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The Question

If I'm drawing up a table that describes some variables -- a data dictionary, say -- and I consider whether a variable is "ordinal", or "nominal", or "interval", or "ratio", I'm said to be thinking about the levels of measurement of that variable. (At least according to intro stats textbooks.) "Levels of measurement" is the category that those words belong to.

In the same way, if I'm thinking about the concepts "yellow" and "blue" and "red", those belong in the category "colors".

But if I'm thinking about whether a variable is dependent (my outcome) or independent (my predictor), what category does that belong to? Being a dependent or independent variable is what kind of thing? Does that status have a commonly used name?

For you Americans out there, I can phrase it in the form of one of those classic SAT questions:

Ordinal is to level of measurement as dependent variable is to _________.

Can anyone fill in the blank?

(Note that I'm not saying that levels of measurement have anything to do with whether a variable is independent or dependent. I'm just using "levels of measurement" as an analogy for "name of category".)

What I (and others) have come up with

My best guess at an answer is type of variable, as in

Q: Which type of variable is 'smoking status'?

A: Oh, 'smoking status' is my independent variable.

But that's too ambiguous, isn't it? People could confuse "variable type" with "level of measurement" or "numeric" or "string" or something.

This was a difficult question to phrase, so while I searched CV for previous answers before I asked, I may well have missed something. In fact I may well have missed an extremely obvious answer to this question (though I checked two textbooks to see how they talk about this topic and neither gave a category or kind).

EDIT

He may not have intended it, but @whuber has posed a possible answer in the discussion below: he's called it "the role of a variable in a regression model" (my emphasis). That's getting a lot warmer, in terms of what I'd been looking for, but it doesn't sound that official. (Maybe it is!) But it's a good one.

logjammin
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    Many sources are discussing elements of Stevens 1946. This comes down to what, if any, group structure you want to preserve with transformations of your variables. – Galen Mar 28 '22 at 01:39
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    See: https://en.wikipedia.org/wiki/Dependent_and_independent_variables – Galen Mar 28 '22 at 01:40
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    This reminds me of Lewis Carroll's (joke) riddle, "why is a raven like a writing desk?" The organizing principle of Stevens' typology (groups of transformations) has absolutely nothing to do with the role of a variable in a regression model (that is, "dependent" vs. "independent"). This makes it very hard to determine what you're trying to ask. – whuber Mar 28 '22 at 01:41
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    Also contrast to: https://en.wikipedia.org/wiki/Independence_(probability_theory) – Galen Mar 28 '22 at 01:44
  • @whuber Thanks, yes, I know -- it was an analogy. I might have said "Volvo" and "type of car" just as easily. – logjammin Mar 28 '22 at 01:44
  • @DifferentialCovariance thanks, but Stevens doesn't mention dependent or independent. (Though this is an extremely cool old paper, thanks for referring to it.) Also, the wikipedia for ind/dep variables does not name a category they belong to. – logjammin Mar 28 '22 at 01:45
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    logjammin Indeed, which is why I agree with @whuber that it isn't clear what is being asked by comparing these two topics. – Galen Mar 28 '22 at 01:46
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    One way to fill in the blank is that a dependent variable is a 'variable'. But I suspect you are not looking for something that obvious. – Galen Mar 28 '22 at 01:49
  • I'm not comparing them directly at all. I know they have nothing to do with each other. I just chose "measurement level" as an analogy because this is a stats website, but it didn't need to be that. The SAT question could easily be "Yellow is to color as dependent variable is to _____" – logjammin Mar 28 '22 at 01:49
  • @DifferentialCovariance yeah that's getting warmer -- seriously! They're "variable types", of course, but what type of type? If I just call those words "types of variable" people are liable to go "oh, like measurement levels?" – logjammin Mar 28 '22 at 01:50
  • Let us continue this discussion in chat. – logjammin Mar 28 '22 at 01:59
  • "Official"?? – Alexis Mar 30 '22 at 15:32

1 Answers1

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If you want to split variables into 'roles' you might get some joy out of categorizing them as 'observed' vs 'unobserved' plus mentioning their position in a DAG describing your study setup. Discussed in depth in https://xcelab.net/rm/statistical-rethinking/

There's not really a right or wrong with terminology/categorization because the 'right' answer is whatever is most convenient for your purpose! But this is one way. And I do think this language is convenient for describing why dependent and independent variables are usefully distinct, while also extending very naturally to inference in observational studies where the experimental language doesn't apply. It also naturally handles situations were there might be occasional NA gaps in any of the variables, forcing you to do inference over them regardless of their 'role', which is totally a thing that happens sometimes.

steveLangsford
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  • This is a neat line of thought -- thanks!. I've admired McElreath from a distance for a while now, and have him on the top of my list for "people to read when I try and get into Bayesian stats", so I'm eager to take a look at this. But ultimately my question wasn't about splitting variables into roles, nor about right or wrong; it was just about whether there's a commonly accepted name for a certain category of thing. Trying to cover my bases for a table I'm making in a study. If there isn't such a name, I'll feel better about making up my own at the top of my Data Dictionary. – logjammin Mar 28 '22 at 03:56
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    While observable vs latent variables is a worthwhile distinction, it is not clear how it relates to a general class for which dependent variables are a member as asked for in the question. Dependent vs independent variables is a logically independent distinction from observable vs latent variables. – Galen Mar 28 '22 at 04:46