R/Simulation.R
In McKers/hidiTS_backup:
Defines functions
prep_data_hidi
#-------------------------------------------------------------------------------------------------#
# #
# Replicate the Paper #
# #
#-------------------------------------------------------------------------------------------------#
# Load Packages
#-------------------------------------------------------------------------------------------------
install.packages("devtools") #load/install
devtools::install_github("manuhuth/hidiTS")
library(hidiTS)
library(optimParallel) #load/install
library(ggplot2) #load/install
library(xtable) #load/install
library(reshape2) #load/install
library(ggpubr) #load/install
library(plotly) #load/install
library(tidyr) #load/install
library(fbi) #load/install
# Prepare Multi Core Work
#-------------------------------------------------------------------------------------------------
cl <- makeCluster(detectCores()-1)
setDefaultCluster(cl = cl)
# 1. - Data Simulation Difference MSE PCA vs. ML - 500 Samples
#-------------------------------------------------------------------------------------------------
# 1.1 - b = 0.5, Set-up as described in Table 1
#-------------------------------------------------------------------------------------------------
#link to function
df_table_1_1 <- simulation_mse_vs_pca(b=0.5, n_simulation=c(5, 15, 20, 30), T_simulation=c(7, 15, 20, 30, 40), number_samples = 500, start_seed = 1)
# 1.2 - b = 3^0.5, Set-up as described in Table 1
#-------------------------------------------------------------------------------------------------
df_table_1_2 <-simulation_mse_vs_pca(b=3^0.5, n_simulation=c(5, 15, 20, 30), T_simulation=c(7, 15, 20, 30, 40), number_samples = 500, start_seed = 1)
# 2. - Data Simulation PCA Simulation Study - 1000 Samples
#-------------------------------------------------------------------------------------------------
# 2.1 b = 0.5, Set-up as described in Figure 3
#-------------------------------------------------------------------------------------------------
df_pca_b_low <- simulation_pca(b=0.5, T_simulation = c(7,15,30,40,seq(50,300,50)), n_simulation = c(5,10,seq(10,40,10),seq(50,300,50)), number_samples = 2, start_seed = 1)
# 2.2 b = 3^0.5, Set-up as described in Figure 3
#-------------------------------------------------------------------------------------------------
df_pca_b_medium <- simulation_pca(b=3^0.5, T_simulation = c(7,15,30,40,seq(50,300,50)), n_simulation = c(5,10,seq(10,40,10),seq(50,300,50)), number_samples = 2, start_seed = 1)
# 3. - Tables and Figures
#-------------------------------------------------------------------------------------------------
# 3.1 - Table 1 - MSEs PCA vs. ML
#-------------------------------------------------------------------------------------------------
df_table_1_2['mse_diff_f'] <- df_table_1_2$mse_pca_f-df_table_1_2$mse_ml_f
df_table_1_2['mse_diff_f.1'] <- df_table_1_2$mse_pca_f.1-df_table_1_2$mse_ml_f.1
df_table_1_2['mse_diff_f.2'] <- df_table_1_2$mse_pca_f.2-df_table_1_2$mse_ml_f.2
sim_data_medium <- df_table_1_2[!duplicated(df_table_1_1[c('n','T')]),]
ns <- 1:400
Ts <- 1:400
data_medium <- sim_data_medium[ which(sim_data_medium$T %in% Ts & sim_data_medium$n %in% ns), ]
ics_medium <- data_medium[,c('mse_diff_f', 'mse_diff_f.1', 'mse_diff_f.2')]
names(ics_medium) <- c('factor1', 'factor2', 'factor3')
df_table_1_1['mse_diff_f'] <- df_table_1_1$mse_pca_f-df_table_1_1$mse_ml_f
df_table_1_1['mse_diff_f.1'] <- df_table_1_1$mse_pca_f.1-df_table_1_1$mse_ml_f.1
df_table_1_1['mse_diff_f.2'] <- df_table_1_1$mse_pca_f.2-df_table_1_1$mse_ml_f.2
sim_data_small <- df_table_1_1[!duplicated(df_table_1_2[c('n','T')]),]
data_small <- sim_data_small[ which(sim_data_small$T %in% Ts & sim_data_small$n %in% ns), ]
ics_small<- data_small[,c('n', 'T','mse_diff_f', 'mse_diff_f.1', 'mse_diff_f.2')]
names(ics_small) <- c('n', 'T','factor1', 'factor2', 'factor3')
data_final <- cbind(ics_small, ics_medium)
data_final['n'] <- as.integer(data_final[,'n'])
data_final['T'] <- as.integer(data_final[,'T'])
print(xtable(data_final, type = "latex", digits=c(0,0,0,4,4,4, 4,4,4) ), include.rownames=FALSE)
# 3.2 - Figure 2 - Eigenvalue Structure of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
df <- df_pca_b_low[c("ev1","ev2" ,"ev3","ev4", "ev5", 'n', 'T' )]
for (index in 1:5) {
df[c(paste('ev',index, sep=''))] <- df[c(paste('ev',index, sep=''))] / df['n']
}
ns <- c(5, 20, 50, 100)
Ts <- c(7, 15, 30, 100)
width <- 0.6
list_df <- list()
for (index in 1:length(Ts)) {
list_df[[index]] <- melt(df[ which( (df$T == Ts[index]) & (df$n %in% ns) ),
c("ev1","ev2" ,"ev3","ev4", "ev5", 'n')], id = 'n')
list_df[[index]]$n <- as.factor(list_df[[index]]$n)
colnames(list_df[[index]]) <- c('n', 'Eigenvalue','Magnitude')
}
t7 <- ggplot(list_df[[1]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity", width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=7') + theme(text = element_text(size=22))
#t15 <- ggplot(list_df[[2]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=15') + theme(text = element_text(size=20)) + ylab('')
t30 <- ggplot(list_df[[3]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity",width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=30') + theme(text = element_text(size=22))
#t100 <- ggplot(list_df[[4]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=100') + theme(text = element_text(size=20)) + ylab('')
(figure <- ggarrange(t7,t30, ncol = , nrow=2, common.legend = TRUE, legend="bottom"))
df <- df_pca_b_medium[c("ev1","ev2" ,"ev3","ev4", "ev5", 'n', 'T' )]
for (index in 1:5) {
df[c(paste('ev',index, sep=''))] <- df[c(paste('ev',index, sep=''))] / df['n']
}
ns <- c(5, 20, 50, 100)
Ts <- c(7, 15, 30, 100)
width <- 0.6
list_df <- list()
for (index in 1:length(Ts)) {
list_df[[index]] <- melt(df[ which( (df$T == Ts[index]) & (df$n %in% ns) ),
c("ev1","ev2" ,"ev3","ev4", "ev5", 'n')], id = 'n')
list_df[[index]]$n <- as.factor(list_df[[index]]$n)
colnames(list_df[[index]]) <- c('n', 'Eigenvalue','Magnitude')
}
t7_med <- ggplot(list_df[[1]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity", width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=7') + theme(text = element_text(size=22))
#t15 <- ggplot(list_df[[2]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=15') + theme(text = element_text(size=20)) + ylab('')
t30_med <- ggplot(list_df[[3]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity",width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=30') + theme(text = element_text(size=22))
#t100 <- ggplot(list_df[[4]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=100') + theme(text = element_text(size=20)) + ylab('')
(figure_med <- ggarrange(t7_med,t30_med, ncol = , nrow=2, common.legend = TRUE, legend="bottom"))
#ggsave("static/eigenvalues_medium_lambda.png")
# 3.3 - Figure 7 & Figure 8 - Average Accuracy of the BIC_nT and the BNIC of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
list_accuracy_plots_low_b <- accuracy_plots(df_pca_b_low, maxn=300, maxt=300)
list_accuracy_plots_medium_b <- accuracy_plots(df_pca_b_medium, maxn=300, maxt=300)
list_accuracy_plots_low_b[[1]] #3D plots can be rotated manually
list_accuracy_plots_low_b[[2]]
list_accuracy_plots_low_b[[3]]
list_accuracy_plots_low_b[[4]]
list_accuracy_plots_medium_b[[1]]
list_accuracy_plots_medium_b[[2]]
list_accuracy_plots_medium_b[[3]]
list_accuracy_plots_medium_b[[4]]
# 3.4 - Table 3 - Average Accuracy of the BIC_nT and the BNIC of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
sim_data_medium <- df_pca_b_medium[!duplicated(df_pca_b_medium[c('n','T')]),]
ns <- c(5, 10, 30, 50, 100,300)
Ts <- c(7, 15, 30, 50, 100, 300)
data_medium <- sim_data_medium[ which(sim_data_medium$T %in% Ts
& sim_data_medium$n %in% ns), ]
ics_medium <- data_medium[,c('pca_bai_right', 'pca_bic_right', 'pca_bic_T_right', 'pca_bic_nT_right')]
names(ics_medium) <- c('BNIC_med', 'BIC_n_med', 'BIC_T_med', 'BIC_nT_med')
sim_data_small <- simulated_small[!duplicated(df_pca_b_small[c('n','T')]),]
data_small <- sim_data_small[ which(sim_data_small$T %in% Ts
& sim_data_small$n %in% ns), ]
ics_small<- data_small[,c('n', 'T','pca_bai_right', 'pca_bic_right', 'pca_bic_T_right', 'pca_bic_nT_right')]
names(ics_small) <- c('n', 'T','BNIC_small', 'BIC_n_small', 'BIC_T_small', 'BIC_nT_small')
data_final <- cbind(ics_small, ics_medium)
data_final['n'] <- as.integer(data_final[,'n'])
data_final['T'] <- as.integer(data_final[,'T'])
print(xtable(data_final, type = "latex", digits=c(0,0,0,2,2,2,2,2, 2,2,2)), include.rownames=FALSE)
# 3.5 - Figure 3 & Figure 9 - MSEs of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
list_MSE_plots_low_b <- MSE_plots(df_pca_b_low, Ts = c(7,15,30, 50, 100,300))
list_MSE_plots_medium_b <- MSE_plots(df_pca_b_medium, Ts = c(7,15,30, 50, 100,300))
list_MSE_plots_low_b[[1]]
list_MSE_plots_low_b[[2]]
list_MSE_plots_low_b[[3]]
list_MSE_plots_medium_b[[1]]
list_MSE_plots_medium_b[[2]]
list_MSE_plots_medium_b[[3]]
# 3.6 - Table 4 - MSEs of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
sim_data_medium <- df_pca_b_medium[!duplicated(df_pca_b_medium[c('n','T')]),]
ns <- c(5, 10, 30, 50, 100, 300)
Ts <- c(7, 15, 30, 50, 100, 300)
data_medium <- sim_data_medium[ which(sim_data_medium$T %in% Ts & sim_data_medium$n %in% ns), ]
ics_medium <- data_medium[,c('mse_pca_f', 'mse_pca_f.1', 'mse_pca_f.2')]
names(ics_medium) <- c('factor1', 'factor2', 'factor3')
sim_data_small <- df_pca_b_low[!duplicated(df_pca_b_low[c('n','T')]),]
data_small <- sim_data_small[ which(sim_data_small$T %in% Ts & sim_data_small$n %in% ns), ]
ics_small<- data_small[,c('n', 'T','mse_pca_f', 'mse_pca_f.1', 'mse_pca_f.2')]
names(ics_small) <- c('n', 'T','factor1', 'factor2', 'factor3')
data_final <- cbind(ics_small, ics_medium)
data_final['n'] <- as.integer(data_final[,'n'])
data_final['T'] <- as.integer(data_final[,'T'])
print(xtable(data_final, type = "latex", digits=c(0,0,0,4,4,4, 4,4,4) ), include.rownames=FALSE)
# 3.7 - Figure 5 - Time ML vs PCA
#-------------------------------------------------------------------------------------------------
df_Figure_5 <-simulation_mse_vs_pca(b=3^0.5, n_simulation=c(seq(5, 125,10)),
T_simulation=c(20), number_samples = 20, start_seed = 1)
df_help <- df_Figure_5[df_Figure_5$T==20,]
df_plot <- df_help[c('time_pca', 'time_ml', 'n')]
colnames(df_plot) <- c('PCA', 'ML', 'n')
df_plot_long <- melt(df_plot, id='n')
colnames(df_plot_long) <- c('n', 'Method', 'Time')
ggplot(df_plot_long, aes(x=n, y=Time, colour=Method)) + geom_line() +
ggtitle(' ',
subtitle = 'q = 3, T = 20, maximal optimizer iterations = 5, parallelized optimization') +
labs(fill = "Methods")
# 3.8 - Figure 6 - Example Eigenvalue Structure
#-------------------------------------------------------------------------------------------------
n <- 20
T <- 20
set.seed(123)
data <- sim_data(p = n, T = T, dim_F= 3, lags_F=1, lags_X=0, ar_F=1, ar_Y=1, low_X = -3, up_X = 3,
low_F = 0.3, up_F = 0.6, burn_in = 20, data_only = FALSE, only_stationary = TRUE, vcv_mu = diag(n),
adjust_diag = FALSE, geometric_F =TRUE, diag_F = TRUE, geometric_X =FALSE, geometric_Y =FALSE)
vec <- c()
vec_bic <- c()
for (k in 1:20) {
pc <- pca_estimator(data$X, k)
x_hat <- pc$Lambda %*% pc$F
rss <- mean((data$X - x_hat)^2)
bic <- n * log(rss/(n*T)) + k * log(n)
bai <- log(rss/(n*T)) + k *(n+T)/(n*T) * log(min(n,T))
vec <- cbind(vec, bai)
vec_bic <- c(vec_bic, bic)
}
data_smooth <- sim_data(p = n, T = T, dim_F= q, lags_F=1, lags_X=0, ar_F=1, ar_Y=1, low_X = -1, up_X = 1,
low_F = 0.3, up_F = 0.6, burn_in = 20, data_only = FALSE, only_stationary = TRUE, vcv_mu = 10*diag(n),
adjust_diag = FALSE, geometric_F =TRUE, diag_F = TRUE, geometric_X =FALSE, geometric_Y =FALSE)
df <- data.frame(cbind(eigen(var(t(data$X)))$values,eigen(var(t(data_smooth$X)))$values, 1:length(eigen(var(t(data$X)))$values)))
colnames(df) <- c('Sharp Cut-Off','Smooth', 'Eigenvalue')
df_long <- melt(df, id='Eigenvalue')
colnames(df_long) <- c('Eigenvalue', 'Shape', 'Magnitude')
ggplot(df_long, aes(x=Eigenvalue, y=Magnitude, colour=Shape)) + geom_point(aes(size = 2)) +
theme(text = element_text(size=28))
# 4. - Application
#-------------------------------------------------------------------------------------------------
rm(list = ls())
# 4.1 - Figure 4 a)/b) & Figure 10
#-------------------------------------------------------------------------------------------------
prep_data_hidi <- function(data){
data_hidi <- as.matrix(t(data))
output <- list("data_fbi"= data, "X"=data_hidi )
return(output)
}
df_paper=fredqd(date_end =as.Date(c("1985/12/01")), date_start=as.Date(c("1960/03/01")),transform = TRUE)
# remove dates
df_temp=df_paper[,2:(length(df_paper))]
#drop Nas
Na_names <- colnames(df_temp)[colSums(is.na(df_temp)) > 0]
df_colnames <- colnames(df_temp)
col_keeps <- setdiff(df_colnames,Na_names)
df_no_na <- subset(df_temp, select=(col_keeps))
df_final <- prep_data_hidi(df_no_na)
X <- df_final$X
T <- ncol(X)
n <- nrow(X)
ic_BIC_n <- c()
ic_BIC_T <- c()
ic_BIC_nT <- c()
ic_BNIC <- c()
for (r in 1:n){
pca_est <- pca_estimator(X, r)
f_hat <- pca_est$F
l_hat <- pca_est$Lambda
x_hat <- l_hat %*% f_hat
u_hat <- X - x_hat
RSS <- sum(u_hat^2)
RSS_part <- log(RSS/n/T)
BIC_n <- RSS_part + r * log(n)/n
BIC_T <- RSS_part + r * log(T)/T
BIC_nT <- RSS_part + r * log(n*T)/n/T * (n+T-r)
BNIC <- RSS_part + r * log(min(n,T))/n/T * (n+T)
ic_BIC_n[r] <- BIC_n
ic_BIC_T[r] <- BIC_T
ic_BIC_nT[r] <- BIC_nT
ic_BNIC[r] <- BNIC
print(paste(' r=',r, sep=''))
}
df <- cbind(ic_BIC_n, ic_BIC_T, ic_BIC_nT)[1:200,]
colnames(df) <- c('BIC_n', 'BIC_T', 'BIC_nT')
df_long <- melt(df)
colnames(df_long) <- c('r', 'IC', 'Value')
(figure1 <- ggplot(df_long, aes(x=r, y=Value, color=IC)) + geom_line() +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') )
ggsave("static/application_BICs_full.png")
df_long2 <- melt(df[1:20,])
colnames(df_long2) <- c('r', 'IC', 'Value')
(figure2 <- ggplot(df_long2, aes(x=r, y=Value, color=IC)) + geom_line() + geom_point() +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') )
ggsave("static/application_BICs_n20.png")
(figure3 <- ggplot(as.data.frame(cbind('BNIC'=ic_BNIC, 'r'=1:n)[1:200,]), aes(x=r, y=BNIC, lty = 'BNIC')) +
geom_line() + theme(text = element_text(size=28), legend.position="bottom") + ylab('Value') + scale_linetype(''))
ggsave("static/application_Bai_full.png")
(figure4 <- ggplot(as.data.frame(cbind('BNIC'=ic_BNIC, 'r'=1:n)[1:20,]), aes(x=r, y=BNIC, lty = 'BNIC')) +
geom_line() + geom_point() + theme(text = element_text(size=28), legend.position="bottom") + ylab('Value')+ scale_linetype(''))
ggsave("static/application_Bai_n20.png")
# 4.2 - Figure 4 c)/D) & Figure 11
#-------------------------------------------------------------------------------------------------
set.seed(1)
n <- 211
T <- 104
q <- 10
BIC_n_df <- c()
BIC_T_df <- c()
BIC_nT_df <- c()
BNIC_df <- c()
for (index in 1:1000) {
data <- sim_data(p = n, T = T, dim_F= q, lags_F=1, lags_X=0, ar_F=1, ar_Y=1, low_X = -3^0.5, up_X = 3^0.5,
low_F = 0.3, up_F = 0.6, burn_in = 20, data_only = FALSE, only_stationary = TRUE, vcv_mu = diag(n),
adjust_diag = FALSE, geometric_F =TRUE, diag_F = TRUE, geometric_X =FALSE, geometric_Y =FALSE)
X <- data$X
ic_BIC_n <- c()
ic_BIC_T <- c()
ic_BIC_nT <- c()
ic_BNIC <- c()
for (r in 1:n){
pca_est <- pca_estimator(X, r)
f_hat <- pca_est$F
l_hat <- pca_est$Lambda
x_hat <- l_hat %*% f_hat
u_hat <- X - x_hat
RSS <- sum(u_hat^2)
RSS_part <- log(RSS/n/T)
BIC_n <- RSS_part + r * log(n)/n
BIC_T <- RSS_part + r * log(T)/T
BIC_nT <- RSS_part + r * log(n*T)/n/T * (n+T-r)
BNIC <- RSS_part + r * log(min(n,T))/n/T * (n+T)
ic_BIC_n[r] <- BIC_n
ic_BIC_T[r] <- BIC_T
ic_BIC_nT[r] <- BIC_nT
ic_BNIC[r] <- BNIC
print(paste('sample=', index, ' r=',r, sep=''))
}
BIC_n_df <- rbind(BIC_n_df, ic_BIC_n)
BIC_T_df <- rbind(BIC_T_df, ic_BIC_T)
BIC_nT_df <- rbind(BIC_nT_df, ic_BIC_nT)
BNIC_df <- rbind(BNIC_df, ic_BNIC)
}
alpha = 0.1
up <- 1 - alpha/2
low <- alpha/2
mean_n <- colMeans(BIC_n_df)
high_n <- apply(BIC_n_df, 2, quantile, up)
low_n <- apply(BIC_n_df, 2, quantile, low)
BIC_n_df_plot <- cbind('low'=low_n, 'mean'=mean_n, 'high'=high_n, 'r'= 1:n, 'IC' = rep(1, n) )
mean_T <- colMeans(BIC_T_df)
high_T <- apply(BIC_T_df, 2, quantile, up)
low_T <- apply(BIC_T_df, 2, quantile, low)
BIC_T_df_plot <-cbind('low'=low_T, 'mean'=mean_T, 'high'=high_T, 'r'= 1:n, 'IC' = rep(2, n) )
mean_nT <- colMeans(BIC_nT_df)
high_nT <- apply(BIC_nT_df, 2, quantile, up)
low_nT <- apply(BIC_nT_df, 2, quantile, low)
BIC_nT_df_plot <- cbind('low'=low_nT, 'mean'=mean_nT, 'high'=high_nT, 'r'= 1:n, 'IC' = rep(3, n) )
mean_bai <- colMeans(BNIC_df)
high_bai <- apply(BNIC_df, 2, quantile, up)
low_bai <- apply(BNIC_df, 2, quantile, low)
BNIC_df_plot <- as.data.frame(cbind('low'=low_bai, 'mean'=mean_bai, 'high'=high_bai, 'r'= 1:n))
df <- as.data.frame(rbind(BIC_n_df_plot[1:200,], BIC_T_df_plot[1:200,], BIC_nT_df_plot[1:200,]))
df['IC'][df['IC'] == 1] <- 'BIC_n'
df['IC'][df['IC'] == 2] <- 'BIC_T'
df['IC'][df['IC'] == 3] <- 'BIC_nT'
#df['IC'][df['IC'] == 4] <- 'BNIC'
(fig1 <- ggplot(df, aes(x=r, y=mean, color=IC)) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high, color=IC),linetype=2, alpha = 0.2) +
scale_color_manual(
values = c(BIC_n="#F8766D", BIC_nT="#619CFF", BIC_T="#00BA38")) +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') ) + ylab('Value')
df2 <- as.data.frame(rbind(BIC_n_df_plot[1:20,], BIC_T_df_plot[1:20,], BIC_nT_df_plot[1:20,]))
df2['IC'][df2['IC'] == 1] <- 'BIC_n'
df2['IC'][df2['IC'] == 2] <- 'BIC_T'
df2['IC'][df2['IC'] == 3] <- 'BIC_nT'
#df2['IC'][df2['IC'] == 4] <- 'BNIC'
(fig2 <- ggplot(df2, aes(x=r, y=mean, color=IC)) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high, color=IC),linetype=2, alpha = 0.2) +
scale_color_manual(
values = c(BIC_n="#F8766D", BIC_nT="#619CFF", BIC_T="#00BA38")) +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') ) + ylab('Value')
(fig3 <- ggplot(BNIC_df_plot[1:200,], aes(x=r, y=mean, lty = 'BNIC')) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high),linetype=2, alpha = 0.2) +
theme(text = element_text(size=28), legend.position="bottom") + scale_linetype('') + ylab('Value'))
df_BNIC_n20 <- BNIC_df_plot[1:20,]
(fig4 <- ggplot(df_BNIC_n20, aes(x=r, y=mean, lty = 'BNIC')) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high),linetype=2, alpha = 0.2) +
theme(text = element_text(size=28), legend.position="bottom") + scale_linetype('') + ylab('Value'))
McKers/hidiTS_backup documentation built on Feb. 26, 2021, 12:23 a.m.
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Defines functions prep_data_hidi
#-------------------------------------------------------------------------------------------------#
# #
# Replicate the Paper #
# #
#-------------------------------------------------------------------------------------------------#
# Load Packages
#-------------------------------------------------------------------------------------------------
install.packages("devtools") #load/install
devtools::install_github("manuhuth/hidiTS")
library(hidiTS)
library(optimParallel) #load/install
library(ggplot2) #load/install
library(xtable) #load/install
library(reshape2) #load/install
library(ggpubr) #load/install
library(plotly) #load/install
library(tidyr) #load/install
library(fbi) #load/install
# Prepare Multi Core Work
#-------------------------------------------------------------------------------------------------
cl <- makeCluster(detectCores()-1)
setDefaultCluster(cl = cl)
# 1. - Data Simulation Difference MSE PCA vs. ML - 500 Samples
#-------------------------------------------------------------------------------------------------
# 1.1 - b = 0.5, Set-up as described in Table 1
#-------------------------------------------------------------------------------------------------
#link to function
df_table_1_1 <- simulation_mse_vs_pca(b=0.5, n_simulation=c(5, 15, 20, 30), T_simulation=c(7, 15, 20, 30, 40), number_samples = 500, start_seed = 1)
# 1.2 - b = 3^0.5, Set-up as described in Table 1
#-------------------------------------------------------------------------------------------------
df_table_1_2 <-simulation_mse_vs_pca(b=3^0.5, n_simulation=c(5, 15, 20, 30), T_simulation=c(7, 15, 20, 30, 40), number_samples = 500, start_seed = 1)
# 2. - Data Simulation PCA Simulation Study - 1000 Samples
#-------------------------------------------------------------------------------------------------
# 2.1 b = 0.5, Set-up as described in Figure 3
#-------------------------------------------------------------------------------------------------
df_pca_b_low <- simulation_pca(b=0.5, T_simulation = c(7,15,30,40,seq(50,300,50)), n_simulation = c(5,10,seq(10,40,10),seq(50,300,50)), number_samples = 2, start_seed = 1)
# 2.2 b = 3^0.5, Set-up as described in Figure 3
#-------------------------------------------------------------------------------------------------
df_pca_b_medium <- simulation_pca(b=3^0.5, T_simulation = c(7,15,30,40,seq(50,300,50)), n_simulation = c(5,10,seq(10,40,10),seq(50,300,50)), number_samples = 2, start_seed = 1)
# 3. - Tables and Figures
#-------------------------------------------------------------------------------------------------
# 3.1 - Table 1 - MSEs PCA vs. ML
#-------------------------------------------------------------------------------------------------
df_table_1_2['mse_diff_f'] <- df_table_1_2$mse_pca_f-df_table_1_2$mse_ml_f
df_table_1_2['mse_diff_f.1'] <- df_table_1_2$mse_pca_f.1-df_table_1_2$mse_ml_f.1
df_table_1_2['mse_diff_f.2'] <- df_table_1_2$mse_pca_f.2-df_table_1_2$mse_ml_f.2
sim_data_medium <- df_table_1_2[!duplicated(df_table_1_1[c('n','T')]),]
ns <- 1:400
Ts <- 1:400
data_medium <- sim_data_medium[ which(sim_data_medium$T %in% Ts & sim_data_medium$n %in% ns), ]
ics_medium <- data_medium[,c('mse_diff_f', 'mse_diff_f.1', 'mse_diff_f.2')]
names(ics_medium) <- c('factor1', 'factor2', 'factor3')
df_table_1_1['mse_diff_f'] <- df_table_1_1$mse_pca_f-df_table_1_1$mse_ml_f
df_table_1_1['mse_diff_f.1'] <- df_table_1_1$mse_pca_f.1-df_table_1_1$mse_ml_f.1
df_table_1_1['mse_diff_f.2'] <- df_table_1_1$mse_pca_f.2-df_table_1_1$mse_ml_f.2
sim_data_small <- df_table_1_1[!duplicated(df_table_1_2[c('n','T')]),]
data_small <- sim_data_small[ which(sim_data_small$T %in% Ts & sim_data_small$n %in% ns), ]
ics_small<- data_small[,c('n', 'T','mse_diff_f', 'mse_diff_f.1', 'mse_diff_f.2')]
names(ics_small) <- c('n', 'T','factor1', 'factor2', 'factor3')
data_final <- cbind(ics_small, ics_medium)
data_final['n'] <- as.integer(data_final[,'n'])
data_final['T'] <- as.integer(data_final[,'T'])
print(xtable(data_final, type = "latex", digits=c(0,0,0,4,4,4, 4,4,4) ), include.rownames=FALSE)
# 3.2 - Figure 2 - Eigenvalue Structure of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
df <- df_pca_b_low[c("ev1","ev2" ,"ev3","ev4", "ev5", 'n', 'T' )]
for (index in 1:5) {
df[c(paste('ev',index, sep=''))] <- df[c(paste('ev',index, sep=''))] / df['n']
}
ns <- c(5, 20, 50, 100)
Ts <- c(7, 15, 30, 100)
width <- 0.6
list_df <- list()
for (index in 1:length(Ts)) {
list_df[[index]] <- melt(df[ which( (df$T == Ts[index]) & (df$n %in% ns) ),
c("ev1","ev2" ,"ev3","ev4", "ev5", 'n')], id = 'n')
list_df[[index]]$n <- as.factor(list_df[[index]]$n)
colnames(list_df[[index]]) <- c('n', 'Eigenvalue','Magnitude')
}
t7 <- ggplot(list_df[[1]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity", width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=7') + theme(text = element_text(size=22))
#t15 <- ggplot(list_df[[2]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=15') + theme(text = element_text(size=20)) + ylab('')
t30 <- ggplot(list_df[[3]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity",width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=30') + theme(text = element_text(size=22))
#t100 <- ggplot(list_df[[4]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=100') + theme(text = element_text(size=20)) + ylab('')
(figure <- ggarrange(t7,t30, ncol = , nrow=2, common.legend = TRUE, legend="bottom"))
df <- df_pca_b_medium[c("ev1","ev2" ,"ev3","ev4", "ev5", 'n', 'T' )]
for (index in 1:5) {
df[c(paste('ev',index, sep=''))] <- df[c(paste('ev',index, sep=''))] / df['n']
}
ns <- c(5, 20, 50, 100)
Ts <- c(7, 15, 30, 100)
width <- 0.6
list_df <- list()
for (index in 1:length(Ts)) {
list_df[[index]] <- melt(df[ which( (df$T == Ts[index]) & (df$n %in% ns) ),
c("ev1","ev2" ,"ev3","ev4", "ev5", 'n')], id = 'n')
list_df[[index]]$n <- as.factor(list_df[[index]]$n)
colnames(list_df[[index]]) <- c('n', 'Eigenvalue','Magnitude')
}
t7_med <- ggplot(list_df[[1]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity", width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=7') + theme(text = element_text(size=22))
#t15 <- ggplot(list_df[[2]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=15') + theme(text = element_text(size=20)) + ylab('')
t30_med <- ggplot(list_df[[3]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
geom_bar(stat="identity",width = width, position=position_dodge())+
scale_fill_brewer(palette="Paired") + ggtitle('T=30') + theme(text = element_text(size=22))
#t100 <- ggplot(list_df[[4]], aes(x=n, y=Magnitude, fill=Eigenvalue)) +
# geom_bar(stat="identity",width = width, position=position_dodge())+
# scale_fill_brewer(palette="Paired") + ggtitle('T=100') + theme(text = element_text(size=20)) + ylab('')
(figure_med <- ggarrange(t7_med,t30_med, ncol = , nrow=2, common.legend = TRUE, legend="bottom"))
#ggsave("static/eigenvalues_medium_lambda.png")
# 3.3 - Figure 7 & Figure 8 - Average Accuracy of the BIC_nT and the BNIC of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
list_accuracy_plots_low_b <- accuracy_plots(df_pca_b_low, maxn=300, maxt=300)
list_accuracy_plots_medium_b <- accuracy_plots(df_pca_b_medium, maxn=300, maxt=300)
list_accuracy_plots_low_b[[1]] #3D plots can be rotated manually
list_accuracy_plots_low_b[[2]]
list_accuracy_plots_low_b[[3]]
list_accuracy_plots_low_b[[4]]
list_accuracy_plots_medium_b[[1]]
list_accuracy_plots_medium_b[[2]]
list_accuracy_plots_medium_b[[3]]
list_accuracy_plots_medium_b[[4]]
# 3.4 - Table 3 - Average Accuracy of the BIC_nT and the BNIC of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
sim_data_medium <- df_pca_b_medium[!duplicated(df_pca_b_medium[c('n','T')]),]
ns <- c(5, 10, 30, 50, 100,300)
Ts <- c(7, 15, 30, 50, 100, 300)
data_medium <- sim_data_medium[ which(sim_data_medium$T %in% Ts
& sim_data_medium$n %in% ns), ]
ics_medium <- data_medium[,c('pca_bai_right', 'pca_bic_right', 'pca_bic_T_right', 'pca_bic_nT_right')]
names(ics_medium) <- c('BNIC_med', 'BIC_n_med', 'BIC_T_med', 'BIC_nT_med')
sim_data_small <- simulated_small[!duplicated(df_pca_b_small[c('n','T')]),]
data_small <- sim_data_small[ which(sim_data_small$T %in% Ts
& sim_data_small$n %in% ns), ]
ics_small<- data_small[,c('n', 'T','pca_bai_right', 'pca_bic_right', 'pca_bic_T_right', 'pca_bic_nT_right')]
names(ics_small) <- c('n', 'T','BNIC_small', 'BIC_n_small', 'BIC_T_small', 'BIC_nT_small')
data_final <- cbind(ics_small, ics_medium)
data_final['n'] <- as.integer(data_final[,'n'])
data_final['T'] <- as.integer(data_final[,'T'])
print(xtable(data_final, type = "latex", digits=c(0,0,0,2,2,2,2,2, 2,2,2)), include.rownames=FALSE)
# 3.5 - Figure 3 & Figure 9 - MSEs of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
list_MSE_plots_low_b <- MSE_plots(df_pca_b_low, Ts = c(7,15,30, 50, 100,300))
list_MSE_plots_medium_b <- MSE_plots(df_pca_b_medium, Ts = c(7,15,30, 50, 100,300))
list_MSE_plots_low_b[[1]]
list_MSE_plots_low_b[[2]]
list_MSE_plots_low_b[[3]]
list_MSE_plots_medium_b[[1]]
list_MSE_plots_medium_b[[2]]
list_MSE_plots_medium_b[[3]]
# 3.6 - Table 4 - MSEs of PCA Simulation Data
#-------------------------------------------------------------------------------------------------
sim_data_medium <- df_pca_b_medium[!duplicated(df_pca_b_medium[c('n','T')]),]
ns <- c(5, 10, 30, 50, 100, 300)
Ts <- c(7, 15, 30, 50, 100, 300)
data_medium <- sim_data_medium[ which(sim_data_medium$T %in% Ts & sim_data_medium$n %in% ns), ]
ics_medium <- data_medium[,c('mse_pca_f', 'mse_pca_f.1', 'mse_pca_f.2')]
names(ics_medium) <- c('factor1', 'factor2', 'factor3')
sim_data_small <- df_pca_b_low[!duplicated(df_pca_b_low[c('n','T')]),]
data_small <- sim_data_small[ which(sim_data_small$T %in% Ts & sim_data_small$n %in% ns), ]
ics_small<- data_small[,c('n', 'T','mse_pca_f', 'mse_pca_f.1', 'mse_pca_f.2')]
names(ics_small) <- c('n', 'T','factor1', 'factor2', 'factor3')
data_final <- cbind(ics_small, ics_medium)
data_final['n'] <- as.integer(data_final[,'n'])
data_final['T'] <- as.integer(data_final[,'T'])
print(xtable(data_final, type = "latex", digits=c(0,0,0,4,4,4, 4,4,4) ), include.rownames=FALSE)
# 3.7 - Figure 5 - Time ML vs PCA
#-------------------------------------------------------------------------------------------------
df_Figure_5 <-simulation_mse_vs_pca(b=3^0.5, n_simulation=c(seq(5, 125,10)),
T_simulation=c(20), number_samples = 20, start_seed = 1)
df_help <- df_Figure_5[df_Figure_5$T==20,]
df_plot <- df_help[c('time_pca', 'time_ml', 'n')]
colnames(df_plot) <- c('PCA', 'ML', 'n')
df_plot_long <- melt(df_plot, id='n')
colnames(df_plot_long) <- c('n', 'Method', 'Time')
ggplot(df_plot_long, aes(x=n, y=Time, colour=Method)) + geom_line() +
ggtitle(' ',
subtitle = 'q = 3, T = 20, maximal optimizer iterations = 5, parallelized optimization') +
labs(fill = "Methods")
# 3.8 - Figure 6 - Example Eigenvalue Structure
#-------------------------------------------------------------------------------------------------
n <- 20
T <- 20
set.seed(123)
data <- sim_data(p = n, T = T, dim_F= 3, lags_F=1, lags_X=0, ar_F=1, ar_Y=1, low_X = -3, up_X = 3,
low_F = 0.3, up_F = 0.6, burn_in = 20, data_only = FALSE, only_stationary = TRUE, vcv_mu = diag(n),
adjust_diag = FALSE, geometric_F =TRUE, diag_F = TRUE, geometric_X =FALSE, geometric_Y =FALSE)
vec <- c()
vec_bic <- c()
for (k in 1:20) {
pc <- pca_estimator(data$X, k)
x_hat <- pc$Lambda %*% pc$F
rss <- mean((data$X - x_hat)^2)
bic <- n * log(rss/(n*T)) + k * log(n)
bai <- log(rss/(n*T)) + k *(n+T)/(n*T) * log(min(n,T))
vec <- cbind(vec, bai)
vec_bic <- c(vec_bic, bic)
}
data_smooth <- sim_data(p = n, T = T, dim_F= q, lags_F=1, lags_X=0, ar_F=1, ar_Y=1, low_X = -1, up_X = 1,
low_F = 0.3, up_F = 0.6, burn_in = 20, data_only = FALSE, only_stationary = TRUE, vcv_mu = 10*diag(n),
adjust_diag = FALSE, geometric_F =TRUE, diag_F = TRUE, geometric_X =FALSE, geometric_Y =FALSE)
df <- data.frame(cbind(eigen(var(t(data$X)))$values,eigen(var(t(data_smooth$X)))$values, 1:length(eigen(var(t(data$X)))$values)))
colnames(df) <- c('Sharp Cut-Off','Smooth', 'Eigenvalue')
df_long <- melt(df, id='Eigenvalue')
colnames(df_long) <- c('Eigenvalue', 'Shape', 'Magnitude')
ggplot(df_long, aes(x=Eigenvalue, y=Magnitude, colour=Shape)) + geom_point(aes(size = 2)) +
theme(text = element_text(size=28))
# 4. - Application
#-------------------------------------------------------------------------------------------------
rm(list = ls())
# 4.1 - Figure 4 a)/b) & Figure 10
#-------------------------------------------------------------------------------------------------
prep_data_hidi <- function(data){
data_hidi <- as.matrix(t(data))
output <- list("data_fbi"= data, "X"=data_hidi )
return(output)
}
df_paper=fredqd(date_end =as.Date(c("1985/12/01")), date_start=as.Date(c("1960/03/01")),transform = TRUE)
# remove dates
df_temp=df_paper[,2:(length(df_paper))]
#drop Nas
Na_names <- colnames(df_temp)[colSums(is.na(df_temp)) > 0]
df_colnames <- colnames(df_temp)
col_keeps <- setdiff(df_colnames,Na_names)
df_no_na <- subset(df_temp, select=(col_keeps))
df_final <- prep_data_hidi(df_no_na)
X <- df_final$X
T <- ncol(X)
n <- nrow(X)
ic_BIC_n <- c()
ic_BIC_T <- c()
ic_BIC_nT <- c()
ic_BNIC <- c()
for (r in 1:n){
pca_est <- pca_estimator(X, r)
f_hat <- pca_est$F
l_hat <- pca_est$Lambda
x_hat <- l_hat %*% f_hat
u_hat <- X - x_hat
RSS <- sum(u_hat^2)
RSS_part <- log(RSS/n/T)
BIC_n <- RSS_part + r * log(n)/n
BIC_T <- RSS_part + r * log(T)/T
BIC_nT <- RSS_part + r * log(n*T)/n/T * (n+T-r)
BNIC <- RSS_part + r * log(min(n,T))/n/T * (n+T)
ic_BIC_n[r] <- BIC_n
ic_BIC_T[r] <- BIC_T
ic_BIC_nT[r] <- BIC_nT
ic_BNIC[r] <- BNIC
print(paste(' r=',r, sep=''))
}
df <- cbind(ic_BIC_n, ic_BIC_T, ic_BIC_nT)[1:200,]
colnames(df) <- c('BIC_n', 'BIC_T', 'BIC_nT')
df_long <- melt(df)
colnames(df_long) <- c('r', 'IC', 'Value')
(figure1 <- ggplot(df_long, aes(x=r, y=Value, color=IC)) + geom_line() +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') )
ggsave("static/application_BICs_full.png")
df_long2 <- melt(df[1:20,])
colnames(df_long2) <- c('r', 'IC', 'Value')
(figure2 <- ggplot(df_long2, aes(x=r, y=Value, color=IC)) + geom_line() + geom_point() +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') )
ggsave("static/application_BICs_n20.png")
(figure3 <- ggplot(as.data.frame(cbind('BNIC'=ic_BNIC, 'r'=1:n)[1:200,]), aes(x=r, y=BNIC, lty = 'BNIC')) +
geom_line() + theme(text = element_text(size=28), legend.position="bottom") + ylab('Value') + scale_linetype(''))
ggsave("static/application_Bai_full.png")
(figure4 <- ggplot(as.data.frame(cbind('BNIC'=ic_BNIC, 'r'=1:n)[1:20,]), aes(x=r, y=BNIC, lty = 'BNIC')) +
geom_line() + geom_point() + theme(text = element_text(size=28), legend.position="bottom") + ylab('Value')+ scale_linetype(''))
ggsave("static/application_Bai_n20.png")
# 4.2 - Figure 4 c)/D) & Figure 11
#-------------------------------------------------------------------------------------------------
set.seed(1)
n <- 211
T <- 104
q <- 10
BIC_n_df <- c()
BIC_T_df <- c()
BIC_nT_df <- c()
BNIC_df <- c()
for (index in 1:1000) {
data <- sim_data(p = n, T = T, dim_F= q, lags_F=1, lags_X=0, ar_F=1, ar_Y=1, low_X = -3^0.5, up_X = 3^0.5,
low_F = 0.3, up_F = 0.6, burn_in = 20, data_only = FALSE, only_stationary = TRUE, vcv_mu = diag(n),
adjust_diag = FALSE, geometric_F =TRUE, diag_F = TRUE, geometric_X =FALSE, geometric_Y =FALSE)
X <- data$X
ic_BIC_n <- c()
ic_BIC_T <- c()
ic_BIC_nT <- c()
ic_BNIC <- c()
for (r in 1:n){
pca_est <- pca_estimator(X, r)
f_hat <- pca_est$F
l_hat <- pca_est$Lambda
x_hat <- l_hat %*% f_hat
u_hat <- X - x_hat
RSS <- sum(u_hat^2)
RSS_part <- log(RSS/n/T)
BIC_n <- RSS_part + r * log(n)/n
BIC_T <- RSS_part + r * log(T)/T
BIC_nT <- RSS_part + r * log(n*T)/n/T * (n+T-r)
BNIC <- RSS_part + r * log(min(n,T))/n/T * (n+T)
ic_BIC_n[r] <- BIC_n
ic_BIC_T[r] <- BIC_T
ic_BIC_nT[r] <- BIC_nT
ic_BNIC[r] <- BNIC
print(paste('sample=', index, ' r=',r, sep=''))
}
BIC_n_df <- rbind(BIC_n_df, ic_BIC_n)
BIC_T_df <- rbind(BIC_T_df, ic_BIC_T)
BIC_nT_df <- rbind(BIC_nT_df, ic_BIC_nT)
BNIC_df <- rbind(BNIC_df, ic_BNIC)
}
alpha = 0.1
up <- 1 - alpha/2
low <- alpha/2
mean_n <- colMeans(BIC_n_df)
high_n <- apply(BIC_n_df, 2, quantile, up)
low_n <- apply(BIC_n_df, 2, quantile, low)
BIC_n_df_plot <- cbind('low'=low_n, 'mean'=mean_n, 'high'=high_n, 'r'= 1:n, 'IC' = rep(1, n) )
mean_T <- colMeans(BIC_T_df)
high_T <- apply(BIC_T_df, 2, quantile, up)
low_T <- apply(BIC_T_df, 2, quantile, low)
BIC_T_df_plot <-cbind('low'=low_T, 'mean'=mean_T, 'high'=high_T, 'r'= 1:n, 'IC' = rep(2, n) )
mean_nT <- colMeans(BIC_nT_df)
high_nT <- apply(BIC_nT_df, 2, quantile, up)
low_nT <- apply(BIC_nT_df, 2, quantile, low)
BIC_nT_df_plot <- cbind('low'=low_nT, 'mean'=mean_nT, 'high'=high_nT, 'r'= 1:n, 'IC' = rep(3, n) )
mean_bai <- colMeans(BNIC_df)
high_bai <- apply(BNIC_df, 2, quantile, up)
low_bai <- apply(BNIC_df, 2, quantile, low)
BNIC_df_plot <- as.data.frame(cbind('low'=low_bai, 'mean'=mean_bai, 'high'=high_bai, 'r'= 1:n))
df <- as.data.frame(rbind(BIC_n_df_plot[1:200,], BIC_T_df_plot[1:200,], BIC_nT_df_plot[1:200,]))
df['IC'][df['IC'] == 1] <- 'BIC_n'
df['IC'][df['IC'] == 2] <- 'BIC_T'
df['IC'][df['IC'] == 3] <- 'BIC_nT'
#df['IC'][df['IC'] == 4] <- 'BNIC'
(fig1 <- ggplot(df, aes(x=r, y=mean, color=IC)) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high, color=IC),linetype=2, alpha = 0.2) +
scale_color_manual(
values = c(BIC_n="#F8766D", BIC_nT="#619CFF", BIC_T="#00BA38")) +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') ) + ylab('Value')
df2 <- as.data.frame(rbind(BIC_n_df_plot[1:20,], BIC_T_df_plot[1:20,], BIC_nT_df_plot[1:20,]))
df2['IC'][df2['IC'] == 1] <- 'BIC_n'
df2['IC'][df2['IC'] == 2] <- 'BIC_T'
df2['IC'][df2['IC'] == 3] <- 'BIC_nT'
#df2['IC'][df2['IC'] == 4] <- 'BNIC'
(fig2 <- ggplot(df2, aes(x=r, y=mean, color=IC)) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high, color=IC),linetype=2, alpha = 0.2) +
scale_color_manual(
values = c(BIC_n="#F8766D", BIC_nT="#619CFF", BIC_T="#00BA38")) +
theme(text = element_text(size=28), legend.position="bottom") + labs(color='') ) + ylab('Value')
(fig3 <- ggplot(BNIC_df_plot[1:200,], aes(x=r, y=mean, lty = 'BNIC')) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high),linetype=2, alpha = 0.2) +
theme(text = element_text(size=28), legend.position="bottom") + scale_linetype('') + ylab('Value'))
df_BNIC_n20 <- BNIC_df_plot[1:20,]
(fig4 <- ggplot(df_BNIC_n20, aes(x=r, y=mean, lty = 'BNIC')) + geom_line() +
geom_ribbon(aes(x=r, ymin=low, ymax=high),linetype=2, alpha = 0.2) +
theme(text = element_text(size=28), legend.position="bottom") + scale_linetype('') + ylab('Value'))
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