Coding Categorical Variables in Regression: Indicator or Dummy Variables. Professor George S. Easton
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1 Coding Categorical Variables in Regression: Indicator or Dummy Variables Professor George S. Easton
2 DataScienceSource.com This video is embedded on the following web page at DataScienceSource.com: DataScienceSource.com/DummyVariables On that page you will find links to a copy of these slides as well as links to the code file used in the video. It is best to start from that page! (c) 2016 George S. Easton 1
3 Introduction Indicator or dummy variables are regression X variables that take on only the values 0 and 1. Dummy variables are use to indicate the presence or absence of something. Examples: Own a dog. Is college educated. Is a male. (c) 2016 George S. Easton 2
4 Introduction (con d) It is very natural to use a dummy variable to represent a binary x-variable in a regression. For example, we can code gender using Female = 0 and Male = 1. But we can also use dummy variables to code more than two categories. (c) 2016 George S. Easton 3
5 Reminder - Terminology Quite a few different terms are used to describe variables that have categories (like defective or good, spam or ham, or grades A, B, C, D, F): Categorical variable Nominal variable Attribute variable Ordinal variable (ordered categorical) (c) 2016 George S. Easton 4
6 Note: The development that follows is about using dummy variables to represent a categorical variable as an explanatory variable in regression. That is, it is about coding a categorical variable as an x-variable in a regression (LS or logistic). This is not about Y-variables. (c) 2016 George S. Easton 5
7 Multiple Categories To represent a categorical variable with multiple categories, we will need multiple dummy variables one fewer than the number of categories. Example: If we have four categories ( red, blue, green, and yellow ), we will need three dummy variables. (c) 2016 George S. Easton 6
8 Multiple Categories We will need to select one of the categories as a base case. For example, we might select yellow as the base case. The three dummy variables will then be used to indicate the presence of the other colors. Absent other considerations, I usually select the most frequent case as the base case. (c) 2016 George S. Easton 7
9 Multiple Categories D1 = 1 if color is red, 0 otherwise D2 = 1 if color is blue, 0 otherwise D3 = 1 if color is green, 0 otherwise. (c) 2016 George S. Easton 8
10 Multiple Categories The following table shows how the dummy variables will encode the four categories: Case D1 D2 D3 Red Blue Green Yellow (c) 2016 George S. Easton 9
11 Multiple Categories We will then use the variables D1, D2, and D3 as X-variables in our regression to encode the four color categories. Note that the base case (yellow) correspond to all of the dummy variables taking on a value of 0. Note that this approach requires that the regression be run with an intercept term. (c) 2016 George S. Easton 10
12 Understanding Dummy Variables To really understand the effects of dummy variables, you need to understand their effects on the regression equations. (c) 2016 George S. Easton 11
13 Indicator Variable 2 Categories Y X I Model: Reference Group: When Indicator Variable is 0: Y X nd Category: When Indicator variable is 1 Y X We have fit 2 parallel lines! X (c) 2016 George S. Easton 12
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15 Indicator Variable 3 Categories Model: Y X I I Reference Group: When Both Indicator Variables are 0: Y X nd Category: When first Indicator variable is 1 and 2 nd is 0. Y X X (c) 2016 George S. Easton 14
16 3 Categories (continued) 3 rd Category: When first Indicator variable is 0 and 2 nd is 1. Y X X β 2 (the coefficient on the 1 st Indicator variable) is the change in the intercept between the first category (the base case) and the second (c) 2016 George S. Easton 15
17 3 Categories (continued) β 3 (the coefficient on the 2nd Indicator variable) is the change in the intercept between the first category (the base case) and the 3 rd category. We have fit 3 parallel lines! (c) 2016 George S. Easton 16
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