Question

I am creating some artificial data. I need to create household ID (H_ID) and personal ID (P_ID, in each household).

I found a way how to create H_ID in vectorized way.

N <- 50

### Household ID
# loop-for
set.seed(20110224)
H_ID <- vector("integer", N)
H_ID[1] <- 1
for (i in 2:N) if (runif(1) < .5) H_ID[i] <- H_ID[i-1]+1 else H_ID[i] <- H_ID[i-1]
print(H_ID)

# vectorised form
set.seed(20110224)
r <- c(0, runif(N-1))
H_ID <- cumsum(r < .5)
print(H_ID)

But I can not figure out how to create P_ID in vectorized way.

### Person ID
# loop-for
P_ID <- vector("integer", N)
P_ID[1] <- 1
for (i in 2:N) if (H_ID[i] > H_ID[i-1]) P_ID[i] <- 1 else P_ID[i] <- P_ID[i-1]+1
print(cbind(H_ID, P_ID))

# vectorised form
# ???

Answer 1

Inspired by Martin Morgan’s solution to a closely related question, here’s a truly vectorized way to generate the P_ID using the cummax function. It becomes clear once you note that P_ID is closely related to the cumsum of !(r < 0.5):

set.seed(1)
N <- 10
r <- c(0, runif(N-1))
H_ID <- cumsum(r < .5)
r_ <- r >= .5 # flip the coins that generated H_ID.
z <- cumsum(r_)  # this is almost P_ID; just need to subtract the right amount...
# ... and the right amount to subtract is obtained via cummax
P_ID <- 1 + z - cummax( z * (!r_) )
> cbind(H_ID, P_ID)
      H_ID P_ID
 [1,]    1    1
 [2,]    1    2
 [3,]    2    1
 [4,]    3    1
 [5,]    3    2
 [6,]    3    3
 [7,]    3    4
 [8,]    4    1
 [9,]    5    1
[10,]    5    2

I haven’t done detailed timing tests, but it’s probably wicked fast, since these are all internal, vectorized functions