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I have multiple items that measure the risk tolerance of a person. The items are measured on different ordinal scales. Now, I would like to combine all these items to one measure. What is the best way to combine the items which are measured with different ordinal scales? As a result, I want only one variable that measures risk tolerance.

Example

  • Item 1 has an ordinal scale from 1 to 3
  • Item 2 has an ordinal scale from 1 to 5

Example of a result from the survey:

  • Item 1 was scored with 2
  • Item 2 was scored with 4

One option: I just sum up the scores so that the resulting score is 6, which I then use in my regression model. Is that a good idea or are there any better options that are not too difficult to understand?

Many thanks in advance :)

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  • $\begingroup$ If you insist that your items are ordinal you cannot sum their scores. $\endgroup$ – ttnphns Sep 30 '20 at 0:22
  • $\begingroup$ What method can I use instead? $\endgroup$ – Jensxy Sep 30 '20 at 7:10
  • $\begingroup$ @ttnphns do you have any suggestions? $\endgroup$ – Jensxy Sep 30 '20 at 12:41
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Optimal procedures may differ depending on how many ordinal variables you have, how widely the number of categories differs from variable to variable, and whether all variables are of equal importance.

The following tentative suggestion may work best for a few variables of equal importance and numbers of categories between 3 and 7. That is, labels $1,2,3$ (fewest) and $1,2,\dots,7$ (most). I offer this suggestion with hope it may give you ideas for an improved version or a better method.

Roughly speaking, the idea is to re-scale all variables so to have lowest label $1$ and highest $7,$ treating variables as if they have interval scales, so that label numbers feel "equally spaced" to respondents. And then "averaging" or taking the median, depending on how comfortable you are with the 'equal spacing' assumption.

In particular, for the specific example in your Question:

  • Item 1 scored 2 on a 3-point scale becomes $(7/3)2 = 4.67.$
  • Item 2 scored 4 on a 5-point scale becomes $(7/5)4 = 5.6.$
  • Composite score is average $5.13$, perhaps rounded down to $5$ on a 7-point scale. This may be about right because the composite of a middle score and a next to highest score is a score slightly above the middle.

Most important, with whatever method you decide to use, look at a few dozen composite scores to see if results seem sensible. [If some scores in the composite are more important than others, you may want to consider weighted averages. Perhaps look most carefully at cases where component scores vary between low and high.]

Note: One could argue that my suggested method is more fair if scales are treated as if they start at 0 (so a 7-point scale runs from 0 to 6, etc.). Then treating scores as if they were ratio-numerical, the computations in the example above would be $(6/2)1 = 3, (6/4)3 = 4.5,$ and composite $3.75,$ which might round up to $5$ on the usual 7-point scale. My (very limited) personal experience is that, when the versions differ, the one described in the main part of my answer works better.

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  • $\begingroup$ Thank you for your comprehensive answer. If I rightly understand, there is not ONE solution. Your suggestions works in one case. In the other case, however, I have items with 2, 4, and 3 numbers of categories, respectively. What would your suggestion in that case? $\endgroup$ – Jensxy Oct 1 '20 at 7:10
  • $\begingroup$ For smaller numbers of categories may the variation of the method suggested in the Note would be better. Unsure what to do for 2 categories, where might not be clear if categories are really 'ordinal'. Never tried combining 2-category scales with others. Not saying it won't work, but you'd have to try it and see if you're comfortable with outcomes. $\endgroup$ – BruceET Oct 1 '20 at 15:40
  • $\begingroup$ Ok, thank you :) Do you have any name of the method or something like that which I can use for the explanation in my thesis? FYI, I am writing my master thesis and want to explain how and why I used this method to combine my items. $\endgroup$ – Jensxy Oct 1 '20 at 20:23
  • $\begingroup$ People in various fields have been working with Likert (and similar) scales for a long time, and there is some controversy whether such scales must be considered 'ordinal categorical' only. Or whether it is OK, in some cases, to treat scale labels is actual numbers (as here). // A few times I have needed to combine scales and I contrived this method to do the job. I'd be astonished if no one has done something similar, so don't claim this as "my" method, but I don't know of references. If you are going to use something like this, make sure it does what you want and explain why in your report. $\endgroup$ – BruceET Oct 1 '20 at 21:03
  • $\begingroup$ Among people who deal with Likert-like scales it is customary to use the "magic" word normalize (even when it makes no sense) for almost any kind of modification, re-scaling, etc. I just Googled normalizing to Likert-7 which fetched more pages (ranging from authoritative to fanciful) than I'd want to read. Maybe some similar search would fetch an article in a respected journal for you to put in your references. $\endgroup$ – BruceET Oct 1 '20 at 21:24

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