Coding for Nominal Effects

When you enter a column with a nominal modeling type into your model, JMP represents it internally as a set of continuous indicator variables. Each variable assumes only the values –1, 0, and 1. (Note that this coding is one of many ways to use indicator variables to code nominal variables.) If your nominal column has n levels, then n-1 of these indicator variables are needed to represent it. (The need for n-1 indicator variables relates directly to the fact that the main effect associated with the nominal column has n-1 degrees of freedom.) Full details are covered in Nominal Factors in Statistical Details.

Tip: You can view the coding by selecting Save Columns > Save Coding Table from the red-triangle menu for the main report. See Save Coding Table.

Suppose that you have a nominal column with four levels. Take, as an example, the treatment column in the Cholesterol.jmp sample data table. The treatment column has four levels: A, B, Control, and Placebo. Each of the first three levels is represented by an indicator variable. These indicator variables are named treatment[A], treatment[B], and treatment[Control].

The indicator variable for a given level assigns the values 1 to that level, –1 to the last level, and 0 to the remaining levels. Table 3.1 shows the definitions of the treatment[A], treatment[B], and treatment[Control] indicator variables for this example. For example, consider the indicator variable treatment[A]. As shown in Table 3.1, this variable assigns values as follows:

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The value 1 is assigned to rows that have treatment = A

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The value 0 is assigned to rows that have treatment = B or Control

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The value –1 is assigned to rows that have treatment = Placebo

Table 3.1 Illustration of Indicator Variables for treatment in Cholesterol.jmp
Treatment Assigned to Row	treatment[A]	treatment[B]	treatment[Control]
A	1	0	0
B	0	1	0
Control	0	0	1
Placebo	-1	-1	-1

The order of the levels is determined either by the Value Ordering column property, if you have assigned one, or by the default ordering assigned by JMP. The default ordering is typically the numeric sorting order for numbers and the alphanumeric sorting order for character data. However, certain categorical values, such as the names of months, are sorted appropriately by default. For details about value ordering, see Value Ordering in the Using JMP book.

These variables are used to parametrize the model. They do not typically appear in the data table, but the estimated coefficients for these variables are given in the Parameter Estimates and other reports. Although many other codings are possible, this coding has proven to be practical and interpretable.

For information about the coding of ordinal effects, see Ordinal Factors in Statistical Details.