Permutation Pyramid

OK so here’s an update to the permutation pyramid I made.

I had to make a list of different permutations of models but it became hard to keep track of all the different variables and their combinations. Hence, the permutation pyramid. The goal is to make a list of vector combinations and permutations. I found this super useful when generating formulas for AICc/Model selection.

Enjoy!

The function has a few options:

vec
- The vector to draw the combinations/permutations from
order.matters = FALSE
- A simple boolean TRUE / FALSE to add in the permutations of each vector combination. This will generate permutations of the combinations and add them to the list. This may only be useful for certain models
req
- A vector of elements that should be required in the combinations.
interact
- A list of vector combinations that can be found in the original combinations

Function

pyramid <- function( vec, order.matters = FALSE, req, interact ){
  # pyramid of variable combinations
  # this doesn't include different
  # arrangements
  vrz <- lapply(
    1:length( vec ), 
    function( x ){ 
      combn( vec, x ) %>% as.data.frame()
    } 
  ) %>% purrr::flatten() %>% unname()
  
  # If there are interactions
  if( !missing( interact ) ){
    # possible interaction combos
    intx <- seq( from = 1, to = length( interact ), by = 1 ) %>% knp.perm.pyramid()
    
    # extra interactions
    vrz.int <- list()
    
    # look through vars
    for( v in vrz ){
      
      # make a list of interactions
      # and add them to the list
      vrz.int <- append( 
        vrz.int, 
        lapply( intx, function( ints ){
          # count number of matches to compare
          # and filter out unaltered var lists
          mt <- 0
          
          # for each interaction
          # check if its in the array
          # then add it if it is
          for ( int in ints ) {
            if( 
                length( intersect( v, interact[[ int ]] ) ) == length( interact[[ int ]] ) & 
                length( interact[[ int ]] ) > 1 
              ){
                v <- c( v, paste0( interact[[ int ]], collapse = ":" ) )
                mt <- mt + 1
            }
          }
          
          # if the number of matches equals
          # the number of interactions then
          # return the altered array
          if( mt == length(ints) ){
            return( v )
          }
          return( NULL )
          
        }) %>% plyr::compact()
      )
    }
    
    # append interactions
    vrz <- append( vrz, vrz.int )
  }
  
  # order matters so lets rearrange
  if( order.matters ){
    vrz <- lapply( vrz, function( x ){
      combinat::permn( x )
    }) %>% purrr::flatten()
  }
  
  # if there's any required variables in each combination
  if( !missing( req ) ){
    vrz <- lapply(vrz, function( x ){
      if( length( intersect( x, req ) ) == length( req ) ){
        return( x )
      }
      return( NULL )
    }) %>% plyr::compact()
  }
  
  # return list of character
  # permutations
  return( vrz )
}

Examples / Usage

Plain vanilla use

> a <- c( "A", "B", "C" )
> pyramid( a )
[[1]]
[1] "A"

[[2]]
[1] "B"

[[3]]
[1] "C"

[[4]]
[1] "A" "B"

[[5]]
[1] "A" "C"

[[6]]
[1] "B" "C"

[[7]]
[1] "A" "B" "C"

If the order of the elements matters

> a <- c( "A", "B", "C" )
> pyramid( a, order.matters = TRUE )
[[1]]
[1] "A"

[[2]]
[1] "B"

[[3]]
[1] "C"

[[4]]
[1] "A" "B"

[[5]]
[1] "B" "A"

[[6]]
[1] "A" "C"

[[7]]
[1] "C" "A"

[[8]]
[1] "B" "C"

[[9]]
[1] "C" "B"

[[10]]
[1] "A" "B" "C"

[[11]]
[1] "A" "C" "B"

[[12]]
[1] "C" "A" "B"

[[13]]
[1] "C" "B" "A"

[[14]]
[1] "B" "C" "A"

[[15]]
[1] "B" "A" "C"

Require variables

> a <- c( "A", "B", "C", "D", "E" )
> b <- c( "B", "D" )
> pyramid( a, req = b )
[[1]]
[1] "B" "D"

[[2]]
[1] "A" "B" "D"

[[3]]
[1] "B" "C" "D"

[[4]]
[1] "B" "D" "E"

[[5]]
[1] "A" "B" "C" "D"

[[6]]
[1] "A" "B" "D" "E"

[[7]]
[1] "B" "C" "D" "E"

[[8]]
[1] "A" "B" "C" "D" "E"

Include interactions

> a <- c( "A", "B", "C")
> b <- list( c( "A", "B" ), c( "A", "B", "C" ) )
> pyramid( a, interact = b )
[[1]]
[1] "A"

[[2]]
[1] "B"

[[3]]
[1] "C"

[[4]]
[1] "A" "B"

[[5]]
[1] "A" "C"

[[6]]
[1] "B" "C"

[[7]]
[1] "A" "B" "C"

[[8]]
[1] "A"   "B"   "A:B"

[[9]]
[1] "A"   "B"   "C"   "A:B"

[[10]]
[1] "A"     "B"     "C"     "A:B:C"

[[11]]
[1] "A"     "B"     "C"     "A:B"   "A:B:C"