For loops to count concordant and discordant pairs

count_pairs.R

# Table 2.8, Agresti (2002) p. 57
M <- as.table(rbind(c(1, 3, 10, 6), 
                    c(2, 3, 10, 7),
                    c(1, 6, 14, 12),
                    c(0, 1, 9, 11)))
dimnames(M) <- list(`income` = c("<15", "15-25", "25-40", ">40"),
                    `job satisfaction` = c("VD", "LD", "MS","VS"))

# count concordant pairs
n <- nrow(M)
m <- ncol(M)
row.x <- row(M)
col.x <- col(M)
C <- numeric(length = (nrow(M)-1) * (ncol(M)-1))
k <- 1
for(i in 1:(n-1)){
  for(j in 1:(m-1)){
    C[k] <- M[i,j] * sum(M[row.x > i & col.x > j])
    k <- k + 1
  }
}
Concordant <- sum(C)

# count discordant pairs
D <- numeric(length = (nrow(M)-1) * (ncol(M)-1))
k <- 1
for(i in 1:(n-1)){
  for(j in 2:m){
    D[k] <- M[i,j] * sum(M[row.x > i & col.x < j])
    k <- k + 1
  }
}
Discordant <- sum(D)