R/estimate.MT.R

In skewMLRM: Estimation for Scale-Shape Mixtures of Skew-Normal Distributions

estimate.MT <-
function(y,X,max.iter=1000,prec=1e-4,est.var=TRUE,nu.min=2.0001)
{
  lmtr<-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=matrix(0, nrow=p)
  v=as.numeric(P[length(P)])
  d<-matrix(0,n,1)
  e<-matrix(0,n,p)
  for(i in 1:n){
    e[i,]<-y[i,]-X[[i]]%*%b
    d[i]<-t(e[i,])%*%invB%*%invB%*%e[i,]}
  aux=pmax(as.vector(t(h)%*%invB%*%t(e)),-37)
  l=sum(log(2*gamma((v+p)/2)/(gamma(v/2)*(pi*v)^(p/2)*det(B))*(1+d/v)^(-(v+p)/2)*pnorm(aux)))
  return(l)}
lmstvr<-function(v,b,B,h,y,X){
  n=nrow(y)
  p=ncol(y)
  if(missing(X)) {X<-array(1,c(p,1,n))}
  invB=solve2(B)
  d<-matrix(0,n,1)
  e<-matrix(0,n,p)
  for(i in 1:n){
    e[i,]<-y[i,]-X[[i]]%*%as.matrix(b)
    d[i]<-t(e[i,])%*%invB%*%invB%*%e[i,]}
  lv=sum(log(2*gamma((v+p)/2)/(gamma(v/2)*(pi*v)^(p/2))*(1+d/v)^(-(v+p)/2)))
  return(lv)} 
y.or<-y
X.or<-X
y<-as.matrix(y)
if(!is.numeric(nu.min) | nu.min<=0) stop("nu.min should be a positive number")
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)
  if(missing(X)) {X<-array(1,c(p,1,n))}
  q=ncol(X[[n]])
  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<-matrix(0,nrow=p)
  v<-5
  P_0<-c(as.vector(b),vech(B),as.vector(h),v)
  log0=lmtr(P_0,y,X)
  crit<-1
  iter<-0
  while((crit>=prec)&&(iter<=max.iter))
  { 
    iter<-iter+1 
    d<-matrix(0,n,1)
    e<-matrix(0,n,p)
    for(i in 1:n){
      e[i,]<-y[i,]-X[[i]]%*%b
      d[i]<-t(e[i,])%*%invS%*%e[i,]
    }
    u<-(v+p)/(v+d)
    aux<-as.vector(e%*%invB%*%h)
    W<-as.matrix(exp(dnorm(aux,log=TRUE)-pnorm(aux,log.p=TRUE)))
    t<-e%*%invB%*%h+W 
    S<-1/n*(t(e)%*%diag(as.vector(u),n)%*%e)
    invS<-solve2(S)
    B<-matrix.sqrt(S)
    invB<-solve2(B)
    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,])
    }
    b<-solve2(b0)%*%b1
    V<-optim(v,lmstvr,gr=NULL,b,B,h,y,X,method="L-BFGS-B",lower=nu.min,upper=100,control=list(fnscale=-1,maxit=20))
    v<-as.numeric(V$par)
    P<-c(as.vector(b),vech(B),as.vector(h),v)
    logvero=lmtr(P,y,X)
    crit=abs(logvero-log0)
    P_0<-P
    log0=logvero
  }
  })
  npar=length(P)
  AIC=-2*logvero+2*npar
  BIC=-2*logvero+log(nrow(y))*npar
 P<-matrix(P[-c(q+p*(p+1)/2+1:p)],ncol=1)
 colnames(P)<-c("estimate") 
 conv.problem=1
 if(est.var)
 {
 MI.obs<-  FI.MT(P,y,X)
 test=try(solve2(MI.obs),silent=TRUE)
 se=c()
 if(is.numeric(test) & max(diag(test))<0) 
 {
 conv.problem=0
 se=sqrt(-diag(test))
 P<-cbind(P,se)
 colnames(P)<-c("estimate","s.e.")
 }
 }
conv<-ifelse(iter<=max.iter & crit<=prec, 0, 1)
 tempo=as.numeric(aa[3])
 aux=as.list(sapply(1:p,seq,by=1,to=p))
 indices=c()
 for(j in 1:p)
 {indices=c(indices,paste(j,aux[[j]],sep=""))}
 rownames(P)<-c(paste("beta",1:q,sep=""),paste("alpha",indices,sep=""),"nu")
if(conv.problem==0) ll<-list(coefficients=P[,1],se=P[,2],logLik=logvero,AIC=AIC,BIC=BIC,iterations=iter,time=tempo,conv=conv,dist="MT",class="MSMN",n=nrow(y))
else{
  ll<-list(coefficients=P[,1],logLik=logvero,AIC=AIC,BIC=BIC,iterations=iter,time=tempo,conv=conv,dist="MT",class="MSMN",n=nrow(y))
ll$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.MT"
object.out
}