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I have a multilevel model built coinsidering repeated measures on students. Students performance may vary depending on study hours and tutoring hours before each exam.

Should I center the predictors around their grand mean (sample mean)? Should/can I also center the variable representing the time of measurement?

Is it correct to say that if I center all predictors the intercept represents the performance score of a student who has mean values of predictor? Or does it represent the average performance score of students, when predictors have mean values?

Lastly, is it ok to center both in the case that predictors are continuous and discrete variables?

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You center variables in regression models for interpretive purposes. Your decision to center time varying covariates should depend on the extent to which you care about having the clearest meaning of how a time-varying covariate impacts a measurement occasion. You could argue that you should present the clearest possible model to your readers, but that's really up to you.

How time is reflected in your growth model is important because it can paint a disingenuous picture of what is really going on the an uniformed reader. More importantly, it does drastically impact how you interrupt the results. You should read this article for some guidance.

Good luck.

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