As you not provide the dataset by dput function I built a small example by myself.
dput(df)
structure(list(id = 1:10, edu1 = c(1, 0, 0, 0, 0, 0, 0, 0, 1,
0), edu2 = c(0, 0, 0, 0, 0, 1, 0, 1, 0, 0), edu3 = c(0, 0, 0,
0, 0, 0, 0, 0, 0, 0), edu4 = c(0, 1, 1, 0, 1, 0, 0, 0, 0, 0),
edu5 = c(0, 0, 0, 1, 0, 0, 1, 0, 0, 1)), class = "data.frame", row.names = c(NA,
-10L))
Solution
df$edu = factor(apply(df[,paste0("edu", 1:5)], 1, which.max))
Result
> df
id edu1 edu2 edu3 edu4 edu5 edu
1 1 1 0 0 0 0 1
2 2 0 0 0 1 0 4
3 3 0 0 0 1 0 4
4 4 0 0 0 0 1 5
5 5 0 0 0 1 0 4
6 6 0 1 0 0 0 2
7 7 0 0 0 0 1 5
8 8 0 1 0 0 0 2
9 9 1 0 0 0 0 1
10 10 0 0 0 0 1 5