| Title: | Longitudinal Data Analysis |
|---|---|
| Description: | Regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates. Please cite the manuscripts corresponding to this package: Sun, Z. et al. (2023) <arXiv:2305.17715> and Liu, C. et al. (2023) <arXiv:2305.17662>. |
| Authors: | Zhuowei Sun [aut, cre, cph], Congmin Liu [aut], Chen Li [aut], Hongyuan Cao [aut, ctb], Jason Peter Fine [aut] |
| Maintainer: | Zhuowei Sun <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2 |
| Built: | 2024-12-06 06:35:42 UTC |
| Source: | CRAN |
This function provide regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates.
lda(data_res, data_cov, N, bd, omit, method)lda(data_res, data_cov, N, bd, omit, method)
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. |
a list with the following elements:
est |
The estimation for the corresponding parameters. |
se |
The estimation of standard error for the estimated parameters. |
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)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)
This function provide regression analysis of mixed sparse synchronous and asynchronous longitudinal covariates with time-varying coefficients.
ldatv(data_res, data_cov, time, N, bd, method, scb)ldatv(data_res, data_cov, time, N, bd, method, scb)
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. |
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. |
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)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)