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Categorical (Qualitative) Inputs

Qualitative or Categorical inputs can be used with any of the three types of regression (Ordinary Least Squares, Binary Logistic, and Nominal Logistic).

Quantum XL converts categorical inputs into indicator or dummy variables. Some texts classify this approach as General Linear Model when applied to least squares regression.

The process of converting a categorical input into an indicator variable involves creating N-1 new columns in the X matrix where N is the number of unique categorical levels in the input. For example, if the input Vendor has three levels "ACME", "SZ", and "BP", then N=3 and 2 indicator variables will be used.

Example of how indicator variables are created. In the full factorial example below, the input Vendor is categorical. The X matrix on the right has the two indicators variables (SZ and BP) from the vendor variables.

The process of creating indicator variables is relatively straightforward.

• Step #1: Choose a reference level. One of the levels must be used as a reference level. If you don't specify one, then Quantum XL will choose one by default. In this case, the reference level was automatically chosen as ACME.

• Step #2: Create N-1 indicator variables for every level other than the reference level. In this case, the levels SZ and BP were created.

• Step #3: In each row where the reference level is observed, put a -1 in the indicator variable.

• Step #4: For any occurrence of the non-reference level, place a 1 in the indicator variable.

• Step #5: Fill in remaining terms with zeros.