Skip to content

Commit

Permalink
fix code formatting
Browse files Browse the repository at this point in the history
  • Loading branch information
@fabian-s
fabian-s committed Jun 20, 2016
1 parent b3b71f1 commit 6c9f9f6
Showing 1 changed file with 168 additions and 156 deletions.
324 changes: 168 additions & 156 deletions R/fpca.sc.R
View file
Original file line number Diff line number Diff line change
Expand Up @@ -10,7 +10,7 @@
##'
##' FPCA via kernel smoothing of the covariance function, with the diagonal
##' treated separately, was proposed in Staniswalis and Lee (1998) and much
##' extended by Yao et al. (2005), who introduced the "PACE" method.
##' extended by Yao et al. (2005), who introduced the 'PACE' method.
##' \code{fpca.sc} uses penalized splines to smooth the covariance function, as
##' developed by Di et al. (2009) and Goldsmith et al. (2013).
##'
Expand Down Expand Up @@ -57,7 +57,7 @@
##' values. This can be very slow. If set to \code{2} (the default), a two-step
##' method that obtains a naive covariance estimate which is then smoothed.
##' @param integration quadrature method for numerical integration; only
##' \code{"trapezoidal"} is currently supported.
##' \code{'trapezoidal'} is currently supported.
##' @return An object of class \code{fpca} containing:
##' \item{Yhat}{FPC approximation (projection onto leading components)
##' of \code{Y.pred} if specified, or else of \code{Y}.}
Expand Down Expand Up @@ -117,22 +117,22 @@
##' d = as.numeric(colnames(cd4)))
##'
##' ## plot data for one subject, with curve and interval estimates
##' EX.MM.m = melt(EX.MM, id = "d")
##' EX.MM.m = melt(EX.MM, id = 'd')
##' ggplot(EX.MM.m, aes(x = d, y = value, group = variable, color = variable, linetype = variable)) +
##' geom_path() +
##' scale_linetype_manual(values = c(fitted = 1, ptwise.UB = 2,
##' ptwise.LB = 2, simul.UB = 3, simul.LB = 3)) +
##' scale_color_manual(values = c(fitted = 1, ptwise.UB = 2,
##' ptwise.LB = 2, simul.UB = 3, simul.LB = 3)) +
##' labs(x = "Months since seroconversion", y = "Total CD4 Cell Count")
##' labs(x = 'Months since seroconversion', y = 'Total CD4 Cell Count')
##'
##' ## plot estimated mean function
##' ggplot(Fit.mu, aes(x = d, y = mu)) + geom_path() +
##' labs(x = "Months since seroconversion", y = "Total CD4 Cell Count")
##' labs(x = 'Months since seroconversion', y = 'Total CD4 Cell Count')
##'
##' ## plot the first two estimated basis functions
##' Fit.basis.m = melt(Fit.basis, id = "d")
##' ggplot(subset(Fit.basis.m, variable %in% c("phi.1", "phi.2")), aes(x = d,
##' Fit.basis.m = melt(Fit.basis, id = 'd')
##' ggplot(subset(Fit.basis.m, variable %in% c('phi.1', 'phi.2')), aes(x = d,
##' y = value, group = variable, color = variable)) + geom_path()
##'
##' ## input a dataframe instead of a matrix
Expand All @@ -156,168 +156,180 @@
##' @importFrom Matrix nearPD Matrix t as.matrix
##' @importFrom mgcv gam predict.gam
##' @importFrom gamm4 gamm4
fpca.sc <- function(Y = NULL, ydata = NULL, Y.pred=NULL, argvals = NULL, random.int = FALSE,
nbasis = 10, pve = .99, npc = NULL, var = FALSE, simul = FALSE, sim.alpha = .95,
useSymm = FALSE, makePD = FALSE, center=TRUE, cov.est.method = 2,
integration="trapezoidal") {
fpca.sc <- function(Y = NULL, ydata = NULL, Y.pred = NULL, argvals = NULL, random.int = FALSE,
nbasis = 10, pve = 0.99, npc = NULL, var = FALSE, simul = FALSE, sim.alpha = 0.95,
useSymm = FALSE, makePD = FALSE, center = TRUE, cov.est.method = 2, integration = "trapezoidal") {

stopifnot((!is.null(Y) && is.null(ydata))||(is.null(Y) && !is.null(ydata)))
stopifnot((!is.null(Y) && is.null(ydata)) || (is.null(Y) && !is.null(ydata)))

# if data.frame version of ydata is provided
sparseOrNongrid <- !is.null(ydata)
if (sparseOrNongrid) {
stopifnot(ncol(ydata) == 3)
stopifnot(c(".id", ".index", ".value") == colnames(ydata))
stopifnot(is.null(argvals))
Y = irreg2mat(ydata)
argvals = sort(unique(ydata$.index))
}
# if data.frame version of ydata is provided
sparseOrNongrid <- !is.null(ydata)
if (sparseOrNongrid) {
stopifnot(ncol(ydata) == 3)
stopifnot(c(".id", ".index", ".value") == colnames(ydata))
stopifnot(is.null(argvals))
Y = irreg2mat(ydata)
argvals = sort(unique(ydata$.index))
}

if (is.null(Y.pred)) Y.pred = Y
D = NCOL(Y)
I = NROW(Y)
I.pred = NROW(Y.pred)
if (is.null(Y.pred))
Y.pred = Y
D = NCOL(Y)
I = NROW(Y)
I.pred = NROW(Y.pred)

if (is.null(argvals)) argvals = seq(0, 1, length = D)
if (is.null(argvals))
argvals = seq(0, 1, length = D)

d.vec = rep(argvals, each = I)
id = rep(1:I, rep(D, I))
d.vec = rep(argvals, each = I)
id = rep(1:I, rep(D, I))

if (center) {
if (random.int){
ri_data <- data.frame(y = as.vector(Y), d.vec=d.vec, id=factor(id))
gam0 = gamm4(y ~ s(d.vec, k = nbasis), random=~(1|id), data = ri_data)$gam
rm(ri_data)
}
else gam0 = gam(as.vector(Y) ~ s(d.vec, k = nbasis))
mu = predict(gam0, newdata = data.frame(d.vec = argvals))
Y.tilde = Y - matrix(mu, I, D, byrow = TRUE)
}
else {
Y.tilde = Y
mu = rep(0, D)
}
if (center) {
if (random.int) {
ri_data <- data.frame(y = as.vector(Y), d.vec = d.vec, id = factor(id))
gam0 = gamm4(y ~ s(d.vec, k = nbasis), random = ~(1 | id), data = ri_data)$gam
rm(ri_data)
} else gam0 = gam(as.vector(Y) ~ s(d.vec, k = nbasis))
mu = predict(gam0, newdata = data.frame(d.vec = argvals))
Y.tilde = Y - matrix(mu, I, D, byrow = TRUE)
} else {
Y.tilde = Y
mu = rep(0, D)
}

if (cov.est.method==2) { # smooth raw covariance estimate
cov.sum = cov.count = cov.mean = matrix(0, D, D)
for (i in 1:I) {
obs.points = which(!is.na(Y[i, ]))
cov.count[obs.points, obs.points] = cov.count[obs.points, obs.points] + 1
cov.sum[obs.points, obs.points] = cov.sum[obs.points, obs.points] + tcrossprod(Y.tilde[i, obs.points])
}
G.0 = ifelse(cov.count == 0, NA, cov.sum/cov.count)
diag.G0 = diag(G.0)
diag(G.0) = NA
if (!useSymm) {
row.vec = rep(argvals, each = D)
col.vec = rep(argvals, D)
npc.0 = matrix(predict(gam(as.vector(G.0) ~ te(row.vec, col.vec, k = nbasis), weights =as.vector(cov.count)), newdata = data.frame(row.vec = row.vec,col.vec = col.vec)), D, D)
npc.0 = (npc.0 + t(npc.0))/2
}
else {
use <- upper.tri(G.0, diag = TRUE)
use[2, 1] <- use[ncol(G.0), ncol(G.0) - 1] <- TRUE
usecov.count <- cov.count
usecov.count[2, 1] <- usecov.count[ncol(G.0), ncol(G.0) - 1] <- 0
usecov.count <- as.vector(usecov.count)[use]
use <- as.vector(use)
vG.0 <- as.vector(G.0)[use]
row.vec <- rep(argvals, each = D)[use]
col.vec <- rep(argvals, times = D)[use]
mCov <- gam(vG.0 ~ te(row.vec, col.vec, k = nbasis), weights = usecov.count)
npc.0 <- matrix(NA, D, D)
spred <- rep(argvals, each = D)[upper.tri(npc.0, diag = TRUE)]
tpred <- rep(argvals, times = D)[upper.tri(npc.0, diag = TRUE)]
smVCov <- predict(mCov, newdata = data.frame(row.vec = spred, col.vec = tpred))
npc.0[upper.tri(npc.0, diag = TRUE)] <- smVCov
npc.0[lower.tri(npc.0)] <- t(npc.0)[lower.tri(npc.0)]
}
if (cov.est.method == 2) {
# smooth raw covariance estimate
cov.sum = cov.count = cov.mean = matrix(0, D, D)
for (i in 1:I) {
obs.points = which(!is.na(Y[i, ]))
cov.count[obs.points, obs.points] = cov.count[obs.points, obs.points] +
1
cov.sum[obs.points, obs.points] = cov.sum[obs.points, obs.points] + tcrossprod(Y.tilde[i,
obs.points])
}

else if (cov.est.method==1) { # smooth y(s1)y(s2) values to obtain covariance estimate
row.vec = col.vec = G.0.vec = c()
cov.sum = cov.count = cov.mean = matrix(0, D, D)
for (i in 1:I) {
obs.points = which(!is.na(Y[i, ]))
temp = tcrossprod(Y.tilde[i, obs.points])
diag(temp) = NA
row.vec = c(row.vec, rep(argvals[obs.points], each = length(obs.points)))
col.vec = c(col.vec, rep(argvals[obs.points], length(obs.points)))
G.0.vec = c(G.0.vec, as.vector(temp))
# still need G.O raw to calculate to get the raw to get the diagonal
cov.count[obs.points, obs.points] = cov.count[obs.points, obs.points] + 1
cov.sum[obs.points, obs.points] = cov.sum[obs.points, obs.points] + tcrossprod(Y.tilde[i, obs.points])
}
row.vec.pred = rep(argvals, each = D)
col.vec.pred = rep(argvals, D)
npc.0 = matrix(predict(gam(G.0.vec ~ te(row.vec, col.vec, k = nbasis)), newdata = data.frame(row.vec = row.vec.pred, col.vec = col.vec.pred)), D, D)
npc.0 = (npc.0 + t(npc.0))/2
G.0 = ifelse(cov.count == 0, NA, cov.sum/cov.count)
diag.G0 = diag(G.0)
G.0 = ifelse(cov.count == 0, NA, cov.sum/cov.count)
diag.G0 = diag(G.0)
diag(G.0) = NA
if (!useSymm) {
row.vec = rep(argvals, each = D)
col.vec = rep(argvals, D)
npc.0 = matrix(predict(gam(as.vector(G.0) ~ te(row.vec, col.vec, k = nbasis),
weights = as.vector(cov.count)), newdata = data.frame(row.vec = row.vec,
col.vec = col.vec)), D, D)
npc.0 = (npc.0 + t(npc.0))/2
} else {
use <- upper.tri(G.0, diag = TRUE)
use[2, 1] <- use[ncol(G.0), ncol(G.0) - 1] <- TRUE
usecov.count <- cov.count
usecov.count[2, 1] <- usecov.count[ncol(G.0), ncol(G.0) - 1] <- 0
usecov.count <- as.vector(usecov.count)[use]
use <- as.vector(use)
vG.0 <- as.vector(G.0)[use]
row.vec <- rep(argvals, each = D)[use]
col.vec <- rep(argvals, times = D)[use]
mCov <- gam(vG.0 ~ te(row.vec, col.vec, k = nbasis), weights = usecov.count)
npc.0 <- matrix(NA, D, D)
spred <- rep(argvals, each = D)[upper.tri(npc.0, diag = TRUE)]
tpred <- rep(argvals, times = D)[upper.tri(npc.0, diag = TRUE)]
smVCov <- predict(mCov, newdata = data.frame(row.vec = spred, col.vec = tpred))
npc.0[upper.tri(npc.0, diag = TRUE)] <- smVCov
npc.0[lower.tri(npc.0)] <- t(npc.0)[lower.tri(npc.0)]
}

if (makePD) {
npc.0 <- {
tmp <- Matrix::nearPD(npc.0, corr = FALSE, keepDiag = FALSE, do2eigen = TRUE, trace = TRUE)
as.matrix(tmp$mat)
}
} else if (cov.est.method == 1) {
# smooth y(s1)y(s2) values to obtain covariance estimate
row.vec = col.vec = G.0.vec = c()
cov.sum = cov.count = cov.mean = matrix(0, D, D)
for (i in 1:I) {
obs.points = which(!is.na(Y[i, ]))
temp = tcrossprod(Y.tilde[i, obs.points])
diag(temp) = NA
row.vec = c(row.vec, rep(argvals[obs.points], each = length(obs.points)))
col.vec = c(col.vec, rep(argvals[obs.points], length(obs.points)))
G.0.vec = c(G.0.vec, as.vector(temp))
# still need G.O raw to calculate to get the raw to get the diagonal
cov.count[obs.points, obs.points] = cov.count[obs.points, obs.points] +
1
cov.sum[obs.points, obs.points] = cov.sum[obs.points, obs.points] + tcrossprod(Y.tilde[i,
obs.points])
}
### numerical integration for calculation of eigenvalues (see Ramsay & Silverman, Chapter 8)
w <- quadWeights(argvals, method=integration)
Wsqrt <- diag(sqrt(w))
Winvsqrt <- diag(1/(sqrt(w)))
V <- Wsqrt %*% npc.0 %*% Wsqrt
evalues = eigen(V, symmetric = TRUE, only.values = TRUE)$values
###
evalues = replace(evalues, which(evalues <= 0), 0)
npc = ifelse(is.null(npc), min(which(cumsum(evalues)/sum(evalues) > pve)), npc)
efunctions = matrix(Winvsqrt%*%eigen(V, symmetric = TRUE)$vectors[, seq(len = npc)], nrow = D, ncol = npc)
evalues = eigen(V, symmetric = TRUE, only.values = TRUE)$values[1:npc] # use correct matrix for eigenvalue problem
cov.hat = efunctions %*% tcrossprod(diag(evalues, nrow = npc, ncol = npc), efunctions)
### numerical integration for estimation of sigma2
T.len <- argvals[D] - argvals[1] # total interval length
T1.min <- min(which(argvals >= argvals[1] + 0.25*T.len)) # left bound of narrower interval T1
T1.max <- max(which(argvals <= argvals[D] - 0.25*T.len)) # right bound of narrower interval T1
DIAG = (diag.G0 - diag(cov.hat))[T1.min :T1.max] # function values
w2 <- quadWeights(argvals[T1.min:T1.max], method = integration)
sigma2 <- max(weighted.mean(DIAG, w=w2, na.rm = TRUE), 0)
row.vec.pred = rep(argvals, each = D)
col.vec.pred = rep(argvals, D)
npc.0 = matrix(predict(gam(G.0.vec ~ te(row.vec, col.vec, k = nbasis)), newdata = data.frame(row.vec = row.vec.pred,
col.vec = col.vec.pred)), D, D)
npc.0 = (npc.0 + t(npc.0))/2
G.0 = ifelse(cov.count == 0, NA, cov.sum/cov.count)
diag.G0 = diag(G.0)
}

####
D.inv = diag(1/evalues, nrow = npc, ncol = npc)
Z = efunctions
Y.tilde = Y.pred - matrix(mu, I.pred, D, byrow = TRUE)
Yhat = matrix(0, nrow = I.pred, ncol = D)
rownames(Yhat) = rownames(Y.pred); colnames(Yhat) = colnames(Y.pred)
scores = matrix(NA, nrow = I.pred, ncol = npc)
VarMats = vector("list", I.pred)
for (i in 1:I.pred) VarMats[[i]] = matrix(NA, nrow = D, ncol = D)
diag.var = matrix(NA, nrow = I.pred, ncol = D)
crit.val = rep(0, I.pred)
for (i.subj in 1:I.pred) {
obs.points = which(!is.na(Y.pred[i.subj, ]))
if (sigma2 == 0 & length(obs.points) < npc)
stop("Measurement error estimated to be zero and there are fewer observed points than PCs; scores cannot be estimated.")
Zcur = matrix(Z[obs.points, ], nrow = length(obs.points), ncol = dim(Z)[2])
ZtZ_sD.inv = solve(crossprod(Zcur) + sigma2 * D.inv)
scores[i.subj, ] = ZtZ_sD.inv %*% t(Zcur) %*% (Y.tilde[i.subj, obs.points])
Yhat[i.subj, ] = t(as.matrix(mu)) + scores[i.subj, ] %*% t(efunctions)
if (var) {
VarMats[[i.subj]] = sigma2 * Z %*% ZtZ_sD.inv %*% t(Z)
diag.var[i.subj, ] = diag(VarMats[[i.subj]])
if (simul & sigma2 != 0) {
norm.samp = mvrnorm(2500, mu = rep(0, D), Sigma = VarMats[[i.subj]])/matrix(sqrt(diag(VarMats[[i.subj]])), nrow = 2500, ncol = D, byrow = TRUE)
crit.val[i.subj] = quantile(apply(abs(norm.samp), 1, max), sim.alpha)
}
}
if (makePD) {
npc.0 <- {
tmp <- Matrix::nearPD(npc.0, corr = FALSE, keepDiag = FALSE, do2eigen = TRUE,
trace = TRUE)
as.matrix(tmp$mat)
}
}
### numerical integration for calculation of eigenvalues (see Ramsay & Silverman,
### Chapter 8)
w <- quadWeights(argvals, method = integration)
Wsqrt <- diag(sqrt(w))
Winvsqrt <- diag(1/(sqrt(w)))
V <- Wsqrt %*% npc.0 %*% Wsqrt
evalues = eigen(V, symmetric = TRUE, only.values = TRUE)$values
###
evalues = replace(evalues, which(evalues <= 0), 0)
npc = ifelse(is.null(npc), min(which(cumsum(evalues)/sum(evalues) > pve)), npc)
efunctions = matrix(Winvsqrt %*% eigen(V, symmetric = TRUE)$vectors[, seq(len = npc)],
nrow = D, ncol = npc)
evalues = eigen(V, symmetric = TRUE, only.values = TRUE)$values[1:npc] # use correct matrix for eigenvalue problem
cov.hat = efunctions %*% tcrossprod(diag(evalues, nrow = npc, ncol = npc), efunctions)
### numerical integration for estimation of sigma2
T.len <- argvals[D] - argvals[1] # total interval length
T1.min <- min(which(argvals >= argvals[1] + 0.25 * T.len)) # left bound of narrower interval T1
T1.max <- max(which(argvals <= argvals[D] - 0.25 * T.len)) # right bound of narrower interval T1
DIAG = (diag.G0 - diag(cov.hat))[T1.min:T1.max] # function values
w2 <- quadWeights(argvals[T1.min:T1.max], method = integration)
sigma2 <- max(weighted.mean(DIAG, w = w2, na.rm = TRUE), 0)

ret.objects = c("Yhat", "Y", "scores", "mu", "efunctions", "evalues", "npc", "argvals")
####
D.inv = diag(1/evalues, nrow = npc, ncol = npc)
Z = efunctions
Y.tilde = Y.pred - matrix(mu, I.pred, D, byrow = TRUE)
Yhat = matrix(0, nrow = I.pred, ncol = D)
rownames(Yhat) = rownames(Y.pred)
colnames(Yhat) = colnames(Y.pred)
scores = matrix(NA, nrow = I.pred, ncol = npc)
VarMats = vector("list", I.pred)
for (i in 1:I.pred) VarMats[[i]] = matrix(NA, nrow = D, ncol = D)
diag.var = matrix(NA, nrow = I.pred, ncol = D)
crit.val = rep(0, I.pred)
for (i.subj in 1:I.pred) {
obs.points = which(!is.na(Y.pred[i.subj, ]))
if (sigma2 == 0 & length(obs.points) < npc)
stop("Measurement error estimated to be zero and there are fewer observed points than PCs; scores cannot be estimated.")
Zcur = matrix(Z[obs.points, ], nrow = length(obs.points), ncol = dim(Z)[2])
ZtZ_sD.inv = solve(crossprod(Zcur) + sigma2 * D.inv)
scores[i.subj, ] = ZtZ_sD.inv %*% t(Zcur) %*% (Y.tilde[i.subj, obs.points])
Yhat[i.subj, ] = t(as.matrix(mu)) + scores[i.subj, ] %*% t(efunctions)
if (var) {
ret.objects = c(ret.objects, "sigma2", "diag.var", "VarMats")
if (simul) ret.objects = c(ret.objects, "crit.val")
VarMats[[i.subj]] = sigma2 * Z %*% ZtZ_sD.inv %*% t(Z)
diag.var[i.subj, ] = diag(VarMats[[i.subj]])
if (simul & sigma2 != 0) {
norm.samp = mvrnorm(2500, mu = rep(0, D), Sigma = VarMats[[i.subj]])/matrix(sqrt(diag(VarMats[[i.subj]])),
nrow = 2500, ncol = D, byrow = TRUE)
crit.val[i.subj] = quantile(apply(abs(norm.samp), 1, max), sim.alpha)
}
}
ret = lapply(1:length(ret.objects), function(u) get(ret.objects[u]))
names(ret) = ret.objects
class(ret) = "fpca"
return(ret)
}

ret.objects = c("Yhat", "Y", "scores", "mu", "efunctions", "evalues", "npc",
"argvals")
if (var) {
ret.objects = c(ret.objects, "sigma2", "diag.var", "VarMats")
if (simul)
ret.objects = c(ret.objects, "crit.val")
}
ret = lapply(1:length(ret.objects), function(u) get(ret.objects[u]))
names(ret) = ret.objects
class(ret) = "fpca"
return(ret)
}

0 comments on commit 6c9f9f6

Please sign in to comment.