grouping and count

[Xulei Liu]

The original data value is shown as x, first of all, it is hoped that the same value can be next to different stages, as shown in x1; secondly, the number of each stage is expected to be counted, as shown in x2.I'm looking forward to your reply.Thanks!!!
x x1 x2
0 1 1
0 1 2
0 1 3
0 1 4
1 2 1
1 2 2
1 2 3
1 2 4
0 3 1
0 3 2
0 3 3
1 4 1
0 5 1

[William Lisowski]

generate seq = _n
generate x1 = sum(x!=x[_n-1])
bysort x1 (seq): generate x2 = _n
sort seq
drop seq
list, sepby(x1)

. list, sepby(x1)

     +-------------+
     | x   x1   x2 |
     |-------------|
  1. | 0    1    1 |
  2. | 0    1    2 |
  3. | 0    1    3 |
  4. | 0    1    4 |
     |-------------|
  5. | 1    2    1 |
  6. | 1    2    2 |
  7. | 1    2    3 |
  8. | 1    2    4 |
     |-------------|
  9. | 0    3    1 |
 10. | 0    3    2 |
 11. | 0    3    3 |
     |-------------|
 12. | 1    4    1 |
     |-------------|
 13. | 0    5    1 |
     +-------------+

[Nick Cox]

Here's another way to think about it in addition to @William Lisowski's fine answer.

Given a time (time-like, order or sequence) variable and a tsset this falls under the heading of tsspell from SSC. tsspell is a good search term for this forum.

* Example generated by -dataex-. For more info, type help dataex
clear
input float x
0
0
0
0
1
1
1
1
0
0
0
1
0
end
. 
. gen t = _n 

. tsset t 

Time variable: t, 1 to 13
        Delta: 1 unit

. tsspell x 

. 
. list, sepby(_spell)

     +-------------------------------+
     | x    t   _spell   _seq   _end |
     |-------------------------------|
  1. | 0    1        1      1      0 |
  2. | 0    2        1      2      0 |
  3. | 0    3        1      3      0 |
  4. | 0    4        1      4      1 |
     |-------------------------------|
  5. | 1    5        2      1      0 |
  6. | 1    6        2      2      0 |
  7. | 1    7        2      3      0 |
  8. | 1    8        2      4      1 |
     |-------------------------------|
  9. | 0    9        3      1      0 |
 10. | 0   10        3      2      0 |
 11. | 0   11        3      3      1 |
     |-------------------------------|
 12. | 1   12        4      1      1 |
     |-------------------------------|
 13. | 0   13        5      1      1 |
     +-------------------------------+