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Given that much has been written against the change-from-baseline analysis, what would be a principled way to quantify the correlation/association between change scores of 2 ordinal variables? I still see papers performing Spearman correlation analyses on the change scores but I have understood that an ordinal variable minus its baseline value is no longer ordinal (https://discourse.datamethods.org/t/analyzing-change-from-baseline-in-longitudinal-models/1768)

Thank you in advance for any guidance or assistance anyone may have.

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You are right that if you are taking the difference of two ordinal values, that you are implicitly treating them as interval values.

  1. One option is to simply accept that you are treating your data as interval in nature and take the difference of the values in the analysis.

  2. If you want to treat the values as truly ordinal, when you take the difference between two values you can have a result of "greater", "equal", or "less". These would also be ordinal values and could be analyzed accordingly.

  3. Technically, it may be possible to take the difference between two ordinal values, and end up with more than the three results described in 2). For example, you could know that the difference between "agree" and "neutral" is greater than the difference between "strongly agree" and "agree", and then code the results accordingly. But the circumstances where this makes sense are probably few.

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  • $\begingroup$ Thank you for sharing your insight. (1) doesn't strike me as satisfying and (2) will probbaly work if there are only a few levels in the variable. So, I'm wondering if there is a general-purpose model-based approach to tackle this? I understand that for the ordnal response variable, we could fit a model that includes (i) the follow-up ordinal variable as the outcome and (ii) the baseline ordinal variable as the predictor. But I'm not sure how we could incorporate the other ordinal variable into the model. $\endgroup$
    – Yonghao
    Commented Apr 21, 2022 at 5:14
  • $\begingroup$ 2) is the result whenever you take the difference between paired ordinal observation. It doesn't matter how many levels the ordinal variables have. Something like this is implemented in the paired-samples sign test, and in the "probability of superiority" statistic. ... 1) Is pretty common, even with something as coarse as responses from a 5-point Likert-type item. My opinions on this vacillate over time. ... OR: Ordinal regression should be the best approach, but depending on your software, I don't know how it would handle an ordinal independent variable. That's the question. $\endgroup$
    – Sal Mangiafico
    Commented Apr 21, 2022 at 13:16

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