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I am running a multiple regression model. Here is my question. I want to create a dummy variable for the following categorical variable

I have 4 categories for education. One is school, high school, college and university

I know the usual way would be to create three dummies with one reference group. However here is my question.

  1. Can I just create ONE dummy variable called university and say my reference is people who do not have university education and run the regression like this?
  2. My second question is an extension on the first question. Can I create just TWO dummy variables out of these 4 variables. Say just college and university. Why or why not?

I am really having a hard time understanding these things, so would love to know about these things in detail.

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  • $\begingroup$ A categorical MR ("Multiple Response") set is easily recoded into the corresponding dichotomous MR set consisting of binary variables. Note that these binary variables are not called dummies, because they represent not mutually exclusive categories. You may use in regression all the binary indicators or any subset of those, depending of what you want to analyse. $\endgroup$
    – ttnphns
    Commented Feb 4, 2021 at 17:10
  • $\begingroup$ Thank you for the quick response. So basically i can run an analysis with just college and university. So any subset of MR can be coded as binary variable and the interpretation is same as a dummy variable? $\endgroup$
    – Ahsan Tech
    Commented Feb 4, 2021 at 17:33

1 Answer 1

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Clearly you can create a single variable coding school, high school, college and university, as that can be done by just integer codes -- say 1, 2, 3, 4 -- and in other ways too, depending on quite what software you are using and what you want to do. Typically it is both possible and desirable to declare such variables to your software as categorical or factor variables. In this case there is also an ordering, which you may want statistical modelling to respect.

Such a variable would not usually (or, in my view, correctly) be described as an indicator or dummy variable, which to me is defined by there being two and only two possible values, most commonly 0 and 1.

Further, you can reduce the data to indicators in various ways: one such is if university (say 4 in the example above) is mapped to 1 and other codes to 0.

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