implicit ordering problem with mfpca.sc

[julia-wrobel]

issue raised by @andrew-leroux (thank you), bug in MFPCA due to function implicitly assuming ids are ordered. Code below reproduces the bug:

library("refund")
data(DTI)
DTI <- subset(DTI, Nscans < 6)
id <- as.numeric(factor(DTI$ID)); summary(diff(id)) ## IMPORTANT: the IDs are already ordered
Y <- DTI$cca
id2 <- rev(id) ## create new vector of ids which are NOT ordered
mfpca.DTI1 <- mfpca.sc(Y=Y, id = id, twoway = TRUE) ## works
mfpca.DTI2 <- mfpca.sc(Y=Y, id = id2, twoway = TRUE) ## fails

The code below raises a similar issue; there is no bug but estimation is wrong. See the plot, the first row of the first fit and the last row of the second fit should have the same fitted values but they don't.

data(DTI)
library("refund")
DTI <- subset(DTI, Nscans == 4)
id <- as.numeric(factor(DTI$ID)); summary(diff(id))
Y <- DTI$cca

Y2 <- Y[rev(1:nrow(Y)),] ## create new vector of ids which are NOT ordered
id2 <- id[rev(1:nrow(Y))]

mfpca.DTI1 <- mfpca.sc(Y=Y, id = id, twoway = TRUE)
mfpca.DTI2 <- mfpca.sc(Y=Y2, id = id2, twoway = TRUE)

plot(mfpca.DTI1$Yhat[1,])
lines(mfpca.DTI2$Yhat[nrow(Y),])