mahalanobis distance in R between 2 goups

Question

I have two groups, that each group has 3 variables such as following:

Group1:
     cost time quality
[1,]   90    4      70
[2,]    4   27      37
[3,]   82    4         


        

Answer 1

I felt like what you are trying to do must exist in some R package. After a pretty thorough search, I found function D.sq in package asbio which looks very close. This function requires 2 matrices as input, so it doesn't work for your example. I also include a modified version that accepts a vector for the 2nd matrix.

# Original Function
D.sq <- function (g1, g2) {
    dbar <- as.vector(colMeans(g1) - colMeans(g2))
    S1 <- cov(g1)
    S2 <- cov(g2)
    n1 <- nrow(g1)
    n2 <- nrow(g2)
    V <- as.matrix((1/(n1 + n2 - 2)) * (((n1 - 1) * S1) + ((n2 - 
        1) * S2)))
    D.sq <- t(dbar) %*% solve(V) %*% dbar
    res <- list()
    res$D.sq <- D.sq
    res$V <- V
    res
}

# Data
g1 <- matrix(c(90, 4, 70, 4, 27, 37, 82, 4, 17, 18, 41, 4), ncol = 3, byrow = TRUE)
g2 <- c(2, 27, 4)

# Function modified to accept a vector for g2 rather than a matrix
D.sq2 <- function (g1, g2) {
    dbar <- as.vector(colMeans(g1) - g2)
    S1 <- cov(g1)
    S2 <- var(g2)
    n1 <- nrow(g1)
    n2 <- length(g2)
    V <- as.matrix((1/(n1 + n2 - 2)) * (((n1 - 1) * S1) + ((n2 - 
        1) * S2)))
    D.sq <- t(dbar) %*% solve(V) %*% dbar
    res <- list()
    res$D.sq <- D.sq
    res$V <- V
    res
}

However, this doesn't quite give the answer you expect: D.sq2(g1,g2)$D.sq returns 2.2469.

Perhaps you can compare your original matlab method with these details and figure out the source of the difference. A quick look suggests the difference is how the denominator in V is computed. It may well also be an error on my part, but hopefully this gets you going.