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I am working on a Linear Mixed Effects model. All four predictors are continuous variables. Full model: fm15 = lmer (duration ~ A*B*C+D+ ( 1 | subjects ) + ( 1 |words), data=data, REML= FALSE)

I have two questions: a) Should I center the predictors? If so, which way should I use to center it? Why are the results different using different centering methods?

In my case the continuous variables do not contain a significant value of 0. I tried to center the predictors by subtracting the mean and subtracting the min. However, after reducing the model by removing non-significant terms, I got two outputs:

Subtracting the mean:

fm16 = lmer (duration ~ A+B+C+D+AC+ ( 1 | subjects ) + ( 1 |words), data=data, REML= FALSE)

Output:

enter image description here

Subtracting the min:

fm16 = lmer (duration ~ A+B+C+D+AB+BC+ABC ( 1 | subjects ) + ( 1 |words), data=data, REML= FALSE)

Output:

enter image description here

The terms in red are significant.

My second question is how to interpret the output? Such as output containing two-way and three-way interactions?

Many thanks in advance

Ann Li
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  • Does this answer your question? Mean centering interaction terms Centering a predictor involved in an interaction changes the coefficients for the lower-level coefficients of the predictors with which it interacts. The underlying model is the same, however. It's typically not helpful to interpret low-level coefficients of predictors involved in interactions without specifying particular values for other predictors. – EdM May 17 '22 at 11:39
  • @EdM Thank you very much! It answers my first question! Do you have any suggestions for my second question, please? – Ann Li May 17 '22 at 13:06
  • Try this answer and its related links about interpreting interaction coefficients up to 3-way. There are other similar Q&A on this site. An interaction coefficient is an extra difference when all of the corresponding interacting predictors are non-zero. Try writing out the full equation in terms of coefficients for predictors and their interactions, recognizing that an "interaction" is just a product of predictor values. Principles are the same for all types of linear modeling, including mixed models and generalized linear models. – EdM May 17 '22 at 17:24

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