How to generate item variables from total score variable - stata

Question

I want to simulate the item score from total score.
For example, I have generated the total score, which has scores between 5 and 25. I would like to distribute this total score to five items with each having a 5-Likert score.
Then I used a while loop to check the condition in Stata 15. The code takes took too long to finish looping and I do not know whether I have made a mistake.
Perhaps someone would like to suggest another way to simulate the item score from the total score?
My code:
set obs 200
generate id=_n
generate u_i= rnormal(0, 0.5)
generate gr = runiform()>0.5
generate sex = runiform()>0.4
generate age = round(rnormal(65, 10))
expand 5
bysort id: generate time=_n
generate e_ij = rnormal(0, 1.0)
generate run=_n
*Generate Sum score 5-25
generate y = 3.0 + 2.0*gr + 0.2*age -1.2*sex + 0.5*time + u_i + e_ij
summarize y
replace y = round(y)
*Generate each item
forvalues k = 1(1)5 {
generate item`k' = runiform(1, 5)
replace item`k' = round(item`k')
}
egen sum_item=rowtotal(item1 item2 item3 item4 item5)
generate diff = y - sum_item
*Looping check if y=sum_item
forvalues a = 1(1)`=_N' {
quietly gsort -diff
while sum_item!=y[`a'] {
replace sum_item=. if sum_item!=y[_n]
forvalues k = 1(1)5 {
replace item`k' =. if sum_item==.
replace item`k' = runiform(1, 5) if item`k'==.
replace item`k' = round(item`k')
}
replace sum_item= item1 + item2+item3+item4+item5 if sum_item==.
replace diff = y - sum_item
if (sum_item==y[`a']) continue, break
}
}
The expected data that I would like to have:
As you can see, after running the loop I will always get 2-4 cases that the program keep running by generating item score (item1-item5) until the diff variable equals zero.

Answer 1

If I'm understanding correctly, you could loop something like the following (after setting all the items to initial values of 1, since possible values are 1 to 5):
capture generate rand_int = 0
replace rand_int = floor( 5 * runiform() + 1 ) // random int, 1 to 5
capture generate cnd = 0
forvalues k = 1(1)5 {
replace cnd = rand_int == `k' & sum_item < y & item`k' < 6
replace item`k' = item`k' + 1 if cnd
}
replace sum_item = item1+item2+item3+item4+item5
In words, that says is that if sum_item < y, then randomly add 1 to one of the items (as long as that item is not already equal to 5), and then you would keep doing it until sum_item == y for all rows.
So that's going to converge in roughly 20 iterations if the max value of y is 25 and items are from 1 to 5. I say "roughly" because there is a little waste in here when you add 1 to an item that is already equal to 5. You could ad some extra code for that, but I wouldn't bother if this is fast enough. E.g. for high values of item_sum it would be more efficient to start with initial values of 5 and randomly subtract 1 until it converges.
I'm not enough of a statistician to say that's the best or even an adequate way to do it, but intuitively to me it seems OK if you want a fairly uniform distribution of values. If you wanted the modal value to be 4, for example, that's a lot harder and not really a programming question any longer.