ldatv {longitudinalANAL}

Longitudinal data analysis

Description

This function provide regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates with time-varying coefficients.

Usage

ldatv(data_res, data_cov, time, N, bd, method, scb)

Arguments

data_res

An object of class tibble. The structure of the tibble must be: tibble(id_y=ID, ty=measurement time for response, y=observation for response, x=matrix(observation for synchronous covariates), x_add=matrix(observation for uninterested synchronous covariates)).

data_cov

An object of class tibble. The structure of the tibble must be: tibble(id_z=ID, tz=measurement time for response, z=matrix(observation for asynchronous covariates)).

time

An object of class vector. The interest time.

N

An object of class integer. The sample size.

bd

An object of class vector. If use auto bandwidth selection, the structure of the vector must be: bd=c(the maximum bandwidth for h1, the minimum bandwidth for h1, the maximum bandwidth for h2, the minimum bandwidth for h2, the fold of cross-validation, the number of bandwidth divided). If use fixed bandwidth, bd=c(the chosen bandwidth).

method

An object of class integer indicating the method used to do estimation for asynchronous covariates. If use one-stage method, method=1; if use two-stage method with centering method for the first stage, method=1; if use two-stage method with time-varying method for the first stage, method=2.

scb

An object of class vector. If need to construct the simultaneous confidence band, the structure of the vector must be: c(alpha=desirable confidence level, B=repeat times). Otherwise, scb=0.

Value

a list with the following elements:

est.b

The estimation for the parameter of synchronous covariates.

est.g

The estimation for the parameter of asynchronous covariates.

se.b

The estimation of standard error for the parameter of synchronous covariates.

se.g

The estimation of standard error for the parameter of asynchronous covariates.

c_alpha_x

The empirical percentile used to construct the simultaneous confidence band for the parameter of synchronous covariates.

c_alpha_z

The empirical percentile used to construct the simultaneous confidence band for the parameter of asynchronous covariates.

Examples

library(dplyr)
library(MASS)
library(tibble)
N=400
ty=tz=y=x=x1=z=id_y=id_z=list()
beta<-function(t){
 0.3*(t-0.4)^2
}
gamma<-function(t){
 sin(2*pi*t)
}
ny=rpois(N,5)+1
nz=rpois(N,5)+1
for(i in 1:N){
 ty[[i]]=as.matrix(runif(ny[i]))
 tz[[i]]=as.matrix(runif(nz[i]))
 t.temp=rbind(tz[[i]],ty[[i]])
 n.temp=nz[i]+ny[i]
 corr=exp(-abs(rep(1,n.temp)%*%t(t.temp)-t.temp%*%t(rep(1,n.temp))))
 corr.e=2^(-abs(rep(1,n.temp)%*%t(t.temp)-t.temp%*%t(rep(1,n.temp))))
 MX=rep(0, n.temp)
 MZ= 2*(t.temp-0.5)^2
 x.temp=mvrnorm(1,MX,corr)
 z.temp=mvrnorm(1,MZ, corr)
 z[[i]]=as.matrix(z.temp[1:nz[i]])
 x[[i]]=as.matrix(x.temp[-(1:nz[i])])
 id_z[[i]]=rep(i,nz[i])
 id_y[[i]]=rep(i,ny[i])
 y.temp=gamma(t.temp)*z.temp+beta(t.temp)*x.temp+as.matrix(mvrnorm(1,rep(0,n.temp),corr.e))
 y[[i]]=as.matrix(y.temp[-(1:nz[i])])
}
data_cov=tibble(id_z=unlist(id_z),tz=unlist(tz),z=matrix(unlist(z),length(unlist(z))))
data_res=tibble(id_y=unlist(id_y),ty=unlist(ty),x=matrix( unlist(x),length(unlist(x))), y=unlist(y))
ldatv(data_res,data_cov,time=0.3,N,bd=c(N^(-0.5),N^(-0.5)),method=1,scb=0)