# dummydn¶

## Purpose¶

Creates a set of dummy (0/1) variables by breaking up a variable into specified categories. The highest (rightmost) category is unbounded on the right, and a specified column of dummies is dropped.

## Format¶

y = dummydn(x, v, p)
Parameters:
• x (Nx1 vector) – data to be broken up into dummy variables

• v ((K-1)x1 vector) – Specifies the $$K - 1$$ breakpoints (these must be in ascending order) that determine the $$K$$ categories to be used. These categories should not overlap.

• p (scalar) – positive integer in the range $$[1, K]$$, specifying which column should be dropped in the matrix of dummy variables.

Returns:

y (Nx(K-1) matrix) – contains the $$K-1$$ dummy variables.

## Examples¶

// Set seed for repeatable random numbers
rndseed 135345;

// Create uniform random integers between 1 and 9
x = ceil(9*rndu(5, 1));

// Set the breakpoints
v = { 1, 5, 7 };

// Column to drop
p = 2;

dm = dummy(x,v);
dm_dn = dummydn(x,v,p);


The code above produces four dummies based upon the breakpoints in the vector v:

x <= 1
1 < x <= 5 // Since p = 2, this column is dropped
5 < x <= 7
7 < x


and then remove the p’th column which will result in:

     0 1 0 0           0 0 0       2
0 0 0 1           0 0 1       9
dm = 0 1 0 0   dm_dn = 0 0 0   x = 4
0 0 1 0           0 1 0       7
1 0 0 0           1 0 0       1


## Remarks¶

• This is just like the function dummy(), except that the pth column of the matrix of dummies is dropped. This ensures that the columns of the matrix of dummies do not sum to 1, and so these variables will not be collinear with a vector of ones.

• Missings are deleted before the dummy variables are created.

• All categories are open on the left (i.e., do not contain their left boundaries) and all but the highest are closed on the right (i.e., do contain their right boundaries). The highest (rightmost) category is unbounded on the right. Thus, only $$K-1$$ breakpoints are required to specify K dummy variables.

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