 70.81 130 0.06
## esp11 42 12 45.05 70 0.86
## esp12 12 7 27.78 55 0.06
## esp13 210 0 14.31 34 0.00
## esp14 36 0 5.67 20 0.00
## esp15 0 0 1.77 7 0.72
## esp16 0 0 0.30 5 1.00
## esp17 658 0 0.05 3 0.00
## esp18 20 0 0.09 4 0.00
## esp19 4 0 0.32 7 0.06
## esp20 0 0 0.69 6 1.00
## esp21 0 0 2.34 14 0.78
## esp22 0 0 6.66 30 0.32
## esp23 0 0 17.20 56 0.06
## esp24 0 0 36.60 95 0.02
## esp25 0 1 73.25 141 0.00
## esp26 0 3 124.89 216 0.00
## esp27 0 22 175.55 226 0.00
## esp28 0 47 201.12 271 0.00
## esp29 0 107 184.69 278 0.00
## esp30 0 47 127.59 266 0.00
## esp31 0 14 66.61 366 0.00
## esp32 1120 4 21.12 231 0.00
## esp33 0 0 2.84 17 0.38
## esp34 0 0 0.26 2 1.00
## esp35 0 0 0.05 1 1.00
## esp49 2 0 0.00 0 0.00
##
## Goodness-of-fit for model statistics
##
## obs min mean max MC p-value
## edges 2498.000 2415.000 2494.770 2583.000 0.96
## gwesp.fixed.0.2 2988.029 2892.077 2984.454 3097.038 0.90
## nodefactor.hdi.low 1722.000 1653.000 1720.310 1797.000 1.00
## nodefactor.hdi.medium 1772.000 1697.000 1766.430 1844.000 0.88
## nodematch.hdi 1254.000 1198.000 1254.720 1301.000 0.96
## nodefactor.PR.low 2504.000 2394.000 2504.180 2608.000 0.96
## nodefactor.PR.medium 1394.000 1323.000 1391.620 1466.000 1.00
## nodematch.PR 1440.000 1380.000 1438.230 1501.000 0.96
## nodefactor.Region.Asia 68.000 12.000 59.900 93.000 0.72
## nodefactor.Region.Eurasia 344.000 309.000 342.240 373.000 0.96
## nodefactor.Region.Europe 716.000 661.000 715.650 769.000 1.00
## nodefactor.Region.MENA 570.000 520.000 572.170 614.000 0.82
## nodefactor.Region.Other 6.000 0.000 6.220 16.000 1.00
## nodefactor.Region.SSA 966.000 878.000 965.330 1037.000 0.96
## nodematch.Region 2204.000 2146.000 2200.980 2251.000 0.94summary(fit_gwesp_all)## Length Class Mode
## network.size 1 -none- numeric
## GOF 2 formula call
## pval.model 75 -none- numeric
## summary.model 75 -none- numeric
## pobs.model 15 -none- numeric
## psim.model 1500 -none- numeric
## bds.model 30 -none- numeric
## obs.model 15 -none- numeric
## sim.model 1500 -none- numeric
## pval.dist 705 -none- numeric
## summary.dist 705 -none- numeric
## pobs.dist 141 -none- numeric
## psim.dist 14100 -none- numeric
## bds.dist 282 -none- numeric
## obs.dist 141 -none- numeric
## sim.dist 14100 -none- numeric
## pval.ideg 705 -none- numeric
## summary.ideg 705 -none- numeric
## pobs.ideg 141 -none- numeric
## psim.ideg 14100 -none- numeric
## bds.ideg 282 -none- numeric
## obs.ideg 141 -none- numeric
## sim.ideg 14100 -none- numeric
## pval.espart 700 -none- numeric
## summary.espart 700 -none- numeric
## pobs.espart 140 -none- numeric
## psim.espart 14000 -none- numeric
## bds.espart 280 -none- numeric
## obs.espart 140 -none- numeric
## sim.espart 14000 -none- numeric
## pval.triadcensus 80 -none- numeric
## summary.triadcensus 80 -none- numeric
## pobs.triadcensus 16 -none- numeric
## psim.triadcensus 1600 -none- numeric
## bds.triadcensus 32 -none- numeric
## obs.triadcensus 16 -none- numeric
## sim.triadcensus 1600 -none- numericplot(fit_gwesp_all)
par(mfrow=c(2,2))
plot(fit_match_all)
plot(fit_gwesp_all)
dev.off()## null device
## 1We now compare the general fit of the simulation on the observed number of edges, node density, number of triangles, and triad census. Unfortunately, this analysis shows that the models were not very good at predicting the observed network structure. We can see that our observed statistics (thick lines) often does not fall within the range of simulated values.