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regress_miss.R
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regress_miss.R
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regress_miss <- function(Y,X,disp=FALSE,itmax=1000,reltol=10^-10,n1=NULL,Yimp1=NULL){
# fit regression model (also multivariate) under MAR on y
# intercept is automatically included
#
# INPUT:
# Y = matrix of responses
# X = design matrix or list of design matrices of each response
# Preliminaries
ldnorm1 <-function(y,mu,si2) lf = -(y-mu)^2/si2/2-log(2*pi*si2)/2
ldmvnorm1 <-function(y,mu,Si) lf = -c((y-mu)%*%solve(Si)%*%(y-mu))/2-log(det(2*pi*Si))/2
Y = as.matrix(Y)
n = nrow(Y)
if(is.list(X)){
for(j in 1:ncol(Y)) X[[j]] = cbind(1,X[[j]])
}else{
X = cbind(1,X)
}
if(is.null(n1)) n1 = n
### multiple regression
if(ncol(Y)==1){
if(is.list(X)) X = X[[1]]
# fit model for non-missing data
ind = !is.na(Y)
modlm = lm(Y~-1+X)
be = modlm$coefficients
lk = logLik(modlm)[1]
# compute likelihood
Yimp = Y
if(any(!ind)) Yimp[!ind] = X[!ind,,drop=FALSE]%*%be
np = length(be)+1
bic = -2*lk + log(n1)*np
si2 = summary(modlm)$sigma^2
# output
out = list(be=be,si2=si2,lk=lk,np=np,bic=bic,yimp=Yimp)
}else{
### multivariate regression
miss = any(is.na(Y))
ncy = ncol(Y)
if(is.list(X)){
ncx = rep(0,ncy)
for(j in 1:ncy) ncx[j] = ncol(X[[j]])
}else{
ncx = ncol(X)
}
if(is.list(X)){
XX = array(0,c(ncy,sum(ncx),n))
ind = 0
for(j in 1:ncy){
ind = max(ind)+(1:ncx[j])
XX[j,ind, ] = t(X[[j]])
}
}
## with missing data
if(miss){
R = (!is.na(Y))
# starting values
if(is.null(Yimp1)) Yimp2 = Y else Yimp2 = Yimp1
B = matrix(0,ncx,ncy)
if(is.list(X)){
B = vector("list",ncy)
Mu = matrix(0,n,ncy)
for(j in 1:ncy){
if(nrow(X[[j]])==1) out = regress_miss(Yimp2[,j],matrix(0,n,0)) else out = regress_miss(Yimp2[,j],X[[j]][,-1])
B[[j]] = out$be
Mu[,j] = X[[j]]%*%B[[j]]
}
}else{
for(j in 1:ncy){
out = regress_miss(Yimp2[,j],X[,-1])
B[,j] = out$be
}
Mu = X%*%B
}
if(is.null(Yimp1)){
Yimp = Y
for(i in 1:n){
indo = R[i,]
if(sum(indo)<ncy) Yimp[i,!indo] = Mu[i,!indo]
}
}else{
Yimp = Yimp1
}
E = Yimp-Mu
Si = (t(E)%*%E)/n
# compute log-likelihood
lk = 0
for(i in 1:n){
indo = R[i,]
if(sum(indo)==1){
lk = lk+ldnorm1(Y[i,indo],Mu[i,indo],Si[indo,indo])
}else if(sum(indo)>1){
lk = lk+ldmvnorm1(Y[i,indo],Mu[i,indo],Si[indo,indo])
}
}
it = 0; lko = lk
if(disp){
cat("------------|-------------|-------------|\n")
cat(" step | lk | lk-lko |\n")
cat("------------|-------------|-------------|\n")
cat(sprintf("%11g",c(0,lk)),"\n",sep = " | ")
}
while(((lk-lko)/abs(lko)>reltol | it==0) & it<itmax){
# t0 = proc.time()
it = it+1
# E-step
Yimp = Y; Vc = matrix(0,ncy,ncy)
sing = 0
for(i in 1:n){
indo = R[i,]
if(sum(indo)==0){
Yimp[i,] = Mu[i,]
Vc = Vc+Si
}else if(sum(indo)<ncy){
iSi = try(solve(Si[indo,indo]),silent=TRUE)
if(inherits(iSi,"try-error")){
sing = sing+1
iSi = ginv(Si[indo,indo])
}
Tmp = Si[!indo,indo]%*%iSi
Yimp[i,!indo] = Mu[i,!indo]+Tmp%*%(Y[i,indo]-Mu[i,indo])
Vc[!indo,!indo] = Vc[!indo,!indo]+Si[!indo,!indo]-Tmp%*%Si[indo,!indo]
}
}
if(sing>0) cat("***",sing,"singular matrices ***\n")
# print(c(1,proc.time()-t0))
# M-step
if(is.list(X)){
iSi = try(solve(Si),silent=TRUE)
if(inherits(iSi,"try-error")) iSi = ginv(Si)
NUM = DEN = 0
for(i in 1:n){
Tmp = t(XX[,,i])%*%iSi
NUM = NUM + Tmp%*%Yimp[i,]
DEN = DEN + Tmp%*%XX[,,i]
}
iDEN = try(solve(DEN),silent=TRUE)
if(inherits(iDEN,"try-error")) iDEN = ginv(DEN)
be = iDEN%*%NUM
ind = 0
for(j in 1:ncy){
ind = max(ind)+(1:ncx[j])
B[[j]] = be[ind]
Mu[,j] = X[[j]]%*%B[[j]]
}
}else{
M = t(X)%*%X
B = solve(M,t(X))%*%Yimp
Mu = X%*%B
}
E = Yimp-Mu
Si = (Vc+t(E)%*%E)/n
# print(c(2,proc.time()-t0))
# compute log-likelihood
lko = lk; lk = 0
for(i in 1:n){
indo = R[i,]
if(sum(indo)==1){
lk = lk+ldnorm1(Y[i,indo],Mu[i,indo],Si[indo,indo])
}else if(sum(indo)>1){
lk = lk+ldmvnorm1(Y[i,indo],Mu[i,indo],Si[indo,indo])
}
}
# print(c(it,lk,lk-lko))
# print(c(3,proc.time()-t0))
if(disp & it%%100==0) cat(sprintf("%11g",c(it,lk,lk-lko)),"\n",sep = " | ")
}
if(disp & it%%100>0) cat(sprintf("%11g",c(it,lk,lk-lko)),"\n",sep = " | ")
if(disp) cat("------------|-------------|-------------|\n")
}else{
## without missing data
if(is.list(X)){
B = vector("list",ncy)
Mu = matrix(0,n,ncy)
for(j in 1:ncy){
tmp = try(solve(t(X[[j]])%*%X[[j]],t(X[[j]])),silent=TRUE)
if(inherits(tmp,"try-error")) tmp = ginv(t(X[[j]])%*%X[[j]])%*%t(X[[j]])
B[[j]] = c(tmp%*%Y[,j])
Mu[,j] = X[[j]]%*%B[[j]]
}
E = Y-Mu
Si = (t(E)%*%E)/n
lk = 0
for(i in 1:n) lk = lk+dmvnorm(Y[i,],Mu[i,],Si,log=TRUE)
lko = lk; it = 0
while(abs(lk-lko)/abs(lko)>10^-8|it == 0){
lko = lk; it = it+1
iSi = try(solve(Si),silent=TRUE)
if(inherits(iSi,"try-error")) iSi = ginv(Si)
NUM = DEN = 0
for(i in 1:n){
Tmp = t(XX[,,i])%*%iSi
NUM = NUM + Tmp%*%Y[i,]
DEN = DEN + Tmp%*%XX[,,i]
}
iDEN = try(solve(DEN),silent=TRUE)
if(inherits(iDEN,"try-error")) iDEN = ginv(DEN)
be = iDEN%*%NUM
ind = 0
for(j in 1:ncy){
ind = max(ind)+(1:ncx[j])
B[[j]] = be[ind]
Mu[,j] = X[[j]]%*%B[[j]]
}
E = Y-Mu
Si = (t(E)%*%E)/n
lk = 0
for(i in 1:n) lk = lk+dmvnorm(Y[i,],Mu[i,],Si,log=TRUE)
}
}else{
B = solve(t(X)%*%X,t(X))%*%Y
Mu = X%*%B
E = Y-Mu
Si = (t(E)%*%E)/n
lk = 0
for(i in 1:n) lk = lk+dmvnorm(Y[i,],Mu[i,],Si,log=TRUE)
}
Yimp = Y
}
if(is.list(X)){
np = sum(ncx)+ncy*(ncy+1)/2
}else{
np = ncy*ncx+ncy*(ncy+1)/2
}
bic = -2*lk+log(n1)*np
out = list(B=B,Si=Si,lk=lk,np=np,bic=bic,Yimp=Yimp)
}
# output
return(out)
}