#### analysis for trade data

#### normal scores transform 
Z<-array(qnorm( rank(c(Y),na.last="keep")/(sum(!is.na(Y))+1)) , dim(Y) )
dimnames(Z)<-dimnames(Y)
Y<-Z
Y[is.na(Y)]<- 0
####

#### get resids from additive model
a1<-apply(Y,1,mean,na.rm=TRUE)-mean(Y,na.rm=TRUE)
a2<-apply(Y,2,mean,na.rm=TRUE)-mean(Y,na.rm=TRUE)
a3<-apply(Y,3,mean,na.rm=TRUE)-mean(Y,na.rm=TRUE)
a4<-apply(Y,4,mean,na.rm=TRUE)-mean(Y,na.rm=TRUE)

Y<-Y- mean(Y,na.rm=TRUE) - outer(a1,outer(a2,outer(a3,a4,"+"),"+"),"+")
####



m<-dim(Y)
K<-length(m) 

par(mfrow=c(2,2))
for(k in 1:K)
{ 
  d<-svd(mat(Y,k))$d
  plot(d,type="h",ylim=c(0,max(d))) 
}


r<-rep(2,K) 

hYa<-US.als(Y,r) 

plotwtxt(hYa$U[[1]],labels=dimnames(Y)[[1]])

plotwtxt(hYa$U[[2]],labels=dimnames(Y)[[2]])

plotwtxt(hYa$U[[3]],labels=dimnames(Y)[[3]])

plotwtxt(hYa$U[[4]],labels=dimnames(Y)[[4]])

## does changing the rank for one mode affect the SVs of another?
## (a) truncated svd
## (b) ols/als