Are two variables forming a bijection?

[Antonin Dubeauchoux]

I am interested in understanding the "correspondance" between two variables in a dataset that I have to clean. My two variables have no missing values but are not unique identifiers.
For example (see the MWE below) if I could show that one value of var_a is always associated with the same value of var_b, then the two variables are redundant and I could simply drop one of them. I don't expect this to be the case for all but for a lorge number of pairs.

On the contrary I might have surjection in one or the other directions (or even some messy other situations). I have tried:

clear all
input var_a str16 var_b
1 a //var_a and var_b are bijective
1 a
2 b
3 c
1 a
2 b
3 c
4 d //var_a is surjective onto var_b
5 d
5 d
6 e //var_b is surjective onto var_a
6 f
6 f
// 7 e
end

bysort var_a: gen count_a = _N
bysort var_b: gen count_b = _N
gen cat = ""
replace cat = "bij" if count_a == count_b
replace cat = "a_onto_b" if count_a < count_b
replace cat = "b_onto_a" if count_a > count_b

Which gives me the result I want, assuming that all pairwise combination are either bijective or surjective (so that the last observation 7-e never ocurs)
1. Is there a simpler method to achieve the result?
2. How could I report more complicated cases. For example including the last pair (7-e) makes that the mapping from the domain (6-7) to (f-e) is not an onto mapping. That's typically the type of cases that I would like to report in my data if they exist (what my code does not do so far)

Thank you for your help

[Nick Cox]

Next up Nicolas Bourbaki with a Stata question!


A couple of suggestions:

1. FAQ https://www.stata.com/support/faqs/d...ions-in-group/

2. groups from the Stata Journal

The otherwise unpredictable incantation is as follows. Read st0496 but if interested download from st0496_1

.

 search st0496, entry

Search of official help files, FAQs, Examples, and Stata Journals

SJ-18-1 st0496_1  . . . . . . . . . . . . . . . . . Software update for groups
        (help groups if installed)  . . . . . . . . . . . . . . . .  N. J. Cox
        Q1/18   SJ 18(1):291
        groups exited with an error message if weights were specified;
        this has been corrected

SJ-17-3 st0496  . . . . .  Speaking Stata: Tables as lists: The groups command
        (help groups if installed)  . . . . . . . . . . . . . . . .  N. J. Cox
        Q3/17   SJ 17(3):760--773
        presents command for listing group frequencies and percents and
        cumulations thereof; for various subsetting and ordering by
        frequencies, percents, and so on; for reordering of columns;
        and for saving tabulated data to new datasets

Sample results:

clear all
input var_a str16 var_b
1 a //var_a and var_b are bijective
1 a
2 b
3 c
1 a
2 b
3 c
4 d //var_a is surjective onto var_b
5 d
5 d
6 e //var_b is surjective onto var_a
6 f
6 f
// 7 e
end

groups var* , sepby(var_a)

  +---------------------------------+
  | var_a   var_b   Freq.   Percent |
  |---------------------------------|
  |     1       a       3     23.08 |
  |---------------------------------|
  |     2       b       2     15.38 |
  |---------------------------------|
  |     3       c       2     15.38 |
  |---------------------------------|
  |     4       d       1      7.69 |
  |---------------------------------|
  |     5       d       2     15.38 |
  |---------------------------------|
  |     6       e       1      7.69 |
  |     6       f       2     15.38 |
  +---------------------------------+