Creating a Pairwise Comparison Matrix for further analysis in R using ahpsurvey

Question

I would like to perform Analytical Hierarchy Analysis in R using ahpsurvey.

I will use the table below as an example of my dataset.

Location	Var1
A	8
B	3
C	7
D	6
E	4

This is the Satty rating I would like to incorporate :

Rating	Explanation
1/9	The preferred characteristics are absolutely less important
1/7	The preferred characteristics are strongly less important
1/5	The preferred characteristics are moderately less important
1/3	The preferred characteristics are slightly less important
1	Two characteristics are equally important
3	The preferred characteristics are slightly more important
5	The preferred characteristics are moderately more important
7	The preferred characteristics are strongly more important
9	The preferred characteristics are absolutely more important

Step 3. This is where I am stuck. I would like to create a loop which compares the values of the variable against one another, make a rating using the Satty ranking above.

num_alternatives <- length(location)
  
mat <- matrix(0, nrow = num_alternatives, ncol = num_alternatives)

colnames(comparison_matrix) <- location
rownames(comparison_matrix) <- location 
  
#making comparisons between the value of Var1 of location A and the others
   
  x_dta$a_diff <- 8 - x_dta$Var1
  x_dta$a_diff <- as.character(x_dta$a_diff)
  
  #assigned Satty ranking to the differences 
  diff_lookup <- c(`0` = 1, `5` = 7, `1` = 3, `2` = 5, `4` =7) 
  
  #location A comparison with other locations.
  mat["A","B"] <- 7 
  mat["A","C"] <- 3
  mat["A","D"] <- 5 
  mat["A","E"] <- 7

#followed the same process until I had a full matrix. The problem is that I have over 100 locations in my dataset and filling the matrix one by one is time consuming. 

Answer 1

Generate 100 location names

(location <- apply(expand.grid(LETTERS, LETTERS), 1, function(x) paste0(x, collapse = ""))[1:100])

IT'S IMPORTANT. Now you should decide about your variable range. Saaty's scale has only 9 values, so differences of the variable values for locations must be only 4 classes. You must aggregate differences into 9 classes or initial values into 4 classes. In your example I see the lowest value is 3 and the highest value is 8. You don't have any 5-s. But if you have them, you will get possible differences

-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5

You can't aggregate it into 9 classes. So your variable's range can be only 4 (e.g. from 3 to 7), not 5 (from 3 to 8).

Generate 100 random values

values <- floor(runif(length(location), 3, 8)) # values from 3 to 7!
table(values)

Make the template matrix

num_alternatives <- length(location)

mat <- matrix(NA, nrow = num_alternatives, ncol = num_alternatives)

colnames(mat) <- location
rownames(mat) <- location 

Make vector of values for Saaty's scores

(saaty_scores <- c(1/seq(9,3,-2), 1, seq(3,9,2))

You have small amount of data, so why you ignore simple loops?

A loop to fill the matrix

for (i in 1:nrow(mat)) {
  for (j in 1:ncol(mat)) {
    mat[i,j] <- saaty_scores[values[i] - values[j] + 5] # 5 - for shifting differences from the range [-4,4] to the range [1:9] to use it as an index
  }
}

You should make (for the ahpsurvey package) a list of some matrices from each decision-maker (even if you have only one maker), so:

my_pairwise_mats <- list()
my_pairwise_mats[[1]] <-  mat