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Functions_for_PJIVE.R
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###########################################################################################################################
####### Functions for JIVE-PNC Project(s) ####################################
####### Author: Raphiel J. Murden ####################################
####### Supervised by Benjamin Risk ####################################
###########################################################################################################################
require(Matrix); require(ggplot2); require(reshape2); require(fields); require(mvtnorm)
require(dplyr); require(xtable); require(MASS); require(extraDistr); require(stringr)
require(MCMCpack); require(CJIVE)
######################################################################################################################
########### Generates K Simulated Datasets that follow JIVE Model using binary subject scores ####################
######################################################################################################################
GenerateToyData <- function(n, p, JntVarEx, IndVarEx, jnt_rank = 1, equal.eig = FALSE, ind_ranks, JntVarAdj = TRUE, mix.probs = NULL,
SVD.plots = TRUE, Error = TRUE, print.cor = TRUE, Loads = "Rademacher", Scores = "Gaussian_Mixture",
error.variances = NULL){
# Write out both joint and indiv subject scores for both data sets first
r.J = jnt_rank
r.I = ind_ranks
K = length(p)
Scores.text = ifelse(is.numeric(Scores), "as defined by user", paste("from", Scores, "distributions"))
Loads.text = ifelse(is.list(Loads), "as defined by user.", paste("from", Loads, "distributions."))
cat(paste0("Generating Scores ", Scores.text, " and Loadings ", Loads.text, ". \n"))
# Generate scores
if(is.numeric(Scores)){
JntScores = Scores[,1:r.J, drop = FALSE]
IndivScores = Scores[,-(1:r.J), drop = FALSE]
} else if(Scores=="Binomial"){
JntScores = matrix(rbinom(n*r.J, size=1, prob=0.2), nrow = n, ncol = r.J)
b = rbinom(n*sum(r.I), size=1, prob=0.4)
b = 1 - 2*b
IndivScores = matrix(b, nrow = n, ncol = sum(r.I))
} else if (Scores=="Gaussian_Mixture"){
if(is.null(mix.probs)){mix.probs = c(0.2, 0.5, 0.3)}
n.groups = length(mix.probs)
n.vals = (n.groups-1)/2
if(is.integer(length(mix.probs)/2)){
group.means = c(-4*(n.vals:1),4*(1:n.vals))
} else {
group.means = c(-4*(n.vals:1),0,4*(1:n.vals))
}
JointScores.groups = list()
for(l in 1:length(mix.probs)){JointScores.groups[[l]] = matrix(rnorm(n*mix.probs[l]*r.J, mean = group.means[l]), ncol = r.J)}
JntScores = do.call(rbind, JointScores.groups)
IndivScores = matrix(rnorm(n*sum(r.I)), nrow = n, ncol = sum(r.I))
} else if(Scores=="Gaussian"){
JntScores = matrix(rnorm(n*r.J), ncol = r.J)
IndivScores = matrix(rnorm(n*sum(r.I)), nrow = n, ncol = sum(r.I))
} else if (is.numeric(Scores)){
if(nrow(Scores == n) & ncol(Scores = r.J+sum(r.I))){
JntScores = Scores[,1:r.J]
IndivScores = Scores[,-(1:r.J)]
} else{
cat("Matrix of subject scores must have n rows and jnt_rank+sum(ind_ranks) columns.")
}
} else {
message("Please use one of the following three options to generate data with corresponding subject scores: 1) 'Gaussian' 2) 'Gaussian_Mixture' 3) Binomial.\n")
message("Alternatively, the user can enter a matrix of subject scores with n rows and jnt_rank+sum(ind_ranks) columns.\n")
}
colnames(JntScores) = paste("Jnt Score", 1:r.J)
IndivScores.names = NULL
for(k in 1:K){
IndivScores.names = c(IndivScores.names, paste0("Indiv X", k, " Score ", 1:r.I[k]))
}
colnames(IndivScores) = IndivScores.names
if(print.cor){cat("The correlation between subject scores is given by"); print(round(cor(cbind(JntScores, IndivScores)),4))}
# Generate Loadings
Jnt.Loads.All = list()
Indiv.Loads.All = list()
D.I = list()
Noise = Joint.Sigs = Indiv.Sigs = list()
Sig.Mats = Data.Mats = list()
temp.fcn = function(x){x[sample(round(length(x)/2))] = 1; x}
if(is.null(error.variances)){
error.variances = rep(1,K)
} else if(is.numeric(error.variances) & length(error.variances) != K){
cat("Number of entries in 'error.variances' must equal number of data sets and thus have the same length as 'p'.\n")
}
for(k in 1:K){
if(length(Loads)==1){
if(Loads == "Gaussian"){
Jnt.Loads.All[[k]] = matrix(rnorm(r.J*p[k]), nrow = r.J, ncol = p[k])
} else if (Loads == "Fixed"){
Jnt.Loads.All[[k]] = matrix(apply(matrix(0, nrow = r.J, ncol = p[k]), 1, temp.fcn), nrow = r.J)
} else if (Loads == "Double_Exp"){
Jnt.Loads.All[[k]] = matrix(rlaplace(p[k]*(r.J)), nrow = r.J)
} else if (Loads == "Rademacher"){
Jnt.Loads.All[[k]] = matrix(rsign(p[k]*(r.J)), nrow = r.J)
}
} else if (is.list(Loads)){
Jnt.Loads.All[[k]] = t(Loads[[1]][[k]])
}
D.J = (1 - equal.eig)*diag(r.J:1) + equal.eig*diag(rep(1,r.J))
# Joint.Sigs[[k]] = JntScores%*%sqrt(D.J[[k]])%*%Jnt.Loads.All[[k]]
Joint.Sigs[[k]] = JntScores%*%D.J%*%Jnt.Loads.All[[k]]
if(SVD.plots){
plot(svd(Joint.Sigs[[k]])$d, ylab = "Singular Values")
title(paste0("SVD of Joint Signal from X", k))
}
temp.IndScores = IndivScores[,(k>1)*sum(r.I[1:(k-1)])+(1:r.I[k])]
if(length(Loads)==1){
if(Loads == "Gaussian"){
Indiv.Loads.All[[k]] = matrix(rnorm(n = p[k]*r.I[k]), nrow = r.I[k], ncol = p[k])
} else if (Loads == "Fixed"){
temp.fcn = function(x){x[sample(round(length(x)/4))] = 1; x}
Indiv.Loads.All[[k]] = matrix(apply(matrix(-1, nrow = r.I[k], ncol = p[k]), 1, temp.fcn), nrow = r.I[k])
} else if (Loads == "Double_Exp"){
Indiv.Loads.All[[k]] = matrix(rlaplace(p[k]*(r.I[k])), nrow = r.I[k])
} else if (Loads == "Rademacher"){
Indiv.Loads.All[[k]] = matrix(rsign(p[k]*(r.I[k])), nrow = r.I[k])
}
} else if (is.list(Loads)){
Indiv.Loads.All[[k]] = t(Loads[[2]][[k]])
}
D.I[[k]] = (1 - equal.eig)*diag(r.I[k]:1) + equal.eig*diag(rep(1,r.I[k]))
Indiv.Sigs[[k]] = temp.IndScores%*%D.I[[k]]%*%Indiv.Loads.All[[k]]
if(SVD.plots){
plot(svd(Indiv.Sigs[[k]])$d, ylab = "Singular Values")
title(paste0("SVD of Individual Signal from X", k))
}
Sig.Mats[[k]] = Joint.Sigs[[k]] + Indiv.Sigs[[k]]
Noise[[k]] = matrix(rnorm(n*p[k], sd = sqrt(error.variances[k])), nrow = n)
Data.Mats[[k]] = AdjSigVarExp(Joint.Sigs[[k]], Indiv.Sigs[[k]], Noise[[k]],
JntVarEx[k], IndVarEx[k])
Joint.Sigs[[k]] = Data.Mats[[k]]$J
Indiv.Sigs[[k]] = Data.Mats[[k]]$I
}
##############################Define Datasets##############################
Blocks = lapply(Data.Mats, function(x) x[["Data"]])
Dat.Comps = list(Joint.Sigs, Indiv.Sigs, Noise)
names(Dat.Comps) = c("JointSignalMatrices", "IndivSignalMatrices", "NoiseMatrices")
Scores = list(JntScores, IndivScores)
names(Scores) = c("Joint", "Indiv")
Loadings = list(list(),list())
names(Loadings) = c("Joint", "Indiv")
for(k in 1:K){
Loadings[["Joint"]][[k]] = D.J%*%Jnt.Loads.All[[k]]
Loadings[["Indiv"]][[k]] = D.I[[k]]%*%Indiv.Loads.All[[k]]
}
out = list(Dat.Comps, Blocks, Scores, Loadings)
names(out) = c("Data Components", "Data Blocks", "Scores", "Loadings")
return(out)
}
#######################################################################################################################
########### Generates 2 Simulated Datasets that follow JIVE Model using binary subject scores ####################
########### NOTE: This version sohuld be archived once confirmed that it coresponds with newer ####################
########### version above built for K>2 ####################
#######################################################################################################################
GenerateToyData_OLD <- function(n, p1, p2, JntVarEx1, JntVarEx2, IndVarEx1, IndVarEx2, jnt_rank = 1, equal.eig = FALSE,
ind_rank1 = 2, ind_rank2 = 2, JntVarAdj = TRUE, SVD.plots = TRUE, Error = TRUE, print.cor = TRUE,
Loads = "Rademacher", Scores = "Gaussian_Mixture"){
# Write out both joint and indiv subject scores for both data sets first
r.J = jnt_rank
r.I1 = ind_rank1
r.I2 = ind_rank2
print(paste("Generating Scores from", Scores, "distributions and Loadings from", Loads, "distributions."))
# Generate Joint scores
if(Scores=="Binomial"){
JntScores = matrix(rbinom(n*r.J, size=1, prob=0.2), nrow = n, ncol = r.J)
b = rbinom(n*(r.I1 + r.I2), size=1, prob=0.4)
b = 1 - 2*b
IndivScores = matrix(b, nrow = n, ncol = (r.I1 + r.I2))
} else if (Scores=="Gaussian_Mixture"){
mix.probs = c(0.2, 0.5, 0.3)
JointScores.g1 = matrix(rnorm(n*mix.probs[1]*r.J), ncol = r.J)
JointScores.g2 = matrix(rnorm(n*mix.probs[2]*r.J, -4, 1), ncol = r.J)
JointScores.g3 = matrix(rnorm(n*mix.probs[3]*r.J, 4, 1), ncol = r.J)
JntScores = rbind(JointScores.g1, JointScores.g2, JointScores.g3)
IndivScores = matrix(rnorm(n*(r.I1+r.I2)), nrow = n, ncol = (r.I1 + r.I2))
} else if(Scores=="Gaussian"){
JntScores = matrix(rnorm(n*r.J), ncol = r.J)
IndivScores = matrix(rnorm(n*(r.I1+r.I2)), nrow = n, ncol = (r.I1 + r.I2))
}
colnames(JntScores) = paste("Jnt Score", 1:r.J)
colnames(IndivScores) = c(paste("Ind X Score", 1:r.I1), paste("Ind Y Score", 1:r.I2))
if(print.cor){print("The correlation between subject scores is given by"); print(round(cor(cbind(JntScores, IndivScores)),4))}
##############################Define X Dataset##############################
if(Loads == "Gaussian"){
AdjJntLoad.X = matrix(rnorm(r.J*p1), nrow = r.J, ncol = p1)
} else if (Loads == "Fixed"){
temp.fcn = function(x){x[sample(round(length(x)/2))] = 1; x}
AdjJntLoad.X = matrix(apply(matrix(0, nrow = r.J, ncol = p1), 1, temp.fcn), nrow = r.J)
} else if (Loads == "Double_Exp"){
AdjLoad.X = matrix(extraDistr::rlaplace(p1*(r.J+r.I1)), nrow = r.J+r.I1)
AdjJntLoad.X = AdjLoad.X[1:r.J, , drop = FALSEALSE]
} else if (Loads == "Rademacher"){
AdjLoad.X = matrix(extraDistr::rsign(p1*(r.J+r.I1)), nrow = r.J+r.I1)
AdjJntLoad.X = AdjLoad.X[1:r.J, , drop = FALSEALSE]
}
#change relavent scaling of joint components
D.J = (equal.eig + 1)*diag(r.J:1) + equal.eig*diag(rep(1,r.J))
JX = JntScores%*%sqrt(D.J)%*%AdjJntLoad.X
if(SVD.plots){
plot(svd(JX)$d, ylab = "Singular Values")
title("SVD of Joint Signal from X")
}
##Note that the individual signal has rank = 2 as well
IndScores.X = IndivScores[,1:r.I1]
IndLoad.X = matrix(rnorm(n = p1*r.I1), nrow = r.I1, ncol = p1)
if(Loads == "Gaussian"){
IndLoad.X = matrix(rnorm(n = p1*r.I1), nrow = r.I1, ncol = p1)
} else if (Loads == "Fixed"){
temp.fcn = function(x){x[sample(round(length(x)/4))] = 1; x}
IndLoad.X = matrix(apply(matrix(-1, nrow = r.I1, ncol = p1), 1, temp.fcn), nrow = r.I1)
} else if (Loads == "Double_Exp"){
IndLoad.X = AdjLoad.X[-(1:r.J), , drop = FALSEALSE]
} else if (Loads == "Rademacher"){
IndLoad.X = AdjLoad.X[-(1:r.J), ,drop = FALSEALSE]
}
D.IX = (equal.eig + 1)*diag((r.I1:1)) + equal.eig*diag(rep(1,r.I1))
IX = IndScores.X%*%sqrt(D.IX)%*%IndLoad.X
if(SVD.plots){
plot(svd(IX)$d, ylab = "Singular Values")
title("SVD of Individual Signal from X")
}
AX = JX + IX
##############################Define Y Dataset##############################
if(Loads == "Gaussian"){
AdjJntLoad.Y = matrix(rnorm(r.J*p2), nrow = r.J, ncol = p2)
} else if (Loads == "Fixed"){
temp.fcn = function(x){x[sample(round(length(x)/2))] = 2; x}
AdjJntLoad.Y = matrix(apply(matrix(1, nrow = r.J, ncol = p2), 1, temp.fcn), nrow = r.J)
} else if (Loads == "Double_Exp"){
AdjLoad.Y = matrix(extraDistr::rlaplace(p2*(r.J+r.I2)), nrow = r.J+r.I2)
AdjJntLoad.Y = AdjLoad.Y[1:r.J, , drop = FALSEALSE]
} else if (Loads == "Rademacher"){
AdjLoad.Y = matrix(extraDistr::rsign(p2*(r.J+r.I2)), nrow = r.J+r.I2)
AdjJntLoad.Y = AdjLoad.Y[1:r.J, , drop = FALSEALSE]
}
##Note that the joint signal has rank = 3
JY = JntScores%*%sqrt(D.J)%*%AdjJntLoad.Y
if(SVD.plots){
plot(svd(JY)$d, ylab = "Singular Values")
title("SVD of Joint Signal from Y")
}
IndScores.Y = IndivScores[,(r.I1 + 1:r.I2)]
IndLoad.Y = matrix(rnorm(n = p2*r.I1), nrow = r.I1, ncol = p2)
if(Loads == "Gaussian"){
IndLoad.Y = matrix(rnorm(n = p2*r.I1), nrow = r.I1, ncol = p2)
} else if (Loads == "Fixed"){
temp.fcn = function(x){x[sample(round(length(x)/4))] = 1; x}
IndLoad.Y = matrix(apply(matrix(-1, nrow = r.I2, ncol = p2), 1, temp.fcn), nrow = r.I2)
} else if (Loads == "Double_Exp"){
IndLoad.Y = AdjLoad.Y[-(1:r.J), , drop = FALSEALSE]
} else if (Loads == "Rademacher"){
IndLoad.Y = AdjLoad.Y[-(1:r.J), ,drop = FALSEALSE]
}
D.IY = (equal.eig + 1)*diag((r.I2:1)) + equal.eig*diag(rep(1,r.I2))
##Note that the individual signal has rank=2
IY = IndScores.Y%*%sqrt(D.IY)%*%IndLoad.Y
if(SVD.plots){
plot(svd(IY)$d, ylab = "Singular Values")
title("SVD of Individual Signal from Y")
}
##Error matrix
EX = matrix(rnorm(n*p1), nrow=n, ncol=p1)*Error
##Error matrix
EY = matrix(rnorm(n*p2), nrow=n, ncol=p2)*Error
Dat.X = AdjSigVarExp(JX, IX, EX, JntVarEx1, IndVarEx1)
JX = Dat.X$J
IX = Dat.X$I
Dat.Y = AdjSigVarExp(JY, IY, EY, JntVarEx2, IndVarEx2)
JY = Dat.Y$J
IY = Dat.Y$I
Blocks = list(Dat.X[["Data"]], Dat.Y[["Data"]])
Dat.Comps = list(JX, JY, IX, IY, EX, EY)
names(Dat.Comps) = c("J1", "J2", "I1", "I2", "E1", "E2" )
Scores = list(JntScores, IndScores.X, IndScores.Y)
names(Scores) = c("Joint", "Indiv_1", "Indiv_2")
Loadings = list(sqrt(D.J)%*%AdjJntLoad.X, sqrt(D.IX)%*%IndLoad.X,
sqrt(D.J)%*%AdjJntLoad.Y, sqrt(D.IY)%*%IndLoad.Y)
names(Loadings) = c("Joint_1", "Indiv_1", "Joint_2", "Indiv_2")
out = list(Dat.Comps, Blocks, Scores, Loadings)
names(out) = c("Data Components", "Data Blocks", "Scores", "Loadings")
out
}
####################################################################################
########### Adjust Dataset Components to get Desired R^2 Values #################
####################################################################################
AdjSigVarExp <-function(J, I, E, JntVarEx, IndVarEx){
simul.quads = function(x, parms){
JJ = parms[1]
II = parms[2]
EE = parms[3]
JE = parms[4]
IE = parms[5]
R_J = parms[6]
R_I = parms[7]
y1 = x[1]^2*II*(1 - R_I) - 2*x[1]*IE*R_I - R_I*(x[2]^2*JJ + 2*x[2]*JE + EE)
y2 = x[2]^2*JJ*(1 - R_J) - 2*x[2]*JE*R_J - R_J*(x[1]^2*II + 2*x[1]*IE + EE)
y = c(y1,y2)
return(y)
}
JJ = MatVar(J)
II = MatVar(I)
EE = MatVar(E)
JE = sum(diag(J%*%t(E)))
IE = sum(diag(I%*%t(E)))
R_J = JntVarEx
R_I = IndVarEx
parms = c(JJ, II, EE, JE, IE, R_J, R_I)
A = J + I
AA = MatVar(A)
EE = MatVar(E)
AE = sum(diag(A%*%t(E)))
##Desired Total Variance Explained
d0 = IndVarEx + JntVarEx
a = AA*(1 - d0)
b = -2*AE
c = -d0*EE
d.A = (-b+sqrt(b^2 - 4*a*c))/(2*a)
start = c(0.5, 0.5)*d.A
roots = rootSolve::multiroot(simul.quads, start, parms = parms)
c = roots$root[1]
d = roots$root[2]
J.d = d*J; I.c = c*I;
Dat = J.d + I.c + E
res = list(J.d, I.c, Dat)
names(res) = c("J", "I", "Data")
return(res)
}
#######################################################################################################################
##################### Convert ProJIVE Simulation Results to a form that will allow ggplot ####################
#######################################################################################################################
ConvSims_gg_ProJIVE<-function(AllSims){
sim.names = colnames(AllSims)
#CompEvals.names = c(sim.names[grep("Scores", sim.names)], sim.names[grep("Loads", sim.names)])
num.sims = dim(AllSims)[1]
p1 = unique(AllSims$p1)
p2 = unique(AllSims$p2)
JVE_1 = c(as.matrix(AllSims[,grep("JntVarEx1",sim.names)]))
JVE1.labs = c(bquote("R"[J1]^2*"=0.05, p"[1]*"="*.(p1)),
bquote("R"[J1]^2*"=0.1, p"[1]*"="*.(p1)),
bquote("R"[J1]^2*"=0.5, p"[1]*"="*.(p1)))
JVE_1.raw = factor(JVE_1, labels = JVE1.labs, levels = c(0.05, 0.1, 0.5))
JVE_2 = c(as.matrix(AllSims[,grep("JntVarEx2",sim.names)]))
JVE2.labs = c(bquote("R"[J2]^2*"=0.05, p"[2]*"="*.(p2)),
bquote("R"[J2]^2*"=0.1, p"[2]*"="*.(p2)),
bquote("R"[J2]^2*"=0.5, p"[2]*"="*.(p2)))
JVE_2.raw = factor(JVE_2, labels = JVE2.labs, levels = c(0.05, 0.1, 0.5))
IVE_1 = c(as.matrix(AllSims[,grep("IndivVarExp_X|Indiv.Var.Exp.X", sim.names)]))
IVE_1 = round(as.numeric(IVE_1), 2)
IVE_2 = c(as.matrix(AllSims[,grep("IndivVarExp_Y|Indiv.Var.Exp.Y", sim.names)]))
IVE_2 = round(as.numeric(IVE_2), 2)
Norm = c(as.numeric(as.matrix(AllSims[,grep("Scores", sim.names)])))
Method1 = sim.names[grep("Scores",sim.names)]
Method2 = str_replace_all(Method1, "\\.\\.\\.", " ")
Method3 = str_replace_all(Method2, "\\.", " ")
Method4 = str_replace_all(Method3, " [:digit:]", "")
Method5 = str_replace_all(Method4, " Joint.+", "")
Method6 = str_replace_all(Method5, " Indiv.+", "")
Method7 = str_replace_all(Method6, "R JIVE", "R.JIVE")
Method = rep(factor(Method7, levels = unique(Method7)), each = num.sims)
Type1 = str_replace_all(Method1, "\\.\\.\\.", " ")
Type2 = str_replace_all(Type1, "\\.", " ")
Type3 = str_replace_all(Type2, " [:digit:]", "")
Type4 = str_replace_all(Type3, "X", "X[1]")
Type5 = str_replace_all(Type4, "Y", "X[2]")
Type6 = str_replace_all(Type5, "^.+Joint", "Joint")
Type7 = str_replace_all(Type6, "^.+Indiv", "Indiv")
Type = rep(as.factor(Type7), each = num.sims)
n.levs = nlevels(Type)*nlevels(Method)
sim.score.norms.gg = data.frame(Norm = Norm, Method = Method, Type = Type, JVE_1 = rep(JVE_1.raw, each = n.levs),
JVE_2 = rep(JVE_2.raw, each = n.levs),
IVE_1 = rep(IVE_1, each = n.levs), IVE_2 = rep(IVE_2, each = n.levs))
Norm = c(as.numeric(as.matrix(AllSims[,grep("Loads", sim.names)])))
Method1 = sim.names[grep("Loads",sim.names)]
Method2 = str_replace_all(Method1, "\\.\\.\\.", " ")
Method3 = str_replace_all(Method2, "\\.", " ")
Method4 = str_replace_all(Method3, " [:digit:]", "")
Method5 = str_replace_all(Method4, " Joint.+", "")
Method6 = str_replace_all(Method5, " Indiv.+", "")
Method7 = str_replace_all(Method6, "R JIVE", "R.JIVE")
Method = rep(factor(Method7, levels = unique(Method7)), each = num.sims)
Type1 = str_replace_all(Method1, "\\.\\.\\.", " ")
Type2 = str_replace_all(Type1, "\\.", " ")
Type3 = str_replace_all(Type2, " [:digit:]", "")
Type4 = str_replace_all(Type3, "X", "X[1]")
Type5 = str_replace_all(Type4, "Y", "X[2]")
Type6 = str_replace_all(Type5, "^.+Joint", "Joint")
Type7 = str_replace_all(Type6, "^.+Indiv", "Indiv")
Type = rep(as.factor(Type7), each = num.sims)
n.levs = nlevels(Type)*nlevels(Method)
JVE_1 = rep(JVE_1.raw, each = n.levs)
JVE_2 = rep(JVE_2.raw, each = n.levs)
sim.load.norms.gg = data.frame(Norm = Norm, Method = Method, Type = Type, JVE_1 = JVE_1, JVE_2 = JVE_2,
IVE_1 = rep(IVE_1, each = n.levs), IVE_2 = rep(IVE_2, each = n.levs))
sim.all.norms.gg = rbind(sim.score.norms.gg, sim.load.norms.gg)
out = sim.all.norms.gg
return(out)
}
#######################################################################################################################
##################### Convert ProJIVE Simulation Results to a form that will allow ggplot ####################
#######################################################################################################################
ConvSims_gg_ProJIVE2<-function(AllSims, n){
sim.names = colnames(AllSims)
#CompEvals.names = c(sim.names[grep("Scores", sim.names)], sim.names[grep("Loads", sim.names)])
num.sims = dim(AllSims)[1]
p1 = unique(AllSims$p1)
p2 = unique(AllSims$p2)
# JVE1.labs = c(bquote("R"[J1]^2*"=0.05, p"[1]*"="*.(p1)*", n="*.(n)), bquote("R"[J1]^2*"=0.5, p"[1]*"="*.(p1)))# *", n="*.(n)))
# JVE2.labs = c(bquote("R"[J2]^2*"=0.05, p"[2]*"="*.(p2)*", n="*.(n)), bquote("R"[J2]^2*"=0.5, p"[2]*"="*.(p2)))# *", n="*.(n)))
JVE1.labs = c(bquote("R"[J1]^2*"=0.05, p"[1]*"="*.(p1)),
bquote("R"[J1]^2*"=0.1, p"[1]*"="*.(p1)),
bquote("R"[J1]^2*"=0.5, p"[1]*"="*.(p1)))
JVE2.labs = c(bquote("R"[J2]^2*"=0.05, p"[2]*"="*.(p2)),
bquote("R"[J2]^2*"=0.1, p"[2]*"="*.(p2)),
bquote("R"[J2]^2*"=0.5, p"[2]*"="*.(p2)))
JVE_1 = c(as.matrix(AllSims[,grep("JntVarEx1",sim.names)]))
JVE_1.raw = factor(JVE_1, labels = JVE1.labs, levels = c(0.05, 0.1, 0.5))
JVE_2 = c(as.matrix(AllSims[,grep("JntVarEx2",sim.names)]))
JVE_2.raw = factor(JVE_2, labels = JVE2.labs, levels = c(0.05, 0.1, 0.5))
IVE_1 = c(as.matrix(AllSims[,grep("Indiv.Var.Exp.X", sim.names)]))
IVE_1 = round(as.numeric(IVE_1), 2)
IVE_2 = c(as.matrix(AllSims[,grep("Indiv.Var.Exp.Y", sim.names)]))
IVE_2 = round(as.numeric(IVE_2), 2)
Norm = c(as.numeric(
as.matrix(
AllSims[,sort(c(grep("Scores..Norm",sim.names), grep("Scores.X..Norm",sim.names), grep("Scores.Y..Norm",sim.names)))])))
Method1 = sim.names[sort(c(grep("Scores..Norm",sim.names), grep("Scores.X..Norm",sim.names), grep("Scores.Y..Norm",sim.names)))]
Method2 = str_replace_all(Method1, "\\.\\.\\.", " ")
Method3 = str_replace_all(Method2, "\\.", " ")
Method4 = str_replace_all(Method3, " [:digit:]", "")
Method5 = str_replace_all(Method4, " Joint.+", "")
Method6 = str_replace_all(Method5, " Indiv.+", "")
Method7 = str_replace_all(Method6, "R JIVE", "R.JIVE")
Method = rep(factor(Method7, levels = unique(Method7)), each = num.sims)
Type1 = str_replace_all(Method1, "\\.\\.\\.", " ")
Type2 = str_replace_all(Type1, "\\.", " ")
Type3 = str_replace_all(Type2, " [:digit:]", "")
Type4 = str_replace_all(Type3, "X", "X[1]")
Type5 = str_replace_all(Type4, "Y", "X[2]")
Type6 = str_replace_all(Type5, "^.+Joint", "Joint")
Type7 = str_replace_all(Type6, "^.+Indiv", "Indiv")
Type = rep(as.factor(Type7), each = num.sims)
n.levs = nlevels(Type)*nlevels(Method)
sim.score.norms.gg = data.frame(Norm = Norm, Method = Method, Type = Type, JVE_1 = rep(JVE_1.raw, each = n.levs),
JVE_2 = rep(JVE_2.raw, each = n.levs),
IVE_1 = rep(IVE_1, each = n.levs), IVE_2 = rep(IVE_2, each = n.levs))
Norm = c(as.numeric(as.matrix(
AllSims[,sort(c(grep("Loads.X..Norm", sim.names), grep("Loads.Y..Norm", sim.names)))])))
Method1 = sim.names[sort(c(grep("Loads.X..Norm", sim.names), grep("Loads.Y..Norm", sim.names)))]
Method2 = str_replace_all(Method1, "\\.\\.\\.", " ")
Method3 = str_replace_all(Method2, "\\.", " ")
Method4 = str_replace_all(Method3, " [:digit:]", "")
Method5 = str_replace_all(Method4, " Joint.+", "")
Method6 = str_replace_all(Method5, " Indiv.+", "")
Method7 = str_replace_all(Method6, "R JIVE", "R.JIVE")
Method = rep(factor(Method7, levels = unique(Method7)), each = num.sims)
Type1 = str_replace_all(Method1, "\\.\\.\\.", " ")
Type2 = str_replace_all(Type1, "\\.", " ")
Type3 = str_replace_all(Type2, " [:digit:]", "")
Type4 = str_replace_all(Type3, "X", "X[1]")
Type5 = str_replace_all(Type4, "Y", "X[2]")
Type6 = str_replace_all(Type5, "^.+Joint", "Joint")
Type7 = str_replace_all(Type6, "^.+Indiv", "Indiv")
Type8 = str_replace_all(Type7, "Loads", "Loadings")
Type = rep(as.factor(Type8), each = num.sims)
n.levs = nlevels(Type)*nlevels(Method)
JVE_1 = rep(JVE_1.raw, each = n.levs)
JVE_2 = rep(JVE_2.raw, each = n.levs)
sim.load.norms.gg = data.frame(Norm = Norm, Method = Method, Type = Type, JVE_1 = JVE_1, JVE_2 = JVE_2,
IVE_1 = rep(IVE_1, each = n.levs), IVE_2 = rep(IVE_2, each = n.levs))
sim.all.norms.gg = rbind(sim.score.norms.gg, sim.load.norms.gg)
PMSE = c(as.numeric(
as.matrix(
AllSims[,sort(c(grep("Scores..PMSE",sim.names), grep("Scores.X..PMSE",sim.names), grep("Scores.Y..PMSE",sim.names)))])))
Method1 = sim.names[sort(c(grep("Scores..PMSE",sim.names), grep("Scores.X..PMSE",sim.names), grep("Scores.Y..PMSE",sim.names)))]
Method2 = str_replace_all(Method1, "\\.\\.\\.", " ")
Method3 = str_replace_all(Method2, "\\.", " ")
Method4 = str_replace_all(Method3, " [:digit:]", "")
Method5 = str_replace_all(Method4, " Joint.+", "")
Method6 = str_replace_all(Method5, " Indiv.+", "")
Method7 = str_replace_all(Method6, "R JIVE", "R.JIVE")
Method = rep(factor(Method7, levels = unique(Method7)), each = num.sims)
Type1 = str_replace_all(Method1, "\\.\\.\\.", " ")
Type2 = str_replace_all(Type1, "\\.", " ")
Type3 = str_replace_all(Type2, " [:digit:]", "")
Type4 = str_replace_all(Type3, "X", "X[1]")
Type5 = str_replace_all(Type4, "Y", "X[2]")
Type6 = str_replace_all(Type5, "^.+Joint", "Joint")
Type7 = str_replace_all(Type6, "^.+Indiv", "Indiv")
Type = rep(as.factor(Type7), each = num.sims)
n.levs = nlevels(Type)*nlevels(Method)
sim.score.pmse.gg = data.frame(PMSE = PMSE, Method = Method, Type = Type, JVE_1 = rep(JVE_1.raw, each = n.levs),
JVE_2 = rep(JVE_2.raw, each = n.levs),
IVE_1 = rep(IVE_1, each = n.levs), IVE_2 = rep(IVE_2, each = n.levs))
PMSE = c(as.numeric(as.matrix(AllSims[,sort(c(grep("Loads.X..PMSE", sim.names), grep("Loads.Y..PMSE", sim.names)))])))
Method1 = sim.names[sort(c(grep("Loads.X..PMSE", sim.names), grep("Loads.Y..PMSE", sim.names)))]
Method2 = str_replace_all(Method1, "\\.\\.\\.", " ")
Method3 = str_replace_all(Method2, "\\.", " ")
Method4 = str_replace_all(Method3, " [:digit:]", "")
Method5 = str_replace_all(Method4, " Joint.+", "")
Method6 = str_replace_all(Method5, " Indiv.+", "")
Method7 = str_replace_all(Method6, "R JIVE", "R.JIVE")
Method = rep(factor(Method7, levels = unique(Method7)), each = num.sims)
Type1 = str_replace_all(Method1, "\\.\\.\\.", " ")
Type2 = str_replace_all(Type1, "\\.", " ")
Type3 = str_replace_all(Type2, " [:digit:]", "")
Type4 = str_replace_all(Type3, "X", "X[1]")
Type5 = str_replace_all(Type4, "Y", "X[2]")
Type6 = str_replace_all(Type5, "^.+Joint", "Joint")
Type7 = str_replace_all(Type6, "^.+Indiv", "Indiv")
Type8 = str_replace_all(Type7, "Loads", "Loadings")
Type = rep(as.factor(Type8), each = num.sims)
n.levs = nlevels(Type)*nlevels(Method)
JVE_1 = rep(JVE_1.raw, each = n.levs)
JVE_2 = rep(JVE_2.raw, each = n.levs)
sim.load.pmse.gg = data.frame(PMSE = PMSE, Method = Method, Type = Type, JVE_1 = JVE_1, JVE_2 = JVE_2,
IVE_1 = rep(IVE_1, each = n.levs), IVE_2 = rep(IVE_2, each = n.levs))
sim.all.pmse.gg = rbind(sim.score.pmse.gg, sim.load.pmse.gg)
temp = as.matrix(AllSims[,grep("VarExp_", sim.names)])
temp = temp[,str_which(colnames(temp), "True", negate = T)]
temp.names = colnames(temp)
VarEx = c(as.numeric(temp))
Method1 = rep(temp.names[grep("VarExp_",temp.names)], each = num.sims)
Method2 = str_replace_all(Method1, "JIVE_Oracle", "JIVE-Oracle")
Method3 = str_replace(Method2, "\\.[:digit:]", "") #
Method4 = str_replace_all(Method3, "_.+", "")
Method5 = str_replace_all(Method4, "Joint.+", "")
Method6 = str_replace_all(Method5, "Indiv.+", "")
Method = factor(Method6, levels = unique(Method6)[c(4,3,1,2,5)])#, levels = unique(Method6)[c(4,3,1,2,5)])
#table(Method, Method6)
Type1 = rep(temp.names[grep("VarExp_", temp.names)], num.sims)
Type2 = str_replace(Type1, "\\.[:digit:]", "")
Type3 = str_replace(Type2, "_X", "_X\\[1\\]")
Type4 = str_replace(Type3, "_Y", "_X\\[2\\]")
Type5 = str_replace(Type4, ".+Joint", "Joint")
Type6 = str_replace(Type5, ".+Indiv", "Indiv")
Type = as.factor(Type6)
n.levs = nlevels(Type)*nlevels(Method)
JVE_1 = rep(JVE_1.raw, each = n.levs)
JVE_2 = rep(JVE_2.raw, each = n.levs)
VarEx.out = data.frame(VarEx = VarEx, Type = Type, Method = Method, JVE_1 = JVE_1.raw, JVE_2 = JVE_2.raw,
IVE_1 = rep(IVE_1, each = n.levs), IVE_2 = rep(IVE_2, each = n.levs))
out = list(sim.all.norms.gg, sim.all.pmse.gg, VarEx.out)
names(out) = c("Norms", "PMSEs", "VarEx")
out
}
#################################################################################################
##################### Plot PJIVE Norms from Simulation Study #######################
#################################################################################################
gg.score.pmse.plot<-function(pmse.dat, cols, show.legend = F, text.size, lty = 1, y.max = 1){
labs = levels(pmse.dat$Type)[grep("Score",levels(pmse.dat$Type))][c(3,1,2)]
labs.ex = c("Joint Subj Scores", expression("Indiv Subj Scores"*"X"[1]), expression("Indiv Subj Scores"*"X"[2]))
ggplot(data = pmse.dat, aes(x = Type, y = Norm)) +
geom_boxplot(aes(fill = Method), position = "dodge", outlier.alpha = 0, show.legend = show.legend, linetype = lty,
fatten = 0.5) +
# geom_boxplot(aes(color = Method),
# fatten = NULL, fill = NA, coef = 0, outlier.alpha = 0,
# show.legend = F) +
labs(y = "Chordal Norm", x = "Type") +
facet_grid(JVE_2 ~ JVE_1, labeller = label_parsed) +
scale_x_discrete(limits = labs, labels = labs.ex) +
scale_fill_manual(values=cols) +
scale_colour_manual(values=cols) +
theme_bw() + coord_cartesian(ylim = c(0, y.max)) +
theme(axis.title.x = element_blank(), axis.text.x = element_text(face = "bold", hjust = 01, angle = 70, size = text.size-3),
text = element_text(size = text.size))
}
#################################################################################################
##################### Plot PJIVE Norms from Simulation Study #######################
#################################################################################################
gg.load.pmse.plot<-function(pmse.dat, cols, show.legend = F, text.size, lty = 1, y.max = 1){
labs = levels(pmse.dat$Type)[grep("Load",levels(pmse.dat$Type))][c(3,4,1,2)]
labs.ex = c(expression("Joint Variable Loadings"*"X"[1]),expression("Joint Variable Loadings"*"X"[2]),
expression("Indiv Variable Loadings"*"X"[1]), expression("Indiv Variable Loadings"*"X"[2]))
ggplot(data = pmse.dat, aes(x = Type, y = Norm)) +
geom_boxplot(aes(fill = Method), position = "dodge", outlier.alpha = 0, show.legend = show.legend, linetype = lty,
fatten = 0.5) +
# geom_boxplot(aes(color = Method),
# fatten = NULL, fill = NA, coef = 0, outlier.alpha = 0,
# show.legend = F) +
labs(y = "Chordal Norm", x = "Type") +
facet_grid(JVE_2 ~ JVE_1, labeller = label_parsed) +
scale_x_discrete(limits = labs, labels = labs.ex) +
scale_fill_manual(values=cols) +
scale_colour_manual(values=cols) +
theme_bw() + coord_cartesian(ylim = c(0, y.max)) +
theme(axis.title.x = element_blank(), axis.text.x = element_text(face = "bold", hjust = 01, angle = 70, size = text.size-3),
text = element_text(size = text.size))
}
## Calculate empirical observed information matrix
ProJIVE_AsymVar<-function(W.mats, error.vars, theta, r.J, Y){
K1 = length(W.mats)
K2 = length(error.vars)
if(K1!=K2){stop("W matrices and error variances must have the same length.")}
K = K1; rm(K1, K2)
r = ncol(theta) ##r_J + r_I1 + ... + r_I2
r_k = sapply(W.mats, ncol)
p_k = sapply(W.mats, nrow)
r_Ik = r_k - r.J
n = nrow(Y)
theta_k = list()
theta_k[[1]] = theta[,1:r_k[1]]
Y_k = list()
Y_k[[1]] = Y[,1:p_k[1]]
for(k in 2:K){
theta_k[[k]] = theta[,c(1:r.J, r.J + cumsum(r_Ik)[k-1] + (1:r_Ik[k]))]
Y_k[[k]] = Y[,cumsum(p_k)[k-1]+(1:p_k[k])]
}
score_i = list()
for(i in 1:nrow(Y)){
score_wk = score_sigmak = NULL
for(k in 1:K){
epsilon_ik = (Y_k[[k]][i,] - W.mats[[k]]%*%t(t(theta_k[[k]][i,])))
score_wk = c(score_wk, c(epsilon_ik%*%t(theta_k[[k]][i,])/error.vars[k]))
score_sigmak = c(score_sigmak, (t(epsilon_ik)%*%epsilon_ik/error.vars[k] - p_k[k])/(2*error.vars[k]))
}
score_i[[i]] = matrix(c(score_wk, score_sigmak),ncol = 1)
}
mean.score = info.mat = 0
for(i in 1:n){
mean.score = mean.score + score_i[[i]]/nrow(Y)
}
for(i in 1:n){
info.mat = info.mat + (score_i[[i]]-mean.score)%*%t(score_i[[i]]-mean.score)
}
out = list(mean.score, info.mat)
names(out) = c("MeanScoreVector", "ObservedEmpericalInformationMatrix")
tryCatch(
{
inv.info = Matrix::chol2inv(Matrix::chol(info.mat))
out = list(mean.score, info.mat, inv.info)
names(out) = c("MeanScoreVector", "ObservedEmpericalInformationMatrix", "Inverse_ObservedEmpericalInformationMatrix")
},
error = function(cond){
message("Warning: Information matrix is not positive definite.
Generalized inverse used to estimate covariance matrix.")
inv.info = MASS::ginv(info.mat)
inv.info
}
)
return(out)
}
############################# Bootstrap #############################
ProJIVE_BootsratVar = function(B = 50, P, Q, theta.hat, W.hat, error.vars){
nobs = nrow(theta.hat)
bstrap.mean = 0
bstraps = list()
for(b in 1:B){
errors = NULL
for(k in 1:length(P)){
errors = cbind(errors, matrix(sqrt(error.vars[k])*rnorm(n=nobs*(P[k])),nrow=nobs))
}
tempdata = theta.hat%*%t(W.hat)+errors
temp.res = ProJIVE_EM(Y=tempdata, P=P, Q=Q, Max.iter=10000, diff.tol=1e-7, sig_hat = "MLE",
init.loads = "CJIVE", plots = FALSE)#, verbose = FALSE)
Procrustes.Loading = MCMCpack::procrustes(X = temp.res$LoadingMatrix, Xstar = W.hat)$X.new
bstrap.mean = bstrap.mean + temp.res$LoadingMatrix/B
bstraps[[b]] = temp.res$LoadingMatrix
}
bstrap.var = 0
for(b in 1:B){
bstrap.var = bstrap.var + matrix(bstraps[[b]] - bstrap.mean, ncol = 1)%*%matrix(bstraps[[b]] - bstrap.mean, nrow = 1)/(B-1)
}
round(bstrap.var)
bstrap.se = sqrt(diag(bstrap.var))
out = list(bstrap.var, bstrap.se);
names(out) = c("Boostrap_Covariance", "Bootstrap_StdErrs")
return(out)
}
## FUNC to generate list of W_k matrices from W
w_to_w_k=function(w, P, Q){
P=c(0,P)
K=length(P[-1])
w_k=list()
for(k in 1:K){
w_k[[k]] = w[sum(P[1:k])+(1:P[k+1]),c(1:Q[1],sum(Q[1:k])+1:Q[k+1])]
}
return(w_k)
}
###############################################################################################################
########### pJIVE ML estimation of JIVE model that uses EM algorithm ##################
########### This version was originally built for K>2 ##################
###############################################################################################################
ProJIVE_EM=function(Y,P,Q,Max.iter=10000,diff.tol=1e-8,plots=TRUE,chord.tol=-1,sig_hat=NULL, init.loads = NULL){
########################################################################
####################START OF PRE-DEFINED FUNCS##########################
########################################################################
## FUNC to Generate the corresponding Ak and Bk:
generate_ab=function(m,n){
return(matrix(rep(0,n*m),nrow=n,ncol=m))
}
## FUNC to generate list(G) of W matrix with right dimension
generate_w=function(k, wk_hat, P, Q){
r=lapply(Q,generate_ab,P[k])
r[[1]]=as.matrix(wk_hat[[k]][1:P[k],1:Q[1]], nrow=P[k], ncol=Q[1])
r[[k+1]]=as.matrix(wk_hat[[k]][1:P[k],Q[1]+1:Q[k+1]], nrow=P[k], ncol=Q[k+1])
return(do.call('cbind',r))
}
## FUNC to generate list(G) of W matrix from W_k matrices
wk_to_w=function(wk, P, Q){
w=do.call('rbind',lapply(1:length(wk),function(k)generate_w(k, wk, P, Q)))
return(w)
}
## FUNC to generate list of W_k matrices from W
w_to_w_k=function(w, P, Q){
P=c(0,P)
K=length(P[-1])
w_k=list()
for(k in 1:K){
w_k[[k]] = w[sum(P[1:k])+(1:P[k+1]),c(1:Q[1],sum(Q[1:k])+1:Q[k+1])]
}
return(w_k)
}
## FUNC to generate list(G) of D matrix from sigma vectors
generate_d=function(sig_lst, p_vec){
d=NULL
for(k in 1:length(p_vec)){
d = c(d, rep(sig_lst[k],p_vec[k]))
}
D=diag(d)
return(D)
}
obs_LogLik<-function(Y, mu, w, d){
##############################################
# input: -mu :a G list of d dimension vectors
# -w :a G list of dxp matrices
# -d :a G list of d length vector indicating the noise
# -Y :a nxd data frame as the observations
#
# output: a real value of the log likelihood
##############################################
N=dim(Y)[1]
lik<-rep(0, N)
# w=cbind(do.call(rbind,wj[[g]]),as.matrix(bdiag(wi[[g]])))
s=w%*%t(w)+d
lik=dmvnorm(Y,mu,s)
LogLik=sum(log(lik))
return(LogLik)
}
complete_LogLik<-function(Y, theta, mu, w, d){
##############################################
# input: -mu :a G list of d dimension vectors
# -w :a G list of dxp matrices
# -d :a G list of d length vector indicating the noise
# -Y :a nxd data frame as the observations
#
# output: a real value of the log likelihood
##############################################
N=dim(Y)[1]
constant.term = -(N/2)*(sum(c(ncol(Y),ncol(w)))*log(2*pi) + log(det(d)))
kernel.term = 0
for(i in 1:N){
Yi = matrix(Y[i,], ncol = 1)
theta_i = matrix(theta[i,], ncol = 1)
kernel.term = kernel.term + t(Yi - w%*%theta_i)%*%diag(diag(d)^-1)%*%(Yi - w%*%theta_i) + sum(theta_i^2)
}
LogLik=constant.term-0.5*kernel.term
return(LogLik)
}
## FUNC to evaluate convergence in the loop
eval_converge=function(vals_vec, diff.tol){
len = length(vals_vec)
if(length(vals_vec)==1) {
return(TRUE)
}else{
if(vals_vec[length(vals_vec)]==-Inf){
return(TRUE)
}else{
diff.ll = vals_vec[len]-vals_vec[len-1]
return((diff.ll>=(diff.tol)))
}
}
}
########################################################################
####################END OF PRE-DEFINED FUNCS############################
########################################################################
# Total sample size
N=dim(Y)[1]
# Total number feature blocks
if(length(P)==(length(Q)-1)){
K=length(P)
} else{
stop("Error: The number of feature blocks does not match the number of invididual signals.")
}
Q.tot = Q[1] + Q[-1]
# Selection matrices A_k and B_k
A=list()
B=list()
for(k in 1:K){
up=lapply(Q,generate_ab,Q[1])
up[[1]]=diag(Q[1])
down=lapply(Q,generate_ab,Q[(k+1)])
down[[(k+1)]]=diag(Q[(k+1)])
B[[k]]=rbind(do.call("cbind",up),
do.call("cbind",down))
a=lapply(P,generate_ab,P[k])
a[[k]]=diag(P[k])
A[[k]]=do.call("cbind",a)
}
# get initial estimates of loadings matrices via cc.jive
wk_hat=wji_hat=list()
if (is.null(init.loads)){
#Default: Initialize loadings as a sub matrix of the Cholesky Decomposition solution L
WJ = WI = list()
for(k in 1:K){
if((k==1)){
L=t(chol(cov(Y[,1:P[k]])))
} else if(k>1){
L=t(chol(cov(Y[,(sum(P[1:(k-1)])+1):sum(P[1:k])])))
}
wji_hat[[k]]=L[,1:(Q[1]+Q[k+1])]
WJ[[k]] = wji_hat[[k]][,1:Q[1]]
WI[[k]] = wji_hat[[k]][,-(1:Q[1])]
}
} else if (is.list(init.loads)){
WJ = init.loads[[1]]
WI = init.loads[[2]]
} else if(init.loads == "AJIVE" | init.loads == "CJIVE"){
dat.blocks = list()
dat.blocks[[1]] = Y[,1:P[1]]
for(k in 2:K){
dat.blocks[[k]] = Y[,cumsum(P[k-1])+(1:P[k])]
}
ajive.solution = cc.jive(dat.blocks, signal.ranks = Q[1]+Q[-1],joint.rank = Q[1], perm.test = FALSE)
WJ = lapply(ajive.solution$sJIVE$joint_matrices, function(x) x$v)
WI = lapply(ajive.solution$sJIVE$indiv_matrices, function(x) x$v)
}
# Block specific loading matrices W_k
for(k in 1:K){
wji_hat[[k]]=cbind(WJ[[k]], WI[[k]])
}