More than two values for a dummy variable (regression)?

[david_q]

How do I deal with the case where I am dealing with more than two values for a dummy variable when doing regression? I know that if there are 2 values for a dummy variable e.g. yes and no then yes is 1 and no is 0. But, how do I deal with more than 2 values for the dummy e.g. what brand of laptop someone uses : Acer, Toshiba, Apple, Dell, HP, Others. Do I put Acer as 1, Toshiba as 2, Apple as 3, Dell as 4, HP as 5 and Others as 6?

[david_q]

please help?

[jrai]

You create n-1 dummy variables where n is the number of levels of the categorical variable. So for your example, you'll have 5 dummy variables. Depending on the interpretation you can use different coding schemes. Here is a very good discussion on them: http://www.ats.ucla.edu/stat/sas/web...r5/sasreg5.htm

Another way is to just keep single variable & use proportions for categories or probit function generated inverse of proportions.

[david_q]

wait i don't understand. why should i have (n-1) variables instead of (n/2)?

[david_q]

*(n/2) rounded up

[jrai]

Ok, here is the exercise for you. Explain how will you denote 6 categories of your example with 3 dummies.

[david_q]

Sure.

variable a: 0 if Acer, 1 if Toshiba.
variable b: 0 if Apple, 1 if Dell
variable c: 0 if HP, 1 if Others

so x = A a + B b + C c

capitals: constants to be determined by regression.

[Dason]

Ok. Now if you want to denote that a computer is an Apple what will your three variables look like? (0, 0, 0). If you want to denote that a computer is an HP what will your three variables look like? (0, 0, 0).

Do you see the problem?

[david_q]

*sheepish*

[Dason]

Haha. Don't worry. Dummy variables definitely take some getting used to. And note that there using reference coding isn't the only way to create the dummy variables.

[jrai]

Just to add 1 more point. You've used equation: x = A a + B b + C c

Your equation doesn't contain an intercept. When the intercept is missing then you need n dummy variables & not n-1. Intercept acts as a reference category & denotes the excluded category but when you omit intercept then you must include all the categories as dummies.

[Dason]

Good catch. I wasn't paying much attention to that.