“Dummy variable” versus “indicator variable” for nominal/categorical data

“Dummy variable” and “indicator variable” are labels frequently used terms to describe membership in a category with 0/1 coding; usually 0: Not a member of category, 1: Member of category.

On 11/26/2014 a quick search on scholar.google.com (with enclosing quotes) reveals “dummy variable” is used in about 318,000 articles, and “indicator variable” is used in about 112,000 articles. The term “dummy variable” also has a meaning in non-statistical mathematics of “bound variable” which is likely contributing to the greater use of “dummy variable” in indexed articles.

My topically-linked questions:

  1. Are these terms always synonymous (within statistics)?
  2. Are either of these terms ever acceptably applied to other forms of categorical coding (e.g. effect coding, Helmert coding, etc.)?
  3. What statistical or disciplinary reasons are there to prefer one term over the other?

Answer

I’d say “dummy variable” is a more general way to refer to (one of) the numerical variable(s) that represents (together represent) a categorical predictor; therefore the term applies also to those used in Helmert & effect coding. That’s mainly owing to the general use of “dummy” to mean “stand-in”. “Indicator variable” I relate to indicator functions—so those can only be one or zero to indicate having or not having some property; therefore the term applies only to those used in reference-level coding. Of course some people use “dummy coding” to mean “reference-level coding”; they presumably have a more restricted definition of “dummy variables”, or at any rate ought to have.

† And if you don’t call those “dummies”, what do you call them?

‡ So e.g. the dummy xi is an indicator variable for when the ith person ui is male (a member of set M):
xi=1M(ui)={1when uiM0when uiM

where 1M() is the indicator function for membership of M.

※ Or, as @gung has pointed out, level-means coding.

Attribution
Source : Link , Question Author : Alexis , Answer Author : Scortchi – Reinstate Monica

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