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Colleagues/moderators, let me bring you attention to the tag . Questions labeled with it show multiple understandings of the term.

Some of the understandings are really special at all (such as indicators as "items loaded in a factor analysis"), but two-three most frequent (seen not only locally but in "literature" at wide) are:

  1. Indicator variable is any binary variable (1 = "present" or "this category"; 0 = "absent" or "not this category").
  2. A narrower definition, indicator variable is just a dummy (aka one-hot) variable, i.e. one of the binary variables constituting the binary set corresponding to a single nominal variable.
  3. Indicator variable is a term wider than for binary coding scheme and is a synonym of contrast variable (i.e. deviation or Helmert codings are also "indicator").

See this and some other threads. My own vote oscillates between definitions (1) and (2), but not with (3).

What is your understanding? What should we do with tag indicator-variables in general? Should it be kept?

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  • $\begingroup$ We seem to have a tag for dummy-variables already which maps onto categorical-data. As far as your three meanings go on a statistics site I go for 2, in mathematics more generally for 1 and 3 seems a non-starter. $\endgroup$ – mdewey Mar 4 '17 at 14:40
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    $\begingroup$ @mdewey Given that "indicator variable" is more or less the same as "dummy variable" (Scortchi in the linked thread argues that the latter is more general, but still, these are very related terms), it is weird that dummy-variables is a synonym of categorical-data, whereas indicator-variable is left alone. I'd say it's inconsistent. I am not sure that dummy-variables -> categorical-data is a good synonym. It seems it was made by whuber back in 2011 but by now there are almost 2k questions in categorical-data so it might makes sense not to lump too much there. $\endgroup$ – amoeba says Reinstate Monica Mar 4 '17 at 22:53
  • $\begingroup$ I would recommend to equate indicator = dummy, as in many ANOVA/general linear model sources. (E.g. "Indicator variable approach" is a overparamerized style to solve general linear model equation). $\endgroup$ – ttnphns Mar 5 '17 at 7:54
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In the meantime, this was extensively discussed in the answers and comments in Tags around categorical data coding / representation and the outcome was as follows:

  1. Master tag has been created, and has the following three synonyms: [dummy-variables], [indicator-variables], and [one-hot]. It currently has 67 threads. Wiki excerpt:

    Representing categorical variables as sets of numerical variables. Necessary in many types of analysis for them to process categorical data. A common example is using a categorical predictor in regression/ANOVA via dummy coding, effect coding, Helmert coding, user-defined contrasts, etc.

  2. New tag was created for mathematical or notational questions about indicator function, that have nothing to do with encoding categorical variables. It currently has 16 threads. Wiki excerpt:

    A function defined on a set indicating membership in a subset and taking values 0 and 1.

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