Dummy Coding

[Page 464]Dummy coding is used when categorical variables (e.g., sex, geographic location, ethnicity) are of interest in prediction. It provides one way of using categorical predictor variables in various kinds of estimation models, such as linear regression. Dummy coding uses only 1s and 0s to convey all the necessary information on group membership. With this kind of coding, the researcher enters a 1 to indicate that a person is a member of a category, and a 0 otherwise.

Dummy codes are a series of numbers assigned to indicate group membership in any mutually exclusive and exhaustive category. Category membership is indicated in one or more columns of 0s and 1s. For example, a researcher could code sex as 1 = female, 0 = male or 1 = male, 0 = female. In this case the researcher would have a column variable indicating status as male or female. In general, with k groups there will be k-1 coded variables. Each of the dummy-coded variables uses 1 degree of freedom, so k groups have k-1 degrees of freedom, just as in analysis of variance (ANOVA). Consider the following example, in which there are four observations within each of the four groups:

For this example we need to create three dummy-coded variables. We will call them d1, d2, and d3. For d1, every observation in Group 1 will be coded as 1 and observations in all other groups will be coded as 0. We will code d2 with 1 if the observation is in Group 2 and zero otherwise. For d3, observations in Group 3 will be coded 1 and zero for the other groups. There is no d4; it is not needed because d1 through d3 have all the information needed to determine which observation is in which group.

Here is how the data look after dummy coding:

Note that every observation in Group 1 has the dummy-coded value of 1 for d1 and 0 for the others. Those in Group 2 have 1 for d2 and 0 otherwise, and for Group 3, d3 equals 1 with 0 for the others. Observations in Group 4 have all 0s on d1, d2, and d3. These three dummy variables contain all the information needed to determine which observations are included in which group. If you are in Group 2, then d2 is equal to 1 while d1 and d3 are 0. The group with all 0s is known as the reference group, which in this example is Group 4.