ptFCReg {fdaconcur}

Functional concurrent regression using pointwise multiple linear regression.

Description

Functional concurrent regression using pointwise multiple linear regression.

Usage

ptFCReg(tGrid, dat)

Arguments

tGrid

A vector of length m with the input time points.

dat

A list of input functional/scalar covariates. Each field corresponds to a functional (a matrix) or scalar (a vector) variable. The last entry is assumed to be the functional response if no entry is names 'Y'. If a field corresponds to a functional variable, it should be an n-by-m matrix, where each row holds the observations for one subject on the common grid tGrid. If a field corresponds to a scalar covariate, it should be a vector of length n.

Value

A list containing the following fields:

beta0

A vector containing the time-varying intercept evaluated on tGrid.

beta

A matrix for the concurrent regression effects, where rows correspond to different predictors and columns to different time points in tGrid.

tGrid

The input tGrid.

R2

A vector of the time-varying R^2(t), evaluated at t in tGrid.

Ldf

A list holding the input data, each element of which is a data frame holding the data observed at one element of tGrid.

Examples

set.seed(1)
n <- 50
nGridIn <- 101
tGrid <- seq(0, 1, length.out=nGridIn) # Functional data support
muX1 <- tGrid * 2 # mean function for X_1
sigma <- 1
beta0 <- 0
beta <- rbind(cos(tGrid), 1.5 + sin(tGrid))
Z <- MASS::mvrnorm(n, rep(0, 2), diag(2))
X_1 <- Z[, 1, drop=FALSE] %*% matrix(1, 1, nGridIn) + matrix(muX1, n, nGridIn, byrow=TRUE)
epsilon <- rnorm(n, sd=sigma)
Y <- t(sapply(seq_len(n), function(i) {
  beta0 + beta[1,] * X_1[i, ] + beta[2,] * Z[i, 2] + epsilon[i]
}))
dat <- list(X1=X_1, Z1=Z[, 2], Y=Y)
res <- ptFCReg(tGrid = tGrid, dat = dat)