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```
################################################################################
# This file is part of growthrate. #
# #
# growthrate is free software: you can redistribute it and/or modify #
# it under the terms of the GNU General Public License as published by #
# the Free Software Foundation, either version 3 of the License, or #
# (at your option) any later version. #
# #
# growthrate is distributed in the hope that it will be useful, #
# but WITHOUT ANY WARRANTY; without even the implied warranty of #
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the #
# GNU General Public License for more details. #
# #
# You should have received a copy of the GNU General Public License #
# along with growthrate. If not, see <http://www.gnu.org/licenses/>. #
################################################################################
cv.growth <- function(data,tobs,d,K,a,b,r) {
obsdata = data;
## The rows of the matrix obsdata correspond to the individuals or subjects
N = dim(obsdata)[1];
n = dim(obsdata)[2];
## Take differences of the observed time points
dobspts = diff(tobs);
## First we construct the yij using all time points
YI = matrix(nrow = N,ncol = (n-1));
for (k in 1:N) {
YI[k,] = diff(obsdata[k,])/dobspts;
}
## Create the vector Xtilde (or ybold) based on YI
Xtilda = matrix(nrow = n,ncol = N);
w = rep(0,n-2);
for (i in 2:(n-1)) {
w[i] = dobspts[i]/(dobspts[i-1]+dobspts[i]);
for (j in 1:N) {
Xtilda[i,j] = w[i]*YI[j,i-1]+(1-w[i])*YI[j,i];
}
}
for (j in 1:N){
Xtilda[1,j] = YI[j,1];
Xtilda[n,j] = YI[j,n-1];
}
ybar = t(Xtilda);
## Estimate the prior mean based on nonparametric approach
muprior = apply(ybar,2,mean);
muprior = t(muprior);
## Estimate the prior variance using CLIME
re.clime = clime(ybar,perturb = TRUE);
re.cv = cv.clime(re.clime,loss = c("likelihood", "tracel2"));
re.clime.opt <- clime(ybar, re.cv$lambdaopt, perturb = TRUE);
Sigma0inv <- re.clime.opt$Omegalist[[1]];
## Take out the rth observed time point
tm = tobs[-r];
dobsptsm = diff(tm);
YIm = matrix(nrow = N,ncol = length(dobsptsm));
obsdatam = obsdata[,-r];
## Construct YIm with one less time point
for (k in 1:N) {
YIm[k,] = diff(obsdatam[k,])/dobsptsm;
}
n = length(dobsptsm)+1;
## Create the vector Xtilde (or ybold in the paper) based on new YIm
Xtilda = matrix(nrow = n,ncol = N);
w = rep(0,n-2);
for (i in 2:(n-1)) {
w[i] = dobsptsm[i]/(dobsptsm[i-1]+dobsptsm[i]);
for (j in 1:N) {
Xtilda[i,j] = w[i]*YIm[j,i-1]+(1-w[i])*YIm[j,i];
}
}
for (j in 1:N) {
Xtilda[1,j] = YIm[j,1];
Xtilda[n,j] = YIm[j,n-1];
}
ybar = t(Xtilda);
## Based on the estimated priors with the full data set select the prior mean and variance-covariance taking out the rth time point
mupriorr = muprior[-r];
Sigma0invr = Sigma0inv[-r,-r];
## Define the values of sigma we are considering and initialize the variables
sigmavec = seq(a,b,length = K);
CVe = rep(0,K);
e = rep(0,N);
for (k in 1:K) {
sigma = sigmavec[k];
## Calculate the posterior mean and variance covariance at observation time points for each value of sigma
resulpost = posteriorobs(Sigma0invr,sigma,mupriorr,Xtilda,tm,YIm);
muhatMatrix = resulpost$muhatMatrix;
Sigmahat = resulpost$Sigmahat;
## Calculate the posterior distribution at the fine grid for each subject
result = posteriordistribcurve(muhatMatrix,Sigmahat,sigma,tm,d,YIm);
muhatcurve = result$muhatcurvematrix;
tgrid = result$tgrid;
t = tobs;
Khat = Khatf(tgrid,tm,sigma,Sigmahat);
## Reconstruct at time point t(r) the value of y for each subject
tgrids = tgrid[tgrid >= t[r-1] & tgrid <= t[r]];
itgrids = which(tgrid >= t[r-1] & tgrid <= t[r]);
ngrids = length(tgrids);
muhatcurve1 = muhatcurve[,itgrids];
N = dim(muhatcurve1)[1];
ng = dim(muhatcurve1)[2];
Khat1 = Khat[itgrids,itgrids];
## Calculate the integral of muhatcurve1
dtgrids = diff(tgrids);
integ = rep(0,N);
for (j in 1:N) {
integ1 = sum(dtgrids*((muhatcurve1[j,1:(ng-1)]+muhatcurve1[j,2:ng])/2));
integ[j] = integ1/(t[r]-t[r-1]);
## Calculate the error in the reconstruction for each subject
e[j] = (YI[j,r-1]-integ[j])^2;
}
int1 = dtgrids%*%Khat1[-1,];
int2 = int1[-1]%*%dtgrids;
CVe[k] = mean(e) + (1/((t[r]-t[r-1])^2))*int2;
}
## Calculate and return the cross-validation error removing observed time point r for the different values of sigma in sigmavec and the vector of sigma values in sigmavec
CVer = CVe;
result = list(CVer = CVer,sigmavec = sigmavec);
return(result);
}
```

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