Do I need to center categorical variables?
Centering is not necessary if only the covariate effect is of interest. Centering (and sometimes standardization as well) could be important for the numerical schemes to converge. Centering does not have to be at the mean, and can be any value within the range of the covariate values.
Why do we mean centered variables?
Many researchers use mean centered variables because they believe it’s the thing to do or because reviewers ask them to, without quite understanding why. Mean centering is the act of subtracting a variable’s mean from all observations on that variable in the dataset such that the variable’s new mean is zero.
Why are interactions included in the centering factor?
This is because when the interaction is included the main effects are relevant to when the other predictors are equal to 0. I.e. x1 = 0 or the binary predictor x2 is at its reference 0 level.
What happens when we center a model with or without an interaction term?
This means that if we center predictors, β1 models the same effect in the data in a model with/without interaction term. This is an attractive property to have when one is interested in comparing models with/without interaction term. Substracting the mean from predictors is a special case of adding constants to predictors.
What happens when you center a predictor in an interaction?
Notice that the intercept, x1, and x2 coefficient estimates are now similar regardless of whether the interaction is included. Now, because we’ve centered the predictors, the predictors equal zero at their mean. So, the main effects are estimating approximately the same thing regardless of whether we include the interaction.
Can a variable x and variable w be centered?
So, assume variable X and variable W, and an interaction XW (W = moderator in Haye’s notation): centering X and W will not impact the test or interpretation of the term for XW. It will change what you get for the CONDITIONAL results for X and W, however.