In Experimental Design, I tried to design a Graeco Latin-Square, which I believe an extended version of Latin Square Design with more factors.. however, I found it behave strangely, here is some snippets by Using Treatment 1, and 2 Simulation with length of 1-26
graeco_design_possibility <- function(test_until=20){
library(agricolae)
k_graeco <- seq(2,test_until,1)
bool_possibility <- c()
for(n in 2:test_until){
b <- design.graeco(LETTERS[1:n], 1:n)
if(is.null(b)){
bool_possibility <- c(bool_possibility, FALSE)
}else{
bool_possibility <- c(bool_possibility, TRUE)
}
}
simulation_graeco <- data.frame(number_k = k_graeco, success_run=bool_possibility)
return(simulation_graeco)
}
And When I test this, the simulation, resulted like below: (Note: More weird bugs happen after k=26)
g <- graeco_design_possibility(26)
g
number_k success_run
1 2 TRUE
2 3 TRUE
3 4 TRUE
4 5 TRUE
5 6 FALSE
6 7 TRUE
7 8 TRUE
8 9 TRUE
9 10 TRUE
10 11 TRUE
11 12 TRUE
12 13 TRUE
13 14 FALSE
14 15 TRUE
15 16 FALSE
16 17 TRUE
17 18 FALSE
18 19 TRUE
19 20 FALSE
20 21 TRUE
21 22 FALSE
22 23 TRUE
23 24 FALSE
24 25 TRUE
25 26 FALSE
And thats how it is, I looked at the documentation, and it says that The function is only for squares of the odd numbers and even numbers (4, 8, 10 and 12) I didnt understand the explanation much, since the result of simulation kinda contradict with the explanation: 6,14,16 is even number right? so why the problem persist in this way?
I removed limitations the developer supposed to limit in design.graeco() function, I honestly didnt know why there should be limitation on specific lengths on treatment, here is the final result of no limitation with Graeco Latin Square designs
design_graeco_custom <- function(trt1, trt2, serie = 2, seed = 0, kinds = "Super-Duper", randomization = TRUE){
number <- 10
if (serie > 0)
number <- 10^serie
r <- length(trt1)
if (seed == 0) {
genera <- runif(1)
seed <- .Random.seed[3]
}
set.seed(seed, kinds)
parameters <- list(design = "graeco", trt1 = trt1,
trt2 = trt2, r = r, serie = serie, seed = seed, kinds = kinds,
randomization)
col <- rep(gl(r, 1), r)
fila <- gl(r, r)
fila <- as.character(fila)
fila <- as.numeric(fila)
plots <- fila * number + (1:r)
C1 <- data.frame(plots, row = factor(fila), col)
C2 <- C1
a <- 1:(r * r)
dim(a) <- c(r, r)
for (i in 1:r) {
for (j in 1:r) {
k <- i + j - 1
if (k > r)
k <- i + j - r - 1
a[i, j] <- k
}
}
m <- trt1
if (randomization)
m <- sample(trt1, r)
C1 <- data.frame(C1, m[a])
m <- trt2
if (randomization)
m <- sample(trt2, r)
C2 <- data.frame(C2, m[a])
ntr <- length(trt1)
C1 <- data.frame(C1, B = 0)
for (k in 1:r) {
x <- C1[k, 4]
i <- 1
for (j in 1:(r^2)) {
y <- C2[(k - 1) * r + i, 4]
if (C1[j, 4] == x) {
C1[j, 5] <- y
i <- i + 1
}
}
}
C1[, 4] <- as.factor(C1[, 4])
C1[, 5] <- as.factor(C1[, 5])
names(C1)[4] <- c(paste(deparse(substitute(trt1))))
names(C1)[5] <- c(paste(deparse(substitute(trt2))))
outdesign <- list(parameters = parameters,
sketch = matrix(paste(C1[,4], C1[,5]),
byrow = TRUE, ncol = r), book = C1)
return(outdesign)
}
And also I found out that with treatment over 26, I decided to use extra helper function to spawn possible letters:
letters_construction <- function(n=27, format_letter="upper"){
if(n > 26 && n <= 702){
letter_result <- NULL
letter_comb <- NULL
if(format_letter=="upper"){
letter_result <- LETTERS[1:26]
letter_comb <- expand.grid(LETTERS[1:26], LETTERS[1:26])
}else if(format_letter=="lower"){
letter_result <- letters[1:26]
letter_comb <- expand.grid(letters[1:26], letters[1:26])
}
letter_comb$comb <- paste0(letter_comb$Var2, letter_comb$Var1)
letter_finalcomb <- as.character(letter_comb$comb)
n_remainder <- n-26
letter_result <- c(letter_result, letter_finalcomb[1:n_remainder])
return(letter_result)
}
}
So I can make an implementation of Big Graeco Latin Square design like this:
b <- letters_construction(30)
design_graeco_custom(b, 1:30)