Is the sum of a number of ordinal variables still ordinal?

I have performed a survey where I have a number of questions which can be answered Strongly Agree, Agree etc. to Strongly Disagree. Some of the questions have been designed to measure the same thing.

I have summed these variables to get a ‘score’ for this underlying trait, and I wish to predict this score in a regression

My question is then, can I still considered this summed variable an ordinal variable? And therefore should be using an ordinal regression. Or should I consider this now a continuous variable and use a simple regression?

There have been a few questions I have seen that discuss whether agree / disagree variables can be considered ordinal at all, and others which question whether it is ok to sum these kinds of questions, but I have not found one that discusses the properties of the new variable.

Answer

When you say things like 4+1 = 3+2 = 5, — which you must do when you sum the components — you (pretty much unavoidably) assumed they were interval at that time.

[If the components weren’t interval, in general 4+1 $\neq$ 3+2 … so you’d certainly have no business calling both of them “5”.]

If the components were interval when you summed them, their sum is certainly interval.

[People may well disagree with me on this, but I can’t see any basis for saying things like 4+1 = 3+2 = 5 — along with all the similar statements that must be made — unless you have assumed an interval scale. What basis would there be for thinking the summed-category-labels are equivalent outside the assumption that all gaps between adjacent values are equi-distant?]

Don’t take this as an assertion that people should not add scale-items; in general I think it’s a pretty reasonable thing to do. But in any case, once you do it, you shouldn’t be uncomfortable about calling the sum interval-scale; you already went there.

Attribution
Source : Link , Question Author : SamPassmore , Answer Author : Glen_b

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