Qualitative and Dummy Variables in Regression Modeling
- Handle qualitative independent variables with a quantitative proxy or use a dummy variable.
- When using a dummy independent variables (such as assigning a number to the degree of consumer confidence), define a collectively exhaustive set of “j” categories, then j-1 (“j minus one”) will give you the number of dummy variables for inclusion in your model.
- Models with dummy independents can easily be misspecified.
Model types with qualitative dependent variables
- Probit models – based on a normal distribution and attempt to estimate the probability that the dependent variable will equal 1.
- Logit models – based on the logistic distribution and like Probit models, they attempt to estimate the probability that the dependent variable will equal 1.
- Discriminant Analysis – creates a score and if the score crosses a threshold then the dependent variable is assigned a 1.
Looking at the big picture, you want your multiple regression model to:
- Have a good theoretical basis and;
- Pass the most stringent statistical tests (refer back to the sub-section “Assumption Violations”).
