Example 7.20: Simulate categorical data

Both SAS and R provide means of simulating categorical data (see section 1.10.4). Alternatively, it is trivial to write code to do this directly. In this entry, we show how to do it once. In a future entry, we'll demonstrate writing a SAS Macro (section A.8.1) and a function in R (section B.5.2) to do it repeatedly.

SAS

data test;
p1 = .1; p2 = .2; p3 = .3;
do i = 1 to 10000;
  x = uniform(0);
  mycat = (x ge 0) + (x gt p1) + (x gt p1 + p2) 
                                + (x gt p1 + p2 + p3);
  output;
  end;
run;

Here the parenthetical logical tests in the mycat = line resolve to 1 if the test is true and 0 otherwise, as discussed in section 1.4.9.
The (x ge 0) makes the categories range from 1 to 4, rather than 0 to 3.

The results can be assessed using proc freq:

proc freq data=test; tables mycat; run;

                                  Cumulative    Cumulative
mycat    Frequency     Percent     Frequency      Percent
----------------------------------------------------------
    1         947        9.47           947         9.47
    2        2061       20.61          3008        30.08
    3        3039       30.39          6047        60.47
    4        3953       39.53         10000       100.00

R

In contrast, the R syntax to get the results is rather dense.

p <- c(.1,.2,.3)
x <- runif(10000)
mycat <- numeric(10000)
for (i in 0:length(p)) { 
    mycat <- mycat + (x >= sum(p[0:i])) 
    }

We can display the results using the summary() function.

summary(factor(mycat))
  1    2    3    4
 990 2047 2978 3985