design#

Purpose#

Creates a design matrix of 0’s and 1’s from a column vector of numbers specifying the columns in which the 1’s should be placed.

Format#

y = design(x)#

Parameters:: x (Nx1 vector) – Vector specifying the columns in which 1’s for the design matrix should be placed.
Returns:: y (NxK matrix) – each row of y will contain a single 1, and the rest 0’s. The one in the ith row will be in the round(x[i, 1]) column. The dimension K is such that K = maxc(x).

Examples#

Example 1: Create dummy variables#

design() makes it easy to create dummy variables from a vector of integers.

 // Vector of classes
 c = { 3, 1, 1, 3, 2 };

// Create dummy variable
d = design(c);

After the above code:

Example 2: Create a permutation matrix#

This example uses design to interchange the rows of a matrix.

// Suppress printing of digits after the decimal place
format /rd 6,0;

// Set the rng seed for repeatable random numbers
rndseed 345425235;

/*
** Create a 4x4 matrix of random integers with a standard
** deviation of 10
*/
x = round(10*rndn(4, 4));
print x;

The code above returns:

   12     -1    -10
   -3     12      8
   -2     21    -21
-7    -13      0     -1

Continuing with the example:

// The order of the rows we want
row_order = { 3, 1, 4, 2 };

// Create a permutation matrix from 'row_order'
p = design(row_order);
print p;

This section returns:

    0      1      0
    0      0      0
    0      0      1
    1      0      0

We can use p to permutate the matrix x

/*
** Create a permuted version of 'x' with our preferred row
** order
*/
x2 = p*x;
print x2;

This final section returns:

   -2     21    -21
   12     -1    -10
-7    -13      0     -1
   -3     12      8

This last print statement shows us that we have indeed changed the order of the rows. In x the row order is 1, 2, 3, 4. However, in x2, the row order is 3, 1, 4, 2 (i.e. the third row is now first, the first row is now second, etc.)

Remarks#

Note that x does not have to contain integers: it will be rounded to nearest integer if necessary.

Source#

design.src