Suppose you are conducting a logistic regression including two continuous predictors. The first predictor does not contain intrinsically meaningful units (i.e., no meaningful 0). The second predictor does have intrinsically meaningful units and a meaningful 0 (i.e., dollars). You want to examine the simple effects of each predictor and also the interaction effect.
Should you center the first predictor? Both predictors? Leave both in raw units?
Thanks,
BT
I am attaching one of the most confusing papers that I have ever seen. This whole topic has been a bone of contention since at least the introduction of ridge regression see the second attachment. If anyone can clarify the situation I would be most pleased to see it. Best wishes to all, David Booth
Jochen Wilhelm
That is definitely the case here. The variable "dollars" displays a large positive skew. Would it be wise to log-transform the "dollars" data rather than centering?
It always gives me pause when I do not completely agree with the advice Jochen Wilhelm
posts. But on this occasion, I would (at least for now) give slightly different advice.Jochen said one should center the two continuous variables that interact, because this will reduce multicollinearity. I agree that it will reduce multicollinearity. But I also agree with Paul Allison who said that multicollinearity of this type (usually) does not matter. See point #2 in this blog:
- https://statisticalhorizons.com/multicollinearity/
But to be fair, and to explain why I said usually, notice that Allison also said centering is sometimes being necessary if/when computational problems arise.
- https://statisticalhorizons.com/multicollinearity/#comment-745
But absent those types of computational problems, I prefer to not center the variables. Why? Suppose I want to use a margins command to estimate (and plot) fitted values of Y at selected combinations of X1 and X2. If I use centered variables, I have to translate those values from original scale to centered scale, and that introduces a possible source of error that I can easily avoid by using the original variables. YMMV.
So, my advice (until Jochen convinces me to change it, at least) is to center the variables only if there are numerical/computational problems that make it necessary. ;-)
Bruce Weaver Interesting take. While the overall model fit (variance explained) and the interaction term estimate/significance do not change whether predictors are centered or not, the simple effects of each predictor do (because the inclusion of an interaction term will change the estimates of individual predictors). For instance, I've analyzed data where a predictor was not significantly associated with the DV when kept in raw units. However, the same predictor was statistically significant when centered. (I can share the data file if you'd like).
Thus, perhaps it could be argued that if you're interested in the effect of individual predictors, you should center. If, however, you are not interested in effects of individual predictors, there is no need to center.
Hi Jochen Wilhelm
. If you are interested in the interaction exclusively, I would argue that there is no need to center the variables. In the model Y = b0 + b1X1 + b2X2 + b3X1X2 + error, you can center X1 and X2 on any values you choose, and it will have no effect on b3 and its SE. E.g., in the attached (text) file, I centered X1 and X2 on their sample means, on their minima, their maxima, and on randomly generated values. And in each model, b3 and its SE were exactly the same. There is a technical term to describe this constancy of the coefficient & SE for the highest order interaction term, but it escapes me right now. Perhaps someone can remind me.Cheers,
Bruce
EDIT. PS - Of course, I mean there is no need to center (when one is exclusively interested in the interaction) provided there are no numerical/computational problems of the sort Paul Allison discussed.
https://statisticalhorizons.com/multicollinearity/#comment-745
And of course, there is certainly no harm in centering on the X1 and X2 means (or some other convenient values) to eliminate the possibility of numerical problems. So in a case like Jochen described, it is arguably a good idea to routinely center X1 and X2.
Look at that, Jochen. I started off appearing to disagree with you somewhat, and talked my way around to agreeing with you! All is well again! ;-)
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