LocKer {LocKer}

Locally sparse estimator of generalized varying coefficient model for asynchronous longitudinal data.

Description

Locally sparse estimator of generalized varying coefficient model for asynchronous longitudinal data by kernel-weighted estimating equation. The function is suitable for generalized varying coefficient model with one covariate.

Usage

LocKer(
  X,
  Y,
  family,
  X_obser_num,
  Y_obser_num,
  X_obser,
  Y_obser,
  timeint,
  L_list,
  roupen_para_list,
  lambda_list,
  absTol_list,
  nfold = 5,
  d = 3
)

Arguments

X

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

Y

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

family

A character string representing the distribution family of the response. The value can be "Gaussian", "binomial", "poisson".

X_obser_num

A vector denoting the observation size of the covariate for each subject.

Y_obser_num

A vector denoting the observation size of the response for each subject.

X_obser

A list of n vectors, where n is the sample size. Each entry contains the observation times of the covariate for each subject.

Y_obser

A list of n vectors, where n is the sample size. Each entry contains the observation times of the response for each subject.

timeint

A vector of length two denoting the supporting interval.

L_list

A vector denoting the candidates for the number of B-spline basis functions. The best L is chosen by cross-validation.

roupen_para_list

A vector denoting the candidates for the roughness parameters. The best roughness parameter is chosen by EBIC together with sparseness parameter.

lambda_list

A vector denoting the candidates for the sparseness parameter. The best sparseness parameter is chosen by EBIC together with roughness parameter.

absTol_list

A vector denoting the threshold of the norm for coefficient function on each sub-interval. The vector is related to L_list, with the same length as L_list.

nfold

An integer denoting the number of fold for the selection of L by cross-validation. (default: 5)

d

An integer denoting the degree of B-spline basis functions. (default: 3)

Value

A list containing the following components:

beta0fd_est

A functional data object denoting the estimated intercept function.

betafd_est

A functional data object denoting the estimated coefficient function.

time

A scalar denoting the computation time.

L

An integer denoting the selected number of B-spline basis function.

roupen_select

A scalar denoting the selected roughness parameter.

lambda_select

A scalar denoting the selected sparseness parameter.

EBIC

A matrix denoting the EBIC scores for various roughness parameters and sparseness parameters belongs to the candidates when using the selected L.

Examples

####Generate data
n <- 200
beta0 <- function(x){cos(2 * pi * x)}
beta <- function(x){sin(2 * pi * x)}
Y_rate <- 15
X_rate <- 15
Y_obser_num <- NULL
X_obser_num <- NULL
Y_obser <- list()
X_obser <- list()
for(i in 1:n){
Y_obser_num[i] <- stats::rpois(1, Y_rate) + 1
Y_obser[[i]] <- stats::runif(Y_obser_num[i], 0, 1)
X_obser_num[i] <- stats::rpois(1, X_rate) + 1
X_obser[[i]] <- stats::runif(X_obser_num[i], 0, 1)
}
## The covariate functions Xi(t)
X_basis <- fda::create.bspline.basis(c(0, 1), nbasis = 74, norder = 5,
breaks = seq(0, 1, length.out = 71))
a <- matrix(0, nrow = n, ncol = 74)
X <- list()
XY <- list() #X at the observation time of Y
muY <- list()
for(i in 1:n){
a[i,] <- stats::rnorm(74)
Xi_B <- splines::bs(X_obser[[i]], knots = seq(0, 1, length.out = 71)[-c(1, 71)],
degree = 4, intercept = TRUE)
X[[i]] <- Xi_B %*% a[i,]
Yi_B <- splines::bs(Y_obser[[i]], knots = seq(0, 1, length.out = 71)[-c(1, 71)],
degree = 4, intercept = TRUE)
XY[[i]] <- Yi_B %*% a[i,]
muY[[i]] <- beta0(Y_obser[[i]]) + XY[[i]] * beta(Y_obser[[i]])
}
Y <- list()
errY <- list()
for(i in 1:n){
errY[[i]] <- stats::rnorm(Y_obser_num[[i]], mean = 0, sd = 1)
Y[[i]] <- muY[[i]] + errY[[i]]
}
L_list <- 20
absTol_list <- 10^(-3)
roupen_para_list <- 1.5 * 10^(-3)
lambda_list <- c(0, 0.001, 0.002)
LocKer_list <- LocKer(X, Y, family = "Gaussian", X_obser_num, Y_obser_num, X_obser,
Y_obser, timeint = c(0, 1), L_list, roupen_para_list, lambda_list, absTol_list)