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Context:

In this previous question @adhesh asked about the benefits of coding a binary variable zero-one rather than one-two. I realised when I wrote this answer that I had quite a lot to say about the topic of coding and scaling variables in order to maximise interpretation of regression coefficients.

Over the while I've also read a fair bit on Andrew Gelman's blog about the importance of thoughtful scaling of variables for interpretability of regression and other models (e.g., here and here).

Nonetheless, I also routinely read papers and theses in psychology that present regression models, where it seems that little thought has gone into the scaling of variables to maximise ease of interpretation of model coefficients. Often, the presentation of standardised betas is the extent of it. I also see this problem come up when presenting means and standard deviations of psychological variables where the scale chosen makes it difficult to interpret where the sample sits on the variable in absolute terms.

Question:

  • What are the principles of scaling variables to maximise interpretation?
  • Or alternatively, what is a good resource that succinctly outlines the principles of scaling variables for maximising interpretation?
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This is one of the few cases where I disagree with Andrew Gelman; I've heard him talk about this, and read him as well, but I still think that, in most instances, using the original units of a scale is most easily interpretable. At least, I have found it so for myself and my clients. To some extent, this depends on the variables being used, and their familiarity. But, even with newly invented variables (e.g. a scale that the researcher has constructed) I think an interpretation of "for each point increase on X, predicted Y goes up XXX" is pretty clear.

For categorical variables, I find dummy coding much easier to interpret and explain than effect coding, although some of my clients have trouble with the idea of a reference group.

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