Consquences of demeaning an ordinal variable

[Tom Kisters]

I have a discrete variable with a scale from 0 (no issue) - 3 (severe issue). Because what constitutes an issue, is really a quite relative concept (especially when comparing different regions), I am considering demeaning this variable by group. This has two advantages:

1. I would argue that is has a better interpretation, because the variable now signals the difference from the mean by group, which I would argue to be much more informative.
2. The variable is no longer ordinal, but continuous (which in my case is a big advantage because I want to instrument this variable icw a control function).

Are there any downsides to this approach, or am I overlooking something important?
I would be very grateful for an authoritative source on this subject.

[Tom Kisters]

Correction, to the post: 2. The variable is no longer ordinal, but continuous, should be the variable is no longer discrete but continuous.

[Nick Cox]

I wouldn't do this.

#2 is definitely an illusion. You just mapped one set of ordered numbers to another. The fact that you no longer have integers doesn't mean that you have somehow escaped ordinal scale measurement.

#1 is up to you. I can't judge what you find easier to think about but imagining myself as a reader of your work I wouldn't want you to do this on my behalf.

I don't mind seeing the means of ordinal variables as descriptive summaries, but deviations in practice do not seem so helpful as they sometimes are for measured variables. I find it hard to put a finger on why not. If I am told this person is 3 cm taller than the mean of that group, that can be helpful. If I am told this person is 0.42 above the mean of a 0-3 scale, that does not seem to help so much.

Just now, fortuitously, I got a message that a post of mine on taking means of an ordinal variable had been upvoted.

The thread at https://stats.stackexchange.com/ques...dinal-variable shows a range of views.

The topic is prone more to authoritarian statements than to authoritative statements.

A much bigger deal #1 or #2 than either in a Stata context (or for that matter in any other statistical software worth mentioning) is that you can exploit factor variable notation and thinking, which has many advantages in fitting and interpreted models. If you want to treat your graded scales as measured -- which for a scale 0 to 3 seems a big stretch -- you can do that any way.

[Tom Kisters]

Nick Cox Thank you for your answer. You make very good points (also, I was the one who just upvoted your answer haha).

With regard to your first point

#2 is definitely an illusion. You just mapped one set of ordered numbers to another. The fact that you no longer have integers doesn't mean that you have somehow escaped ordinal scale measurement.

I should have written discrete instead of ordinal. Does that change anything?

I would prefer to not treat is as a discrete ordinal variable because I need the residuals from a regression where this variable is the dependent variable (this is because I want to instrument this variable into a non-linear second stage, which required a control function and hence residuals, which.an ordinal regression does not naturally have).

[Nick Cox]

Any upvotes on CV are welcome, so thanks for the thanks.

If the mean of a variable with values 3 2 1 0 is 2.34 then possible deviation values are just 0.66, -0.34, -1.34, -2.34. That's still a discrete scale to me. I tend to think graphically (so geometrically) and to me the transformation is like changing axis labels on a graph. What you (or anybody else) can now see has changed but what underlies that has not changed fundamentally.

However, if any mean is calculated for a subset, and other subsets have 4 different possible values, then the question is does that help or not?

Wanting to demean a prediction because you need residuals for something else explains a detail I ignored in answering #1. I was focusing on a variable as an outcome or more likely predictor. As soon as you start talking about instrumental variables and control functions I can't advise, but it seems to me that you have no choice in doing a slightly dubious thing but you want our blessing in doing it. The point is perhaps pragmatic, namely how well does it work?

[Tom Kisters]

Nick Cox

However, if any mean is calculated for a subset, and other subsets have 4 different possible values, then the question is does that help or not?

Just to provide some more information. I have 23,000 observations. Because the group means are relatively continuous (400 groups), the new variable is also relatively continuous.

What do you mean exactly with "how well does it work"? Is this a general question in relation to the concept of demeaning, or specifically related to my data (in which case the answer is: really well).

With regard to:

but you want our blessing in doing it

I have to honestly answer, yes, this is exactly the case.

But I do really believe that with respect to my case, the interpretation of my variable actually improves (and it appears to me that this interpretation remains valid for what I want to do with the IV).

[Nick Cox]

How well does it work? is not a question I can answer because it is a question for you. Does the analysis help in understanding your data given your research goals? Anyone criticising your work as invalid in principle would have a stronger argument if they explained what you should do instead.

[Tom Kisters]

Nick Cox Noted. Thank you very much for your time and patience!