Modeling on the original or log scale

Shravan writes,

Here is a typical problem I keep running into. I’m analyzing eyetracking data of the sort you have already seen in the polarity paper. Specifically, I am analyzing re-reading times at a particular word as a function of some experimental conditions that I will call c1 and c2. I expect an effect of c1 and c2, and an interaction. I get it when I analyze on raw reading times (milliseconds) but get only the interaction when I analyze on the log RTs. The logs’ residuals are normally distributed and the raw RTs’ are not. I am inclined to trust the log RTs more because of the normal residuals (theory, however, is more in line with raw RT-based results). But reviewers keep insisting I analyze on untransformed (raw) reading times, and your book also advises the reader to ignore residuals.

My reply:

1. The log scale makes more sense to me. On the other hand, the last time I analyzed eye-tracking data was 17 years ago, and I didn’t know anything about the experimental setup even then!

2. If an interaction might be important, I’d include it in the model. Then if its coefficient isn’t statistically significant, you can say that.

3. Hey, we do look at residuals in our book! Take a look at Chapter 5.

4. I wouldn’t pick the model based on normality of the residuals. As we discuss in the book, the distribution of the residuals is the least important aspect of the model.

3 thoughts on “Modeling on the original or log scale

  1. Easy. If you are worries about which model to use, do both and look at the Bayes Factors, AIC, BIC or marginal likelihoods. If you really want to get crude, you can look at the R-squared for each model.

  2. The log scale often makes sense, but an interaction in log scales is not the same as an interaction in raw scales. If the effect of A and B is multiplicative (i.e., both factors A and B produce a proportional increase/decrease in Y) rather than additive (adding/substracting a constant) then their effects in log scale will be parallel.

    If the interactions you are interested in are additive ones then the reviewers may merely pointing out that the effects of A and B may be superadditive even if their effects on a log scale are parallel.

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