## 01 March 2016

### Generating combinations of levels

I have a linear model with a 4-level factor in it. I wanted to generate all possible level combinations of this factor. I couldn't find a function to help me do this in R, so I created my own.
``````combLevel <- function(n) {
B <- matrix(1)
for(i in 2:n) {
maxB <- apply(B, 1, max) + 1
B <- B[rep(1:nrow(B), maxB), ]
B <- cbind(B, unlist(lapply(maxB, seq, 1, -1)))
}
dimnames(B) <- list(NULL, NULL)
B
}
``````
With 4 levels, this led to a total of 15 combinations, 1 with 4 levels, 6 with 3 levels, 7 with 2 levels, and 1 with 1 level.
``````> combLevel(4)
[,1] [,2] [,3] [,4]
[1,]    1    2    3    4
[2,]    1    2    3    3
[3,]    1    2    3    2
[4,]    1    2    3    1
[5,]    1    2    2    3
[6,]    1    2    2    2
[7,]    1    2    2    1
[8,]    1    2    1    3
[9,]    1    2    1    2
[10,]    1    2    1    1
[11,]    1    1    2    3
[12,]    1    1    2    2
[13,]    1    1    2    1
[14,]    1    1    1    2
[15,]    1    1    1    1
``````
How did I come up with the function? I pictured the problem as a bifurcating tree, assigning each of the original levels to a new level, one at a time. At each step in the tree, the next level would either be different from one of the previous levels, or the same as one of the previous levels.

The code for producing this diagram is shown below.
``````library(DiagrammeR)

nodes <- create_nodes(
nodes = 1:23,
type = "number",
label = c(1,  2:1,  3:1, 2:1,  4:1, 3:1, 3:1, 3:1, 2:1))

edges <- create_edges(
from = rep(1:8, c(2, 3, 2, 4, 3, 3, 3, 2)),
to =   2:23,
rel = "related")

graph <- create_graph(
nodes_df = nodes,
edges_df = edges,
graph_attrs = "layout = dot")

render_graph(graph)
``````