You could replace random elements in lapply.
set.seed(42)
r1 <- as.data.frame(lapply(dat, \(x) replace(x, sample(length(x), .1*length(x)), NA)))
r1
# X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
# 1 NA 7 NA 10 3 11 4 4 NA 7
# 2 6 6 8 8 4 11 NA 8 10 9
# 3 1 12 4 5 12 3 10 3 11 1
# 4 3 10 6 2 11 NA 3 11 2 11
# 5 8 NA 10 12 5 7 2 9 4 10
# 6 12 4 9 12 9 2 7 9 8 8
# 7 7 5 9 4 2 12 12 3 4 4
# 8 12 5 3 1 6 1 4 7 6 NA
# 9 4 6 12 NA 5 8 4 4 6 7
# 10 3 2 11 3 NA 5 4 NA 2 4
mean(is.na(r1))
# [1] 0.1
However, this replaces .1 of the values in each column with NA. If we want each cell to be replaced with NA with a probability of .1, we could use apply on both MARGINS=1:2.
set.seed(42)
p <- .1
r2 <- as.data.frame(apply(dat, 1:2, \(x) sample(c(x, NA), 1, prob=c((1 - p), p))))
r2
# X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
# 1 NA 7 NA 10 3 11 4 4 12 7
# 2 NA 6 8 8 4 11 NA 8 10 9
# 3 1 NA NA 5 12 3 10 3 11 1
# 4 3 10 NA 2 NA 9 3 11 2 NA
# 5 8 12 10 12 5 7 2 9 4 NA
# 6 12 NA 9 12 NA 2 7 9 8 8
# 7 7 NA 9 4 2 12 12 3 4 4
# 8 12 5 NA 1 6 1 4 7 6 12
# 9 4 6 12 NA NA 8 4 4 6 7
# 10 3 2 11 3 3 5 4 8 2 4
mean(is.na(r2))
# [1] 0.16
If it's possible to coerce the data as.matrix you could treat it like a vector
set.seed(42)
m <- as.matrix(dat)
m[sample(seq_along(m), .1*length(m))] <- NA
m
# X1 X2 X3 X4 X5 X6 X7 X8 X9 X10
# [1,] 6 7 1 10 3 11 4 NA 12 7
# [2,] 6 6 8 8 4 11 10 8 10 9
# [3,] 1 12 4 5 12 3 10 3 11 1
# [4,] 3 10 NA 2 11 9 3 NA 2 11
# [5,] 8 12 NA 12 5 7 NA 9 4 10
# [6,] 12 4 9 12 9 2 7 9 8 8
# [7,] 7 5 9 4 NA 12 12 3 4 4
# [8,] 12 NA 3 1 6 1 4 7 6 12
# [9,] 4 6 12 3 NA 8 4 4 NA 7
# [10,] 3 2 11 3 3 5 4 8 2 NA
mean(is.na(m))
# [1] 0.1
and coerce back to "data.frame".
dat_na <- as.data.frame(m) |> type.convert(as.is=TRUE)
The type.convert takes care of getting back classes like "numeric" and "character", since matrices can only have one mode. Note that you may lose attributes in the process.
Data:
dat <- structure(list(X1 = c(6L, 6L, 1L, 3L, 8L, 12L, 7L, 12L, 4L, 3L
), X2 = c(7L, 6L, 12L, 10L, 12L, 4L, 5L, 5L, 6L, 2L), X3 = c(1L,
8L, 4L, 6L, 10L, 9L, 9L, 3L, 12L, 11L), X4 = c(10L, 8L, 5L, 2L,
12L, 12L, 4L, 1L, 3L, 3L), X5 = c(3L, 4L, 12L, 11L, 5L, 9L, 2L,
6L, 5L, 3L), X6 = c(11L, 11L, 3L, 9L, 7L, 2L, 12L, 1L, 8L, 5L
), X7 = c(4L, 10L, 10L, 3L, 2L, 7L, 12L, 4L, 4L, 4L), X8 = c(4L,
8L, 3L, 11L, 9L, 9L, 3L, 7L, 4L, 8L), X9 = c(12L, 10L, 11L, 2L,
4L, 8L, 4L, 6L, 6L, 2L), X10 = c(7L, 9L, 1L, 11L, 10L, 8L, 4L,
12L, 7L, 4L)), class = "data.frame", row.names = c(NA, -10L))