#### EXAMPLE 1: FIGURES 1 - 3 ####

# Load packages
library("mvtnorm")
library("dplyr")
library("magrittr")
library("qgraph")
library("IsingSampler")
library("IsingFit")

# Function to estimate 3 networks on a subset of data
compNets <- function(n,Data){
  library("IsingSampler")
  library("IsingFit")
  
  # Load function for low-rank approximation
  source("http://sachaepskamp.com/files/MarsmanFun.R")
  source("http://sachaepskamp.com/files/Marsmancodes.R")
  
  Data <- Data[1:n,]
  Data[Data==-1] <- 0
  Res <- EstimateIsing(Data,method = "uni")
  ResLLTrans <- LinTransform(Res$graph,Res$thresholds)
  
  ResIFit <- IsingFit(Data, plot=FALSE)
  ResIFtrans <- LinTransform(ResIFit$weiadj,ResIFit$thresholds)
  
  MarsmanRes <- Marsman(Data, 2, nIter = 100000)$graph
  
  return(list(ll = ResLLTrans, lasso = ResIFtrans, marsman = MarsmanRes ))
}

# True network structures
library("igraph")
set.seed(1)

# Curie-Weiss model
CW <- matrix(0.2,10,10)

# Sparse network
Sparse <- 0.2*as.matrix(get.adjacency(erdos.renyi.game(10,0.2,directed = FALSE)))

# Plot both (Figure 1)
pdf("Figure1.pdf",height=5,width=10)
layout(t(1:2))
qgraph(CW,layout = "circle",maximum = 0.3, title="Network 1: Curie-Weiss")
qgraph(Sparse,layout = "circle",maximum = 0.3, title="Network 2: Sparse")
dev.off()

# Simulate data Curie-Weiss model
Data <- IsingSampler(5000,graph=CW,responses=c(-1,1),thresholds = rep(0,ncol(CW)))

# Sample sizes:
sampleSizes <- c(100,250,500,1000,2500,5000)

# Estimate networks:
ResultsCW <- lapply(seq_along(sampleSizes), function(i){
  compNets(sampleSizes[i],Data) 
})


# Maximums:
maxEdge <- function(x) max(abs(x[upper.tri(x,diag=FALSE)]))
Max <- list(
  ll = max(sapply(lapply(ResultsCW, '[[', 'll'),
                  function(x) maxEdge(x$graph))),
  lasso = max(sapply(lapply(ResultsCW, '[[', 'lasso'),
                     function(x) maxEdge(x$graph))),
  marsman = max(sapply(lapply(ResultsCW, '[[', 'marsman'),
                       maxEdge))
)

# Figure 2
pdf("Figure2.pdf",height=5,width=10)
layout(matrix(c(
  1,4,7,10,13,16,
  2,5,8,11,14,17,
  3,6,9,12,15,18
),3,byrow=TRUE))
for (i in seq_along(sampleSizes)){
  qgraph(ResultsCW[[i]]$ll$graph,weighted=TRUE,title=sprintf("Unregularized (n = %s)",sampleSizes[i]))
  qgraph(ResultsCW[[i]]$lasso$graph,weighted=TRUE,title=sprintf("LASSO (n = %s)",sampleSizes[i]))
  qgraph(ResultsCW[[i]]$marsman,weighted=TRUE,title=sprintf("Rank-2 (n = %s)",sampleSizes[i]),diag=FALSE)
}
dev.off()

# Simulate data sparse model
Data <- IsingSampler(5000,graph=Sparse ,responses=c(-1,1),thresholds = rep(0,ncol(Sparse)))

# Figure 3
sampleSizes <- c(100,250,500,1000,2500,5000)

# Estimate networks:
ResultsSparse <- lapply(seq_along(sampleSizes), function(i){
  compNets(sampleSizes[i],Data) 
})

# Maximums:
maxEdge <- function(x) max(abs(x[upper.tri(x,diag=FALSE)]))
Max <- list(
  ll = max(sapply(lapply(ResultsSparse, '[[', 'll'),
                  function(x) maxEdge(x$graph))),
  lasso = max(sapply(lapply(ResultsSparse, '[[', 'lasso'),
                     function(x) maxEdge(x$graph))),
  marsman = max(sapply(lapply(ResultsSparse, '[[', 'marsman'),
                       maxEdge))
)

# Figure 3
pdf("Figure3.pdf",height=5,width=10)
layout(matrix(c(
  1,4,7,10,13,16,
  2,5,8,11,14,17,
  3,6,9,12,15,18
),3,byrow=TRUE))
for (i in seq_along(sampleSizes)){
  qgraph(ResultsSparse[[i]]$ll$graph,weighted=TRUE,title=sprintf("Unregularized (n = %s)",sampleSizes[i]))
  qgraph(ResultsSparse[[i]]$lasso$graph,weighted=TRUE,title=sprintf("LASSO (n = %s)",sampleSizes[i]))
  qgraph(ResultsSparse[[i]]$marsman,weighted=TRUE,title=sprintf("Rank-2 (n = %s)",sampleSizes[i]),diag=FALSE)
}
dev.off()

#### EXAMPLE 2: FIGURE 5 + SUPPLEMENTARY ####

# Load packages:
library("mvtnorm")
library("dplyr")
library("magrittr")
library("qgraph")

# Load function for low-rank approximation:
source("http://sachaepskamp.com/files/MarsmanFun.R")
source("http://sachaepskamp.com/files/Marsmancodes.R")

### Latent-variable model example ###
# Discrimination matrix:
A <- structure(c(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 
                 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 
                 0, 1.1, -1.1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
                 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1.1, -1.1, 0, 0, 
                 0, 0, 0, 0, 0, 0, 0.75, 0, 0, 0, 0, 0, 0, 0, 0, 0.75, 0, 0, 0, 
                 0, 0, 0, 0, 0, 0, 0, 0.75, 0, 0, 0, 0, 0, 0, 0, 0, 0.75, 0, 0, 
                 0, 0, 0, 0, 0, 0, 0, 0, 0.75, 0, 0, 0, 0, 0, 0, 0, 0, 0.75, 0, 
                 0, 0, 0, 0, 0, 0, 0, 0, 0, 0.75, 0, 0, 0, 0, 0, 0, 0, 0, 0.75
), .Dim = c(19L, 8L))

# Latent variance-covariance matrix:
Psi <- structure(c(1, 0.55, 0, 0, 0, 0, 0, 0, 0.55, 1, 0, 0, 0, 0, 0, 
                   0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 
                   1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 
                   0, 0, 0, 0, 0, 0, 1), .Dim = c(8L, 8L))

# Function to simulate data:
simData <- function(n, A, Psi){
  nFact <- ncol(A)
  nItem <- nrow(A)
  
  # Simulate theta:
  Theta <- rmvnorm(n,rep(0,nFact),Psi)
  
  # Simulate data:
  Data <- 1*(matrix(runif(n*nItem),n,nItem) < exp(Theta %*% t(A)) / (1 + exp(Theta %*% t(A))))
  
  return(Data)
}

# List to store results:
Results <- list()

# Simulate 100.000 rows:
set.seed(3)
Data1 <- simData(10000000, A, Psi)

# Estimate using IsingSampler:
library("IsingSampler")
Results$true <- EstimateIsing(Data1, method = "ll")

# Second data (N = 1000):
set.seed(3)
Data2 <- simData(1000, A, Psi)

# Estimate using IsingFit:
library("IsingFit")
Results$IsingFit <- IsingFit(Data2,plot = FALSE)

# IsingFit with OR rule:
Results$IsingFitOR <- IsingFit(Data2,plot = FALSE,AND = FALSE)

# IsingFit with BIC:
Results$IsingFitBIC <- IsingFit(Data2,plot = FALSE, gamma = 0)

# Estimate using rank-2 approximation:
Results$lowrank <- Marsman(Data2, 2)$graph

# Estimate using max likelihood:
Results$loglin <- EstimateIsing(Data2, method = "ll")

# Estimate using elasticIsing
library("elasticIsing")
Results$elastic <- elasticIsing(Data2)

### Plot results ###
# Layout of graph
Layout <- structure(c(-0.91700922593243, -0.71607690882459, -1, -0.841970887068207, 
                      -0.506700378019609, -0.582211268833235, -0.369952210868241, -0.195488670971024, 
                      -0.562974697146571, -0.206747554869184, 1, 0.730922969999289, 
                      0.508551176680195, 0.997018453214546, 0.975224165663054, 0.361933177193966, 
                      0.581268889708378, 0.275354076567066, 0.603799511172853, 0.0163223231591647, 
                      0.265137401568571, 0.464523298446456, 0.831639167414529, 1, 0.644030028900333, 
                      0.09473424352082, 0.776176800606203, -0.178569692561694, 0.411366413888367, 
                      -0.218782058787729, -0.684466225777628, -1, -0.588461855039565, 
                      0.227595353053499, -0.301670310592772, 0.231174642779848, -0.639366548957921, 
                      -0.114897738179063), .Dim = c(19L, 2L))

# Labels
labels <- c(
  1:10,
  1:9
)

# Groups
groups <- list(
  Dysthymia = 1:10,
  GAD = 11:19
)

# Larger sample size (N = 5000)

# List to store results:
Results2 <- list()
# Second data (N = 1000):
set.seed(3)
Data3 <- simData(5000, A, Psi)

# Estimate using IsingFit:
library("IsingFit")
Results2$IsingFit <- IsingFit(Data3,plot = FALSE)

# IsingFit with OR rule:
Results2$IsingFitOR <- IsingFit(Data3,plot = FALSE,AND = FALSE)

# IsingFit with BIC:
Results2$IsingFitBIC <- IsingFit(Data3,plot = FALSE, gamma = 0)

# Estimate using rank-2 approximation:
Results2$lowrank <- Marsman(Data3, 2)$graph

# Estimate using max likelihood:
Results2$loglin <- EstimateIsing(Data3, method = "ll")

# Estimate using elasticIsing
Results2$elastic <- elasticIsing(Data3)

# Store all graphs in the PDF:
library("qgraph")
pdf("EstimatedNetworks.pdf", height=5 ,width=5)
qgraph(Results$true$graph, layout = Layout, title = "Loglinear model (N = 10,000,000)", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results$loglin$graph, layout = Layout, title = "Loglinear model (N = 1,000)", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results$IsingFit$weiadj, layout = Layout, title = "IsingFit (N = 1,000)", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results$IsingFit$weiadj, layout = Layout, title = "IsingFit (N = 1,000), gamma = 0.25 & AND-rule", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results$IsingFitOR$weiadj, layout = Layout, title = "IsingFit (N = 1,000), gamma = 0.25 & OR-rule", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results$IsingFitBIC$weiadj, layout = Layout, title = "IsingFit (N = 1,000), gamma = 0 & AND-rule", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results$lowrank, layout = Layout,diag=FALSE, title = "Rank 2 approximation (N = 1,000)", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
plot(Results$elastic, layout = Layout,diag=FALSE, title = "Elastic-net (N = 1,000)", vsize = 6,
     labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results2$loglin$graph, layout = Layout, title = "Loglinear model (N = 5,000)", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results2$IsingFit$weiadj, layout = Layout, title = "IsingFit (N = 5,000)", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results2$IsingFit$weiadj, layout = Layout, title = "IsingFit (N = 5,000), gamma = 0.25 & AND-rule", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results2$IsingFitOR$weiadj, layout = Layout, title = "IsingFit (N = 5,000), gamma = 0.25 & OR-rule", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results2$IsingFitBIC$weiadj, layout = Layout, title = "IsingFit (N = 5,000), gamma = 0 & AND-rule", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
qgraph(Results2$lowrank, layout = Layout,diag=FALSE, title = "Rank 2 approximation (N = 5,000)", vsize = 6,
       labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))
plot(Results2$elastic, layout = Layout,diag=FALSE, title = "Elastic-net (N = 5,000)", vsize = 6,
     labels = labels, groups = groups, legend = FALSE, pastel = TRUE, mar = c(2,2,2,2))

dev.off()