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data fit.R
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data fit.R
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# --- READ ME
# title: Getting output from the fit of the model described in:
# "Longitudinal dynamic functional regression" (LDFR)
# by Md Nazmul Islam, Ana-Maria Staicu, and Eric van Heugten
# created by Md Nazmul Islam
# date: 2017/11
# ---
############################################################################################
### ------------------------ defining outputs for the Gaussian fit --------------------- ###
############################################################################################
# IN.MPE.y : IN-sample prediction error
# OUT.MPE.y : OUT-sample prediction error
# RMPE_trj : Root-mean-prediction-error for full response trajectory for existing subjects
# RMPE_trjX : Root-mean-prediction-error for full response trajectory for new subjects; if 999999 then Not available
# FT : object of LDFR() fit for full trajectory
# YijF & Yij.XF : True response trajectories for existing and new subjects
Yestim <- function (A, I, IW, TT, ss, zetamu, zetasigma1, zetasigma2, zetasigma3, zetasigma4,
delta, minJi, maxJi, Cov_Error, mu.e.x1, mu.e.x2, mu.e.x3, var.e.x1, var.e.x2, var.e.x3,
errYbi0mu, errYbijmu, errYbi0sigma, errYbijsigma, errYbi1mu, errYbi1sigma, errYbi12sigma,
mm, J, Yerror, nbf, method, pve, full_traj, pred_interval, alpha, new_subj)
{
set.seed (A)
data <- data_func(A, I, TT, ss, zetamu, zetasigma1, zetasigma2, zetasigma3, zetasigma4,
delta, minJi, maxJi, Cov_Error, mu.e.x1, mu.e.x2, mu.e.x3, var.e.x1,
var.e.x2, var.e.x3, errYbi0mu, errYbijmu, errYbi0sigma,
errYbijsigma, errYbi1mu, errYbi1sigma, errYbi12sigma, mm, J, Yerror)
### -------------------------------------------------------------------------- ###
### ------------------------- extracting information ------------------------- ###
### -------------------------------------------------------------------------- ###
dat.full <- data$dat.full; dat.sparse <- data$dat.sparse; dat.train <- data$dat.train;
dat.test <- data$dat.test; m2 <- data$m2
uTij <- sort(unique(dat.full[,4])); lng <- length(uTij); J <- length(TT); SS <- length(ss);
if ( lng != J ) stop ( "Error: Differences in uTij & TT " )
### ------------------------- observed data ------------------------- ###
IDs <- dat.sparse[,1];
TijS <- dat.sparse[,4];
Vs <- dat.sparse[,3]
obs.func.covS <- as.matrix(dat.sparse[,c(11:111)])
YijS <- dat.sparse[, 113];
sprse_seq <- dat.sparse[, 112];
### ------------------------- train data ------------------------- ###
ID <- dat.train[ , 1];
V <- dat.train[, 3];
Tij <- dat.train[, 4];
obs.func.cov <- as.matrix(dat.train[, c( 11 : 111)]);
red_seq <- dat.train [ , 112];
Yij <- dat.train[ , 113];
### ------------------------- test data ------------------------- ###
ID.test <- dat.test[, 1];
Tij.test <- dat.test[, 4]
obs.func.covT <- as.matrix(dat.test[, c( 11 : 111)]);
Yij.test <- dat.test[, 113];
test_seq <- dat.test [, 112];
### ------------------------- full data ------------------------- ###
YijF <- dat.full[, 113];
IDF <- dat.full[, 1];
### --------------------------------------------------------------------------------------------- ###
### -------------------------------- estimating mean function ----------------------------------- ###
### --- fbps() is used to estimate; and gam() is used to predict the mean for all time points --- ###
### --------------------------------------------------------------------------------------------- ###
ln <- length(Tij)
fbps.fit <- fbps(data = obs.func.cov, covariates = c (Tij, ss))
muhat0 <- matrix(0, nrow = J, ncol = SS)
muhat.dat <- do.call(rbind, lapply(seq_len(J), function(de) {
t1 <- uTij[de]
r1 <- as.vector(which(Tij == t1))[1]
muhat0[de,] <- fbps.fit$Yhat[r1, ] }))
newmu.dat <- data.frame ( y = as.vector(t(muhat.dat)), x1 = rep( ss, J), x2 = rep( uTij, SS) )
MU.gam <- gam(y ~ te(x1, x2, k = c(10, 5), bs ="cr"), data = newmu.dat, method = method)
MU.gam.dat <- data.frame (x1 = rep(ss, ln ), x2 = rep( Tij, SS) )
MU.XA <- matrix (predict.gam(MU.gam , newdata = MU.gam.dat ), nrow = ln, ncol = SS, byrow = T )
MU.gam.dat <- data.frame (x1 = rep(ss, length(TT) ), x2 = rep( TT, SS) )
MU.X <- matrix (predict.gam(MU.gam , newdata = MU.gam.dat ), nrow = length(TT), ncol = SS, byrow = T )
### ---------------------------------------------------------------------------------- ###
### --------------------- demeaning functional predictor (train) -------------------- ###
### ---------------------------------------------------------------------------------- ###
deM.X <- obs.func.cov - fbps.fit$Yhat
### ---------------------------------------------------------------------------------------- ###
### ----------- finding the eigen-components of covariance operator (train) ---------------- ###
### ---------------------------------------------------------------------------------------- ###
covsmooth <- fpca.face (Y = deM.X, pve = pve, var = TRUE)
phi.mat <- covsmooth$efunctions
phi.hat <- phi.mat * sqrt(SS)
K.hat <- covsmooth$npc;
zetaw.hat <- covsmooth$scores / sqrt (SS)
mu <- covsmooth$mu
eigenvalues <- covsmooth$evalues / SS
### -------------------------------------------------------------------------------- ###
### -------------------------- Replacing negative eigenvalues ---------------------- ###
### -------------------------------------------------------------------------------- ###
eigenvalues[which(eigenvalues < 0)] <- 0
### -------------------------------------------------------------------------------- ###
### ----------------------------- checking norm ------------------------------------ ###
### -------------------------------------------------------------------------------- ###
k1 <- all.equal ( as.vector ( do.call( rbind, lapply ( seq_len(K.hat), function (feb)
sqrt(mean ( length(ss) * phi.mat[,feb] ^ 2 )) ) ) ), rep(1, K.hat) )
if ( k1 != "TRUE" ) stop ( "l2 norm mismatches with the simulated basis functions")
### ---------------------------------------------------------------------------------------- ###
### --------------------- estimating mean of functional predictor (train) ------------------ ###
### ---------------------------------------------------------------------------------------- ###
MU.Xi.Hat <- MU.XA + matrix (rep(mu, ln), nrow = ln, ncol = SS, byrow = T )
### ----------------------------------------------------------------------------------------------- ###
### --------------------- predicting the time-varying loadings (train + test) --------------------- ###
### ----------------------------------------------------------------------------------------------- ###
xi.hat0 <- list()
for( k in seq_len (K.hat) )
{
xihat0.vec <- zetaw.hat[, k]
xi.hat0[[ k ]]<-t( sapply( seq_len(I), function(i)
{xi.subj <- matrix(nrow = 1, ncol = J)
xi.subj[V[which( ID == i )]] <- xihat0.vec[ which(ID == i) ]
return( xi.subj )
}))
}
fit2 <- lapply(xi.hat0, function(a) try (fpca.sc(Y = a, pve = pve, var = TRUE)))
xi.hat<- lapply(fit2, function(a) a$Yhat)
### --------------------------------------------------------------------------------------------------------- ###
### ---------- predicting the time-varying loadings for all (observed + unobserved) time-points ------------ ###
### --------------------------------------------------------------------------------------------------------- ###
zetaw.hatF <- do.call (cbind, lapply ( xi.hat, function(gg) as.vector(t(gg)) ))
### ---------------------------------------------------------------------------------------------------------- ###
### ------------ predicting the time-varying loadings for observed time-points for train set ----------------- ###
### ---------------------------------------------------------------------------------------------------------- ###
zetaw.hatN <- do.call (cbind, lapply ( xi.hat, function(gg) as.vector(t(gg))[red_seq] ))
### ----------------------------------------------------------------------------------------------------------- ###
### ------------ predicting the time-varying loadings for observed time-points for test set ------------------- ###
### ----------------------------------------------------------------------------------------------------------- ###
zetaw.hatTst <- do.call (cbind, lapply ( xi.hat, function(gg) as.vector(t(gg))[test_seq] ))
### ------------------------------------------------------------------------------------------------------------ ###
### ------------------------ creating design matrix for SS random effects ------------------------------------- ###
### ------------------------------------------------------------------------------------------------------------ ###
if (Yerror == "CS") {
# ------------------------------------------------ Training ----------------------------------------------------- #
Z1 = matrix(0, nrow = length(Yij), ncol = length(unique(ID)))
for (i in 1 : I) {
Z1[which(ID == unique(ID)[i]), i] = 1
}
fZ <- cbind(Z1)
# -------------------------------------------- Test ------------------------------------------------------------ #
Z1.test = matrix(0, nrow = length(Yij.test), ncol = length(unique(ID.test)))
for (i in 1 : length(unique(ID.test))) {
Z1.test[which(ID.test == sort(unique(ID.test))[i]), i] = 1
}
fZ.test <- cbind(Z1.test)
}
if (Yerror == "IS") {
# --------------------------------------------- Training --------------------------------------------------------- #
Z1 = matrix(0, nrow = length(Yij), ncol = length(unique(ID)))
Z2 = matrix(0, nrow = length(Yij), ncol = length(unique(ID)))
for (i in 1 : I) {
Z1[which(ID == unique(ID)[i]), i] = 1
Z2[which(ID == unique(ID)[i]), i] = Tij[which(ID == unique(ID)[i])]
}
fZ <- cbind(Z1, Z2)
# --------------------------------------------- Test ------------------------------------------------------------- #
Z1.test = matrix(0, nrow = length(Yij.test), ncol = length(unique(ID.test)))
Z2.test = matrix(0, nrow = length(Yij.test), ncol = length(unique(ID.test)))
for (i in 1 : length(unique(ID.test))) {
Z1.test[which(ID.test == sort(unique(ID.test))[i]), i] = 1
Z2.test[which(ID.test == sort(unique(ID.test))[i]), i] = Tij.test[which(ID.test == sort(unique(ID.test))[i])]
}
fZ.test <- cbind(Z1.test, Z2.test)
}
### ---------------------------------------------------------------------------------------------------------- ###
### ------------ creating design matrix smooth intercept using truncated linear splines ------------------- ###
### ---------------------------------------------------------------------------------------------------------- ###
R <- nbf
qtiles <- seq(0, 1, length = R)[- c(1, R)]
knots <- quantile(TT, qtiles)
# ----------------------------------------------- Training ------------------------------------------------------ #
Z0 <- matrix(as.vector(cbind(sapply(knots, function(tau) ((Tij > tau) * (Tij - tau) )))), nrow = length(Tij))
fZ0 <- cbind(1, Tij, Z0)
bigX <- cbind(fZ, fZ0)
# ------------------------------------------------ Test --------------------------------------------------------- #
Z0.test <- matrix(as.vector(cbind(sapply(knots, function(tau) ((Tij.test > tau) * (Tij.test - tau) ) ))), nrow = length(Tij.test))
fZ0.test <- cbind(1, Tij.test, Z0.test)
bigX.test <- cbind(fZ.test, fZ0.test)
### ----------------------------------------------------------------------------------------------------------- ###
### ------- creating design matrix for K smooth time-varying functions using truncated linear splines ------ ###
### ----------------------------------------------------------------------------------------------------------- ###
for(k in 1 : K.hat){
# ----------------------------------------------- Training ---------------------------------------------------- #
DD <- paste("fZ",k," <- zetaw.hatN[,",k,"] * fZ0", sep = "")
DD <- eval(parse(text = DD))
bigX <- cbind(bigX, DD)
rm(DD)
# ---------------------------------------------- Test ---------------------------------------------------------- #
DD <- paste("fZ.test",k," <- zetaw.hatTst[,",k,"] * fZ0.test", sep = "")
DD <- eval(parse(text = DD))
bigX.test <- cbind(bigX.test, DD)
rm(DD)
}
if(dim(bigX)[2] > dim(bigX)[1]) stop("WARNING: Number of observations (n) is smaller than number of parameters (p)")
dim(bigX); dim(bigX.test)
### ------------------------------------------------------------------------------------------------------------- ###
### ----------------------------- defining the terms to be penalized ----------------------------------------- ###
### ------------------------------------------------------------------------------------------------------------- ###
if (Yerror == "CS") {
E <- list()
E[[1]] <- diag(rep(0, dim(bigX)[2]))
diag(E[[1]])[c(1 : I)] <- 1
E[[2]] <- diag(rep(0, dim(bigX)[2]))
diag(E[[2]])[c( (I + 3) : (I + R) )] <- 1
IN <- list()
for(kk in 1:K.hat){
IN[[kk]] <- c( (I + 3 + R + (kk - 1) * R) : (I + R + kk * R))
}
E[[3]] <- diag(rep(0, dim(bigX)[2]))
diag(E[[3]])[unlist(IN)] <- 1
}
if (Yerror == "IS") {
E <- list()
E[[1]] <- diag(rep(0, dim(bigX)[2]))
diag(E[[1]])[c(1 : I)] <- 1
E[[2]] <- diag(rep(0, dim(bigX)[2]))
diag(E[[2]])[ (I + 1) : (2 * I) ] <- 1
E[[3]] <- diag(rep(0, dim(bigX)[2]))
diag(E[[3]])[c( ((2 * I) + 3) : ( (2 * I) + R) )] <- 1
IN <- list()
for(kk in 1 : K.hat){
IN[[kk]] <- c( ( (2 * I) + 3 + R + ((kk - 1) * R) ) : ( (2 * I) + R + (kk * R) ))
}
E[[4]] <- diag(rep(0, dim(bigX)[2]))
diag(E[[4]])[unlist(IN)] <- 1
}
### ---------------------------------------------------------------------------------------------------------- ###
### -------------------------------------------- fitting model --------------------------------------------- ###
### ---------------------------------------------------------------------------------------------------------- ###
time <- system.time(applygam <- bam(Yij ~ bigX - 1, paraPen = list(bigX = E), method = method))[3]
### ---------------------------------------------------------------------------------------------------------- ###
### -------------------------------------- predicting responses in the train set ---------------------------- ###
### ---------------------------------------------------------------------------------------------------------- ###
coefs = applygam$coef
NY.pred <- as.vector(as.matrix(bigX[, 1:length(coefs)]) %*% coefs )
IN.MPE.y <- sqrt(mean(as.vector(do.call(rbind, lapply(seq_len(I), function(hh)
mean((Yij[which(ID == hh)] - NY.pred[which(ID == hh)]) ^ 2))))))
### ----------------------------------------------------------------------------------------------------------- ###
### --------------------------------- predicting responses in the test --------------------------------------- ###
### ----------------------------------------------------------------------------------------------------------- ###
NY.pred.test <- as.vector ( as.matrix(bigX.test[, 1:length(coefs)]) %*% coefs )
OUT.MPE.y <- sqrt(mean(as.vector(do.call(rbind, lapply(seq_len(length(unique(ID.test))), function(hh)
mean((Yij.test[which(ID.test == sort(unique(ID.test))[hh])] - NY.pred.test[which(ID.test == sort(unique(ID.test))[hh])]) ^ 2))))))
### ------------------------------------------------------------------------------------------------------------ ###
### ------------------------------- predicting responses for full trajectory ---------------------------------- ###
### ------------------------------------------------------------------------------------------------------------ ###
if (full_traj == TRUE){
# ----------- Profiles' information of new and existing subjects at sparse time-points -------------------------#
if(new_subj == TRUE){ ## Generate information for (exisiting + new) subjects
rm(data); rm(dat.sparse); rm(dat.full)
set.seed (A)
data <- data_func(A, I = IW, TT, ss, zetamu, zetasigma1, zetasigma2, zetasigma3, zetasigma4,
delta, minJi, maxJi, Cov_Error, mu.e.x1, mu.e.x2, mu.e.x3, var.e.x1,
var.e.x2, var.e.x3, errYbi0mu, errYbijmu, errYbi0sigma,
errYbijsigma, errYbi1mu, errYbi1sigma, errYbi12sigma, mm, J, Yerror)
### ------------------------------------------------------------------------------------------------------ ###
### -------------------------------------- extracting information ---------------------------------------- ###
### ------------------------------------------------------------------------------------------------------ ###
dat.full <- data$dat.full; dat.sparse <- data$dat.sparse;
dat.obs <- data$dat.sparse;
EX <- which (dat.obs[,1] > I) # Last IW - I subjects are the new ones
EXF <- which (dat.full[,1] > I)
Yij.ob <- dat.obs[-EX, 113]; red.seq.ob <- dat.obs[-EX, 112];
obs.func.covX <- as.matrix ( dat.obs [, c( 11 : 111)] );
IDX <- dat.obs[, 1];
VX <- dat.obs[, 3];
TijX <- dat.obs[, 4];
IDF <- dat.full[-EXF, 1]; YijF <- dat.full[-EXF , 113]; # observed subjects full information of response and id
ID.XF <- dat.full[EXF, 1]; Yij.XF <- dat.full[EXF , 113]; # Unobserved subjects full information of response and id
FT <- try(LDFR(ID = IDX, obs.func.cov = obs.func.covX, Tij = TijX, Yij = Yij.ob, V = VX, I, IW, nbf,
method = method, pve = pve, Yerror = Yerror, family = gaussian,
pred_interval = pred_interval, alpha = alpha, out_subj = red.seq.ob))
RMPE_trj <- sqrt(mean(as.vector(do.call(rbind, lapply(seq_len(length(unique(IDF))), function(hh)
mean((YijF[which(IDF == unique(IDF)[hh])] - FT$full_pred_obs[which(IDF == unique(IDF)[hh])]) ^ 2))))))
RMPE_trjX <- sqrt(mean(as.vector(do.call(rbind, lapply(seq_len(length(unique(ID.XF))), function(hh)
mean((Yij.XF[which(ID.XF == unique(ID.XF)[hh])] - FT$full_pred_PA_un[which(ID.XF == unique(ID.XF)[hh])]) ^ 2))))))
}
# -------------- Profiles' information of only existing subjects is available at sparse time-points ------------#
if(new_subj == FALSE){
FT <- try(LDFR(ID = IDs, obs.func.cov = obs.func.covS, Tij = TijS, Yij = YijS, V = Vs, I, IW = NULL, nbf,
method = method, pve = pve, Yerror = Yerror, family = gaussian,
pred_interval = pred_interval, alpha = alpha, out_subj = FALSE))
RMPE_trj <- sqrt(mean(as.vector(do.call(rbind, lapply(seq_len(length(unique(IDF))), function(hh)
mean((YijF[which(IDF == unique(IDF)[hh])] - FT$full_pred_obs[which(IDF == unique(IDF)[hh])]) ^ 2))))))
RMPE_trjX <- 999999 # Not available
}
}
else if (full_traj == FALSE){
FT <- NULL
}
output = list (IN.MPE.y = IN.MPE.y, OUT.MPE.y = OUT.MPE.y, RMPE_trj = RMPE_trj,
RMPE_trjX = RMPE_trjX, fit = FT, YijF = YijF, Yij.XF = Yij.XF)
}