predict.KFPCA {KFPCA}

Predict FPC scores

Description

Predict FPC scores using least square estimate (LSE) for a new sample.

Usage

## S3 method for class 'KFPCA'
predict(object, newLt, newLy, nK, more = FALSE, ...)

Arguments

object

A KFPCA object obtained from KFPCA.

newLt

A list of n vectors, where n is the new sample size. Each entry contains the observation time in ascending order for each new subject.

newLy

A list of n vectors, where n is the new sample size. Each entry contains the measurements of each new subject at the observation time correspond to newLt.

nK

An integer denoting the number of FPCs.

more

Logical; If FALSE, only the predictions of FPC scores are returned. If TRUE, the mean function estimates and the eigenfunction estimates at the new observation time points are also returned.

...

Not used.

Value

If more = FALSE, a n by nK matrix containing the predictions of the FPC scores is returned, where n is the new sample size. If more = TRUE, a list containing the following components is returned:

score_new

a n by nK matrix containing the predictions of the FPC scores.

meanest_new

Mean function estimates at the new observation time points.

FPC_dis_new

Eigenfunction estimates at the new observation time points.

Examples

# Generate training data
n <- 100
interval <- c(0, 10)
lambda_1 <- 9 #the first eigenvalue
lambda_2 <- 1.5 #the second eigenvalue
eigfun <- list()
eigfun[[1]] <- function(x){cos(pi * x/10)/sqrt(5)}
eigfun[[2]] <- function(x){sin(pi * x/10)/sqrt(5)}
score <- cbind(rnorm(n, 0, sqrt(lambda_1)), rnorm(n, 0, sqrt(lambda_2)))
DataNew <- GenDataKL(n, interval = interval, sparse = 6:8, regular = FALSE,
                     meanfun = function(x){0}, score = score,
                     eigfun = eigfun, sd = sqrt(0.1))
basis <- fda::create.bspline.basis(interval, nbasis = 13, norder = 4,
                              breaks = seq(0, 10, length.out = 11))
Klist <- KFPCA(DataNew$Lt, DataNew$Ly, interval, nK = 2, bw = 1,
               nRegGrid = 51, fdParobj = basis)
# Generate test data
n_test <- 20
score_test <- cbind(rnorm(n_test, 0, sqrt(lambda_1)),
                    rnorm(n_test, 0, sqrt(lambda_2)))
Data_test <- GenDataKL(n_test, interval = interval, sparse = 6:8, regular = FALSE,
                       meanfun = function(x){0}, score = score_test,
                       eigfun = eigfun, sd = sqrt(0.1))
# Prediction
score_pre <- predict(Klist, Data_test$Lt, Data_test$Ly, nK = 2)
plot(score_test[,1], score_pre[,1])