Nothing
estimate.MSN <-
function(y,X=NULL,max.iter=1000,prec=1e-4,est.var=TRUE)
{
y.or<-y;X.or<-X
lmsnr<-function(P,y,X){
n=nrow(y)
p=ncol(y)
if(missing(X)) {X<-array(1,c(p,1,n))}
q=ncol(X[[n]])
b=as.matrix(P[1:q])
B=xpnd(P[(q+1):(q+p*(p+1)/2)])
invB=solve2(B)
h=as.matrix(P[(q+p*(p+1)/2+1):length(P)])
e<-matrix(0,n,p)
for(i in 1:n){e[i,]<-y[i,]-X[[i]]%*%b}
aux=pmax(as.vector(t(h)%*%invB%*%t(e)),-37)
l=sum(log(2/det(B)*mvtnorm::dmvnorm(e%*%invB)*pnorm(aux)))
return(l)}
escmsnr<-function(P,y,X){
n=nrow(y)
p=ncol(y)
if(missing(X)) {X<-array(1,c(p,1,n))}
q=ncol(X[[1]])
b=as.matrix(P[1:q])
p0=p*(p+1)/2
B=xpnd(P[(q+1):(q+p0)])
invB=solve2(B)
h=as.matrix(P[(q+p*(p+1)/2+1):length(P)])
d<-matrix(0,n,1)
e<-matrix(0,n,p)
W<-matrix(0,n,1)
u<-matrix(0,n,1)
dldb1<-matrix(0,q,1)
dldb2<-matrix(0,q,1)
dlda<-matrix(0,p0,1)
dldv<-0
dldg<-0
for(i in 1:n){
e[i,]<-y[i,]-X[[i]]%*%b
d[i]<-t(e[i,])%*%invB%*%invB%*%e[i,]
u[i]<-1
auxi<-pmax(as.vector(t(h)%*%invB%*%e[i,]),-37)
W[i]<-dnorm(auxi)/pnorm(auxi)
dldb1<-dldb1+as.numeric(u[i])*t(X[[i]])%*%invB%*%invB%*%e[i,]
dldb2<-dldb2+as.numeric(W[i])*t(X[[i]])%*%invB%*%h
ddida<-matrix(0,p0,1)
dAida<-matrix(0,p0,1)
dldda<-matrix(0,p0,1)
for(j in 1:p0){
ind=rep(0,p0)
ind[j]=1
Bj=xpnd(ind)
dldda[j]<-2*sum(diag(invB%*%Bj))
dAida[j]<--t(h)%*%invB%*%Bj%*%invB%*%e[i,]
ddida[j]<--t(e[i,])%*%invB%*%(Bj%*%invB+invB%*%Bj)%*%invB%*%e[i,]}
dlda<-dlda-1/2*dldda-1/2*as.numeric(u[i])*ddida+as.numeric(W[i])*dAida}
dldb=dldb1-dldb2
dldh=invB%*%t(e)%*%W
el=c(as.vector(dldb),as.vector(dlda),as.vector(dldh))
return(el)}
y<-as.matrix(y)
if(!is.matrix(y))
stop("y must have at least one element")
if(is.null(X)){X<-array(c(diag(ncol(y))),c(ncol(y),ncol(y),nrow(y)))}
if(is.array(X)==FALSE & is.list(X)==FALSE)
stop("X must be an array or a list")
if(is.array(X))
{Xs<-list()
if(ncol(y)>1 | !is.matrix(X)){
for (i in 1:nrow(y)){
Xs[[i]]<- matrix(t(X[,,i]),nrow=ncol(y))}}
if(ncol(y)==1 & is.matrix(X)){
for (i in 1:nrow(y)){
Xs[[i]]<- matrix(t(X[i,]),nrow=1)}}
X<-Xs}
if (ncol(y) != nrow(X[[1]]))
stop("y does not have the same number of columns than X")
if (nrow(y) != length(X))
stop("y does not have the same number of observations than X")
aa=system.time({
n=nrow(y)
p=ncol(y)
q=ncol(X[[1]])
b0<-matrix(0,q,q)
b1<-matrix(0,q,1)
for(i in 1:n){
b0<-b0+t(X[[i]])%*%X[[i]]
b1<-b1+t(X[[i]])%*%y[i,]
}
b<-solve2(b0)%*%b1
e<-matrix(0,n,p)
for(i in 1:n){
e[i,]<-y[i,]-X[[i]]%*%b
}
S<-cov(e)
invS<-solve2(S)
B<-matrix.sqrt(S)
invB<-solve2(B)
h<-as.matrix(moments::skewness(e))
P_0<-c(as.vector(b),vech(B),as.vector(h))
log0=lmsnr(P_0,y,X)
crit<-1
iter<-0
while ((crit>prec)&&(iter<=max.iter))
{
iter<-iter+1
u<-rep(1,n)
aux<-pmax(as.vector(e%*%invB%*%h),-37)
W<-as.matrix(dnorm(aux)/pnorm(aux))
t<-e%*%invB%*%h+W #passo E
S<-1/n*(t(e)%*%diag(as.vector(u),n)%*%e)
invS<-solve2(S)
B<-matrix.sqrt(S)
invB<-solve2(B)
h<-B%*%solve2(t(e)%*%e)%*%t(e)%*%t
b0<-matrix(0,q,q)
b1<-matrix(0,q,1)
for(i in 1:n){
b0<-b0+t(X[[i]])%*%invB%*%(as.numeric(u[i])*diag(p)+h%*%t(h))%*%invB%*%X[[i]]
b1<-b1+t(X[[i]])%*%(as.numeric(u[i])*(invB%*%invB)%*%y[i,]-as.numeric(t[i])*invB%*%h+invB%*%h%*%t(h)%*%invB%*%y[i,])
}
C<-solve2(b0)
b<-C%*%b1
e<-matrix(0,n,p)
for(i in 1:n){
e[i,]<-y[i,]-X[[i]]%*%b}
P<-c(as.vector(b),vech(B),as.vector(h))
logvero=lmsnr(P,y,X)
#crit<-sqrt(sum((P-P_0)^2))
crit=abs(logvero-log0)
P_0<-P
log0=logvero
}
})
npar=length(P)
AIC=-2*logvero+2*npar
BIC=-2*logvero+log(n)*npar
P<-matrix(P,ncol=1)
colnames(P)<-c("estimate")
conv.problem=1
if(est.var){
MI.obs<-FI.MSN(P,y,X)
test=try(solve2(MI.obs),silent=TRUE)
se=c()
if(is.numeric(test) & max(diag(test))<0){
conv.problem=0
se=sqrt(-diag(test))
P<-cbind(P,se)
colnames(P)<-c("estimate","s.e.")}
}
conv<-ifelse(iter<=max.iter & crit<=prec, 0, 1)
tempo=as.numeric(aa[3])#as.numeric(t1-t0)
aux=as.list(sapply(1:p,seq,by=1,to=p))
indices=c()
for(j in 1:p)
{indices=c(indices,paste(j,aux[[j]],sep=""))}
rownames(P)<-c(paste("beta",1:q,sep=""),paste("alpha",indices,sep=""),paste("lambda",1:p,sep=""))
if(conv.problem==0) ll<-list(coefficients=P[,1],se=P[,2],logLik=logvero,AIC=AIC,BIC=BIC,iterations=iter,time=tempo,conv=conv,dist="MSN",class="MSMSN",n=nrow(y))
else{
ll<-list(coefficients=P[,1],logLik=logvero,AIC=AIC,BIC=BIC,iterations=iter,time=tempo,conv=conv,dist="MSN",class="MSMSN",n=nrow(y))
ll$warnings="Standard errors can't be estimated: Numerical problems with the inversion of the information matrix"
}
object.out<-ll
class(object.out) <- "skewMLRM"
object.out$y<-y.or
object.out$X<-X.or
object.out$"function"<-"estimate.MSN"
object.out
}
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