8.3 Incorporating Categorical Data Into A GLM

How can we do computations on categorical data? How do we plug a categorical variable like gender (male/female) into a mathematical equation? Categorical variables must be converted into one or more indicator variables. An indicator variable is a variable that can take on two values: a zero or a one. A zero indicates the absence of the attribute and a one indicates the presence of the attribute. The number of indicator variables needed for a categorical variable with H levels is H - 1.

• Gender can either be male or female. An indicator variable for gender could be:

  xgender	= 0 if female, and
  xgender	= 1 if male.

• Highest level of education obtained, B.A., M.A., or Ph.D.

  x1	= 1 if M.A, and
  x1	= 0 otherwise
  x2	= 1 if Ph.D, and
  x2	= 0 otherwise

  • If x₁ = x₂ = 0 then the highest level of education obtained must be B.A.
• etc.

The figures ?? and ?? illustrate the importance of utilizing indicator variables when analyzing categorical variables, as opposed to treating categorical variables as continuous variables.

Figure 8.2: Proper handling of categorical data within a general linear model.