| Type: | Package |
| Title: | Longitudinal Data Analysis |
| Version: | 0.2 |
| Description: | Regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates. Please cite the manuscripts corresponding to this package: Sun, Z. et al. (2023) <doi:10.48550/arXiv.2305.17715> and Liu, C. et al. (2023) <doi:10.48550/arXiv.2305.17662>. |
| License: | GPL-3 |
| Encoding: | UTF-8 |
| Depends: | dplyr, tibble, MASS, dlm |
| RoxygenNote: | 7.2.3 |
| NeedsCompilation: | no |
| Packaged: | 2023-10-12 12:09:31 UTC; 36922 |
| Author: | Zhuowei Sun [aut, cre, cph], Congmin Liu [aut], Chen Li [aut], Hongyuan Cao [aut, ctb], Jason Peter Fine [aut] |
| Maintainer: | Zhuowei Sun <sunzw21@mails.jlu.edu.cn> |
| Repository: | CRAN |
| Date/Publication: | 2023-10-13 12:00:02 UTC |
Longitudinal data analysis
Description
This function provide regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates.
Usage
lda(data_res, data_cov, N, bd, omit, method)
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)). |
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: d=c(the maximum bandwidth, the minimum bandwidth, the fold of cross-validation, the number of bandwidth divided). If use fixed bandwidth, bd=c(the chosen bandwidth). |
omit |
An object of class integer indicating the method used to do estimation for synchronous covariates. If use plm method, omit=1; if use centering method, omit=2; if use additional covariates information, omit=3. |
method |
An object of class integer indicating the method used to do estimation for asynchronous covariates. If only deal with omit variable, method=0; if use two-stage method, method=1; if use kernel smoothing, method=2. |
Value
a list with the following elements:
est |
The estimation for the corresponding parameters. |
se |
The estimation of standard error for the estimated parameters. |
Examples
library(MASS)
library(tibble)
library(dplyr)
N=100
ty=tz=y=x=z=id_y=id_z=list()
a=b=g=1
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=t.temp^.5
MZ=rep(0, n.temp)
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=a+g*z.temp+x.temp*b+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))
bd=0.1
omit=1
method=1
lda(data_res,data_cov,N,bd,omit,method)
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)