Converting Data into two separate groups - r

Question

I have simulated a Data for two groups coming from a multivariate normal distribution in R as per below:
#Package to generate a multivariate normal distribution
library(mvtnorm)
#The number of simulated variables that can be changed
p=5
set.seed(30)
#Generating the eigenvalues from a uniform distribution.
m=p
eigval <- runif(m,0.25,1)
#Generating a positive symmetric matrix (this will be used as the covariance matrix for generation of the data.
#Ravi Varadhan(2008)
shat <- matrix(ncol=m, rnorm(m^2))
decomp <- qr(shat)
Q <- qr.Q(decomp)
R <- qr.R(decomp)
d <- diag(R)
ph <- d/abs(d)
O <- Q%*%diag(ph)
shat <- t(O)%*%diag(eigval)%*%(O)
#Variance-covariance matrix for the data generation.
sig <- shat
#Mean vectors for two groups where the parameters may be changed accordingly.
m1 <- runif(p,0.1,0.2)
m2 <- runif(p,0.4,0.9)
#Euclidean distance between two groups
dist(rbind(m1,m2), method = "euclidean")
#The number of observations from group1
n1 <- 30
#The number of observation from group2
n2 <- 70
#The total number of observations
n <- n1+n2
#Group Identifier where '1' represent group 1 and '2' represent group 2
G1 <- rep(1,n1)
G2 <- rep(2,n2)
G <- c(G1,G2)
#Generate Data from group
library(mvtnorm)
g1 <- rmvnorm(n=n1, mean=m1, sigma=sig)
g2 <- rmvnorm(n=n2, mean=m2, sigma=sig)
g <-rbind(g1,g2)
Data <- data.frame(G, DV1=g[ , 1], DV2=g[ , 2], DV3=g[ ,3], DV4=g[,4], DV5=g[ ,5])
Now I want to apply the QDA function on this simulated data by using
the below coding which was found online:
https://stat.ethz.ch/R-manual/R-devel/library/MASS/html/qda.html
However in this example it is said that the in-built IRIS data has been split into a data arranged as a 3-dimensional array of size 50 by 4 by 3, as represented by S-PLUS. (see - https://stat.ethz.ch/R-manual/R-devel/library/datasets/html/iris.html)
Can someone tell me how any data can be split into n x m x p?

Answer 1

Not certain if you want an answer to your code or to the question about iris3. I'll talk about the latter for a moment.
The fact that it is a tidy array with 3 dimensions is convenience and for demonstration. It works because Edgar Anderson harvested exactly 50 samples of each species. There is nothing in the immediate documentation that suggests there is a relevant pairing between the first setosa and the first virginica, so the data is not paired. Unfortunately, by arranging species as planes in the cube, it suggests this paired relationship.
Consider this: had Edgar instead sampled 51 setosa instead of 50, but kept the other two species at 50, how would the array look? One of the planes would be a little taller than the other two, not a matrix. What if he sampled the 50 setosa in a different order (because it is not stated that order matters). The array would be different, and analysis that looks at the 3rd margin (iris3[1,1,]) would return different results, but the actual data really didn't change.
So, I believe the fact that it is in a perfectly-arrange 3-D matrix is for the purposes of dealing with multi-dimensional data, not because the data actually belong in that orientation.
EDIT
Given that you want to know how to transform (any) data from 2D to a 3D array, here's an example using iris. This makes a couple of assumptions:
All of the data is of the same class. For example, in the example below I remove the $Species column; because an array requires everything internally to be the same class, if I did not remove it then all of the numbers would be converted to character, probably not what you want.
The pairing within the added dimension is actually relevant, as I discussed above. This process works just fine if the data is not paired, then it is perfectly logical to think that with other data, there may be different counts for data in the different categories.
Similar (and tied) to #2, all categories should have the same amount of data. This can be waved-away if you are willing to accept rows of NA to extend in the shorter categories, but that seems a bit sloppy to me.
Base R
First, we split the current 2D data into groups, conveniently (but necessarily) resulting in elements with the same dimensions (50 x 4). The -5 removes the fifth column, $Species, so that our next step using as.matrix will not convert numeric to character.
irislist <- by(iris, iris$Species, `[`, -5)
Pre-populate a 3D array per the dimensions of the source data.
mtx <- array(NA, dim = c(dim(irislist[[1]]), length(irislist)))
This might be done with one of the *apply functions, but I couldn't get it to work generically. Perhaps somebody can comment with a suggestion.
for (i in seq_along(irislist)) mtx[,,i] <- as.matrix(irislist[[i]])
The 3D matrix is made! It might be nice to add dimension names to it, though not strictly required:
dimnames(mtx) <- list(NULL, colnames(irislist[[1]]), names(irislist))
mtx
# , , setosa
# Sepal.Length Sepal.Width Petal.Length Petal.Width
# [1,] 5.1 3.5 1.4 0.2
# [2,] 4.9 3.0 1.4 0.2
# [3,] 4.7 3.2 1.3 0.2
# [4,] 4.6 3.1 1.5 0.2
# [5,] 5.0 3.6 1.4 0.2
# ...snip...
abind
This can also be done using the abind, without the need to pre-allocation mtx, go through a for loop, or do any dimension naming:
library(abind)
mtx2 <- do.call("abind", c(irislist, list(along = 3)))
str(mtx)
# num [1:50, 1:4, 1:3] 5.1 4.9 4.7 4.6 5 5.4 4.6 5 4.4 4.9 ...
# - attr(*, "dimnames")=List of 3
# ..$ : NULL
# ..$ : chr [1:4] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width"
# ..$ : chr [1:3] "setosa" "versicolor" "virginica"
Wrap-Up
It isn't obvious how this would work with your data. When I ran your code, I ended up with six columns, only one of which (Data$G) would seem to be something you could split into another dimension (i.e., it looks like it could be categorical). Unfortunately:
table(Data$G)
# 1 2
# 30 70
and per my third bullet, this doesn't work.