Cumulative Combinations

[jsberger]

Hi All,

I'm fairly confident this is an easy ask.  Let's assume i have 4 variables A through D.  Each variable is populated with a 1 or is missing (blank).  How can i generate a data set that contains all possible combinations, taking into account the missing (or stated differently, is cumulative beginning by listing a combination with only a single variable value, and so on).

So, given my scenario above, i know there are 15 possible profiles/combinations (shown below in the table) and based on summing acorss the combination formula when the total=1 and chosen =1 (result=4), 2 (result=6), 3 (result=4) and 4 (result=1).  Can i use PROC PLAN to accomplish this?  I've tried unsuccessfully...

A	B	C	D
1
	1
		1
			1
1	1
1		1
1			1
1	1	1
1	1		1
1	1	1
1	1	1	1
	1	1
	1		1
	1	1	1
		1	1

[ballardw]

one way:

data want;
   do a = 1, .;
   do b = 1, .; 
   do c = 1, .;
   do d = 1, .;
   output;
   end;
   end;
   end;
   end;
run;

If you need a specific order that is a significantly different question.

And there are 16 combinations: you missed all missing.

[jsberger]

Thanks...i knew it was going to be easy for someone.

Out of curiosity...is there a formula that can be used to calculate the number (as corrected 16) in this type of scenario?

[Reeza]

These are known as Combinations and permutations

https://www.mathsisfun.com/combinatorics/combinations-permutations.html

[jsberger]

I searched for a solution within permutations and combinations to no avail.  I am only interested in combinations...but i don't want to require an element from each of all 4.  I could not find a solution where SAS PROC PLAN would output all the combinations taking into account each variable with 2 possible values (either 1 or 0).

[Reeza]

CALL ALLCOMB()

[ballardw]

---

@jsberger wrote:

Thanks...i knew it was going to be easy for someone.

Out of curiosity...is there a formula that can be used to calculate the number (as corrected 16) in this type of scenario?

---

If you have k number of variables and all of them have the same n number of levels then the number is n**k  (n to the k-th power).

Your example: 4 variables all 2 levels = 2**4 = 16.

If they do not have all the same number of levels then it is the product of the number of levels of each variable: Suppose you have 3 variables with 2 4 and 6 levels respectively: 2*4*6 combinations.

[Ksharp · Accepted solution]

data have;
 array x{4} a b c d;
 n=dim(x);
 k=-1;
 total=2**n;
 do i=1 to total;
  rc=graycode(k,of x{*});
  output;
 end;
 keep a b c d;
 run;

[jsberger]

Kevin,

Thanks!  I like this...very slick and easily wrapped in a macro for quick calculation:

%macro comb_list(num);
data comb_list;
array vec{&num} var1-var#
k=-1;
total=2**#
do i=1 to total;
rc=graycode(k,of vec{*});
output;
end;
keep var:;
run;
%mend;
%comb_list(num=7);