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With self-reported health scores (as a dependent variable) - such as CES-D for depression which typically ranges from 0 to 60, I was wondering whether log-transforming these scores would allow me to interpret their coefficient as a % change.

My point is that although these scores provide valuable information, it is often unclear what "12 CES-D points" of change would practically mean. In addition, since they are not interval variables, often scores tend to be concentrated within particular range.

Conversely, I thought that log-transforming these dependent variables would allow me to partially flatten their distribution and - more importantly - interpret their change more intuitively. For instance, while it is unclear what 7 point CES-D decrease would mean, 10% decrease in CES-D score can perhaps be construed as similar decrease in their depression symptom.

I believe there are few articles tackling with these transformation issues, but it seems that there no apparent reason not to perform analysis this way.

Any ideas?!

HYL
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  • If it's unclear what a score means, why would it be any clearer what its logarithm means? There are ways to assign numbers to ordinal variables like scores, but they require you to associate the scores with other values in order to accomplish that. There is a huge literature on identifying useful transformations of data. A good place to start is the older literature on exploratory data analysis going back to Tukey's 1977 book EDA. – whuber Mar 31 '22 at 03:03
  • Hi @Whuber. Would love to hear you comment more on some of the methods you know for transforming ordinal variables into continuous scores. I know of a few such as 'ridit scoring' or perhaps estimating a latent continuous variable. But, if you know this area well, would love to hear some further suggestions – EB3112 Mar 31 '22 at 06:56
  • A good search keyword is ordinal regression.. A completely different line of attack is exemplified by "multi-attribute valuation theory," or MAVT. See https://stats.stackexchange.com/a/9361/919 for a quick summary of the latter. – whuber Mar 31 '22 at 13:21

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