missingness mechanism and missing rate - r

Question

I want to apply a missingness mechanism such as(MCAR,MAR,NMAR) to my data under missing rate (5%.15%) if I have tow variables and nine instances:
Aj <- c(48,75,83,58,83,32,45,50,86)
As <- c(24,30,31,35,60,76,81,82,88)
as follows:
for Simulating MAR, we first randomly separated the variables into pairs
(Aj, As), 1 ≤ j , s ≤ r, where Aj was the variable into
which missing values were introduced, and As was the variable
that affected the missingness of Aj . Given a pair of
variables (Aj, As) and missing rate α,we first split the instances
into two equal-sized subsets according to their values
at As . If the variable As is numerical, we would find the
median of As and then assigned all the instances into
two subsets according to weather the instances have bigger
values than median As. for example we may let the instances
whose values at As are lower than the median 60 (instance
number 1–5) to be missing with the probability of 4α, that
is to say, Pr(Aj = missing|As ≤ 60) = 4α.
I wrote this code for missing mechanism in R
ifelse(As<=median(As),Aj==NA,Aj)
[1] NA NA NA NA NA 32 45 50 86
My question is how to add missing rate for example 5% to this code in R or another code for the above example and illustration.

Answer 1

This one-liner would give you missingness at rate alpha:
ifelse( (As <= median(As)) & (runif(length(As)) < alpha), NA, Aj)
If you want to have the observed rate close to alpha (you need to figure out how you want to handle rounding) you can do something like this:
Aj <- c(48,75,83,58,83,32,45,50,86)
As <- c(24,30,31,35,60,76,81,82,88)
# missingness rate
alpha <- 0.05
# create subset less than the median
b <- ifelse( As <= median(As) , NA, Aj)
# get the size of that subset (not known before hand due to tie handling)
n.b <- sum(is.na(b))
b.small <- Aj[is.na(b)]
# sample from the small subset at a fixed rate, setting sampled to NA
b.small[ sample(1:n.b, size=ceiling(n.b * alpha)) ] <- NA
b[is.na(b)] <- b.small
# b is now Aj with missingness
The output should be similar to
[1] 48 NA 83 58 83 32 45 50 86