### SAS Learning Module Working across variables

#### 1. Introduction

This module illustrates (1) how to compute variables manually in a data step and (2) how to work across variables using the array statement in a data step.

Consider the sample program below, which reads in family income data for twelve months.

DATA faminc;
INPUT famid faminc1-faminc12 ;
CARDS;
1 3281 3413 3114 2500 2700 3500 3114 3319 3514 1282 2434 2818
2 4042 3084 3108 3150 3800 3100 1531 2914 3819 4124 4274 4471
3 6015 6123 6113 6100 6100 6200 6186 6132 3123 4231 6039 6215
;
RUN;

PROC PRINT DATA=faminc;
RUN; 
The output is shown below
F      F      F
F      F      F      F      F      F      F      F      F      A      A      A
A      A      A      A      A      A      A      A      A      M      M      M
F     M      M      M      M      M      M      M      M      M      I      I      I
A     I      I      I      I      I      I      I      I      I      N      N      N
O   M     N      N      N      N      N      N      N      N      N      C      C      C
B   I     C      C      C      C      C      C      C      C      C      1      1      1
S   D     1      2      3      4      5      6      7      8      9      0      1      2
1   1   3281   3413   3114   2500   2700   3500   3114   3319   3514   1282   2434   2818
2   2   4042   3084   3108   3150   3800   3100   1531   2914   3819   4124   4274   4471
3   3   6015   6123   6113   6100   6100   6200   6186   6132   3123   4231   6039   6215

#### 2. Computing variables (manually)

Computing variables in a data step can be accomplished a number of ways in SAS. For example, if one wanted to compute the amount of tax (10%) paid for each month, the simplest way to do this is to compute 12 variables (taxinc1-taxinc12) by multiplying each of the (faminc1-faminc12) by .10 as illustrated below.  As you see, this requires entering a command computing the tax for each month of data (for months 1 to 12).

DATA faminc1a;
SET faminc;
taxinc1 = faminc1 * .10 ;
taxinc2 = faminc2 * .10 ;
taxinc3 = faminc3 * .10 ;
taxinc4 = faminc4 * .10 ;
taxinc5 = faminc5 * .10 ;
taxinc6 = faminc6 * .10 ;
taxinc7 = faminc7 * .10 ;
taxinc8 = faminc8 * .10 ;
taxinc9 = faminc9 * .10 ;
taxinc10= faminc10 * .10 ;
taxinc11= faminc11 * .10 ;
taxinc12= faminc12 * .10 ;
RUN;

PROC PRINT DATA=faminc1a;
RUN;

The output is shown below.

                                                              F     F     F
F     F     F     F     F     F     F     F     F     A     A     A     T
A     A     A     A     A     A     A     A     A     M     M     M     A
F    M     M     M     M     M     M     M     M     M     I     I     I     X
A    I     I     I     I     I     I     I     I     I     N     N     N     I
O  M    N     N     N     N     N     N     N     N     N     C     C     C     N
B  I    C     C     C     C     C     C     C     C     C     1     1     1     C
S  D    1     2     3     4     5     6     7     8     9     0     1     2     1

1  1  3281  3413  3114  2500  2700  3500  3114  3319  3514  1282  2434  2818  328.1
2  2  4042  3084  3108  3150  3800  3100  1531  2914  3819  4124  4274  4471  404.2
3  3  6015  6123  6113  6100  6100  6200  6186  6132  3123  4231  6039  6215  601.5                                                                       T        T        T
T        T       T      T      T       T        T        T        A        A        A
A        A       A      A      A       A        A        A        X        X        X
X        X       X      X      X       X        X        X        I        I        I
I        I       I      I      I       I        I        I        N        N        N
O    N        N       N      N      N       N        N        N        C        C        C
B    C        C       C      C      C       C        C        C        1        1        1
S    2        3       4      5      6       7        8        9        0        1        2
1  341.3    311.4    250    270    350    311.4    331.9    351.4    128.2    243.4    281.8
2  308.4    310.8    315    380    310    153.1    291.4    381.9    412.4    427.4    447.1
3  612.3    611.3    610    610    620    618.6    613.2    312.3    423.1    603.9    621.5

#### 3. Computing variables (using the array statement)

Another way to compute 12 variables representing the amount of tax paid (10%) for each month is to use the array statement.  In the example below, two "arrays" are declared:  Afaminc and Ataxinc.  The elements of Afaminc are the variables faminc1-faminc12 and the elements of Ataxinc  are the variables taxinc1-taxinc12.  You can refer to the variables faminc1-faminc12 by referring to the elements of the array Afaminc.  For example, Afaminc(3) refers to faminc3.

Note that the array Afaminc is defined using the existing variables faminc1-faminc12 from the dataset faminc, whereas the values of the array Ataxinc (taxinc1-taxinc12) are created by multiplying Afaminc (faminc1-faminc12) by .10 in the do loop shown below.

DATA faminc1b;
SET faminc ;

ARRAY Afaminc(12) faminc1-faminc12 ;
ARRAY Ataxinc(12) taxinc1-taxinc12 ;

DO month = 1 TO 12;
Ataxinc(month) = Afaminc(month) * .10 ;
END;
RUN;

PROC PRINT DATA=faminc1b;
VAR faminc1-faminc12 taxinc1-taxinc12;
RUN;


The output is shown below:

                                                                     f      f      f
f      f      f      f      f      f      f      f      f      a      a      a      t
a      a      a      a      a      a      a      a      a      m      m      m      a
m      m      m      m      m      m      m      m      m      i      i      i      x
i      i      i      i      i      i      i      i      i      n      n      n      i
O     n      n      n      n      n      n      n      n      n      c      c      c      n
b     c      c      c      c      c      c      c      c      c      1      1      1      c
s     1      2      3      4      5      6      7      8      9      0      1      2      1

1   3281   3413   3114   2500   2700   3500   3114   3319   3514   1282   2434   2818   328.1
2   4042   3084   3108   3150   3800   3100   1531   2914   3819   4124   4274   4471   404.2
3   6015   6123   6113   6100   6100   6200   6186   6132   3123   4231   6039   6215   601.5

t        t        t
t        t       t      t      t       t        t        t        a        a        a
a        a       a      a      a       a        a        a        x        x        x
x        x       x      x      x       x        x        x        i        i        i
i        i       i      i      i       i        i        i        n        n        n
O     n        n       n      n      n       n        n        n        c        c        c
b     c        c       c      c      c       c        c        c        1        1        1
s     2        3       4      5      6       7        8        9        0        1        2

1   341.3    311.4    250    270    350    311.4    331.9    351.4    128.2    243.4    281.8
2   308.4    310.8    315    380    310    153.1    291.4    381.9    412.4    427.4    447.1
3   612.3    611.3    610    610    620    618.6    613.2    312.3    423.1    603.9    621.5

In summary, the new variables become new columns of the dataset faminc1b and one can compute new variables as transformations of these variables, just like any other variables.

Note that the array statement cannot loop over observations for any one variable.  If your data are in this "long" form and you need to loop over observations, you must reshape the data to "wide" form in order to use the array statement.  Another option for looping across observations in the "long" form is to read the variable into a vector array using proc iml (Interactive Matrix Language), loop over the elements of the vector, and then append the results back to the SAS dataset using proc append.

#### 4. Collapsing across variables (manually)

Often one needs to sum across variables (also known as collapsing across variables).  For example, let's say the quarterly income for each family is desired.  In order to get this information, four quarterly variables incqtr1-incqtr4 need to be computed. Again, this can be achieved manually or by using the array statement. Below is an example of how to compute four quarterly income variables incqtr1-incqtr4 by simply adding together the months that comprise a quarter.

DATA faminc2a;
SET faminc;
incqtr1 = faminc1+faminc2+faminc3 ;
incqtr2 = faminc4+faminc5+faminc6 ;
incqtr3 = faminc7+faminc8+faminc9 ;
incqtr4 = faminc10+faminc11+faminc12 ;
RUN;

PROC PRINT DATA=faminc2a;
var faminc1-faminc12 incqtr1-incqtr4;
RUN;

The output is shown below.

                                                 F    F    F
F    F    F    F    F    F    F    F    F    A    A    A    I     I     I     I
A    A    A    A    A    A    A    A    A    M    M    M    N     N     N     N
M    M    M    M    M    M    M    M    M    I    I    I    C     C     C     C
I    I    I    I    I    I    I    I    I    N    N    N    Q     Q     Q     Q
O   N    N    N    N    N    N    N    N    N    C    C    C    T     T     T     T
B   C    C    C    C    C    C    C    C    C    1    1    1    R     R     R     R
S   1    2    3    4    5    6    7    8    9    0    1    2    1     2     3     4
1 3281 3413 3114 2500 2700 3500 3114 3319 3514 1282 2434 2818  9808  8700  9947  6534
2 4042 3084 3108 3150 3800 3100 1531 2914 3819 4124 4274 4471 10234 10050  8264 12869
3 6015 6123 6113 6100 6100 6200 6186 6132 3123 4231 6039 6215 18251 18400 15441 16485

#### 5. Collapsing across variables (using the array statement)

This same result as above can be achieved using the array statement. The example below illustrates how to compute the quarterly income variables incqtr1-incqtr4 using the array statement in a more elegant fashion.  The array Aincqtr has four elements which are computed in the do loop as the sum of sets of three months.  The trick here is that the quarterly intervals begin with months 1,4,7 and 10 respectively, which can be indexed as (month3 - 2)  where month3 is the set of numbers {3,6,9,12}during the execution of the do loop.  Hence, the first element of the array Aincqtr is equal to the sum of the first three elements of Afaminc, the second element of the array Aincqtr is equal to the sum of the next three elements of Afaminc, etc., until the do loop is finished, as shown below.

DATA faminc2b;
SET faminc ;

ARRAY Afaminc(12) faminc1-faminc12 ;
ARRAY Aincqtr(4)  incqtr1-incqtr4 ;

DO qtr = 1 TO 4 ;
month3 = 3*qtr;
Aincqtr(qtr) = Afaminc(month3-2) + Afaminc(month3-1) + Afaminc(month3) ;
END;
RUN;

PROC PRINT DATA=faminc2b;
var faminc1-faminc12 incqtr1-incqtr4;
RUN;

The output is shown below.

                                                 F    F    F
F    F    F    F    F    F    F    F    F    A    A    A    I     I     I     I
A    A    A    A    A    A    A    A    A    M    M    M    N     N     N     N
M    M    M    M    M    M    M    M    M    I    I    I    C     C     C     C
I    I    I    I    I    I    I    I    I    N    N    N    Q     Q     Q     Q
O   N    N    N    N    N    N    N    N    N    C    C    C    T     T     T     T
B   C    C    C    C    C    C    C    C    C    1    1    1    R     R     R     R
S   1    2    3    4    5    6    7    8    9    0    1    2    1     2     3     4
1 3281 3413 3114 2500 2700 3500 3114 3319 3514 1282 2434 2818  9808  8700  9947  6534
2 4042 3084 3108 3150 3800 3100 1531 2914 3819 4124 4274 4471 10234 10050  8264 12869
3 6015 6123 6113 6100 6100 6200 6186 6132 3123 4231 6039 6215 18251 18400 15441 16485

#### 6. Identifying patterns across variables (using the array statement)

The array statement can also be used to identify patterns across variables of a dataset.  Let's say, for example, that one needs to know which months had income that was less than half of the income of the previous month. To obtain this information, dummy indicators can be created to indicate in which months this occurred. In the example below, two arrays are defined, Afaminc and Alowinc, and the elements of Afaminc and Alowinc are the variables faminc1-faminc12 and lowinc2-lowinc12, respectively, in the SAS dataset faminc4.

Note that only 11 dummy indicators are needed for a 12 month period because the interest is in the change from one month to the next.  In the DO loop, when a month has income that is less than half of the income of the previous month, the dummy indicators lowinc2-lowinc12 get assigned a "1".  When this is not the case, they are assigned a "0".

Lastly, a character variable named ever is created (with help from the array statement) indicating whether or not there were any months where income was less than half of the income of the previous month.  This is accomplished by summing up all of the elements of Alowinc (which contains 1's and 0's).  If the sum of the elements of Alowinc is greater than zero, than there was at least one month where income was less than half of the previous month, and ever equals "Y".  Otherwise, if there were no months where income was less than half of the previous month, the sum of the elements of Alowinc is zero, and ever equals "N".

DATA faminc4;
SET faminc ;

ARRAY Afaminc(12) faminc1-faminc12 ;
ARRAY Alowinc(2:12) lowinc2-lowinc12 ;

DO month = 2 to 12 ;
IF Afaminc(month) < ( Afaminc(month-1) / 2) THEN Alowinc(month) = 1;
ELSE Alowinc(month) = 0;
END;

sum_low=0; /*THIS INITIALIZES sum_low TO ZERO AT THE BEGINNING OF THE LOOP*/;
DO month = 2 to 12 ;
sum_low =sum_low + Alowinc(month) ;
END;

IF sum_low GT 0 THEN ever='Y';
IF sum_low EQ 0 THEN ever='N';
RUN;

PROC PRINT DATA=faminc4;
VAR famid faminc1-faminc12 lowinc2-lowinc12 ever;
RUN;

The output is shown below.

                                                   F    F    F                  L L L
F    F    F    F    F    F    F    F    F    A    A    A  L L L L L L L L O O O
A    A    A    A    A    A    A    A    A    M    M    M  O O O O O O O O W W W
F   M    M    M    M    M    M    M    M    M    I    I    I  W W W W W W W W I I I
A   I    I    I    I    I    I    I    I    I    N    N    N  I I I I I I I I N N N E
O M   N    N    N    N    N    N    N    N    N    C    C    C  N N N N N N N N C C C V
B I   C    C    C    C    C    C    C    C    C    1    1    1  C C C C C C C C 1 1 1 E
S D   1    2    3    4    5    6    7    8    9    0    1    2  2 3 4 5 6 7 8 9 0 1 2 R
1 1 3281 3413 3114 2500 2700 3500 3114 3319 3514 1282 2434 2818 0 0 0 0 0 0 0 0 1 0 0 Y
2 2 4042 3084 3108 3150 3800 3100 1531 2914 3819 4124 4274 4471 0 0 0 0 0 1 0 0 0 0 0 Y
3 3 6015 6123 6113 6100 6100 6200 6186 6132 3123 4231 6039 6215 0 0 0 0 0 0 0 0 0 0 0 N

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