44  Centering Visualization

Author

Josh Gilbert

Centering of predictors is an important issue in multilevel modeling. In contrast to single-level regression, how we center variables can really change the interpretation of the slope coefficients. The three main options are:

  1. No centering: leave \(X\) as it is
  2. Grand mean centering: subtract \(\bar{X}\) from every \(X\) so that a value of 0 represents the grand mean. The slope has the same interpretation, but our estimates of random effects may change.
  3. Group mean centering: subtract \(\bar{X}_j\) from every \(X\) so that a value of 0 represents the cluster mean. The slope now represents the within-group relationship (just like fixed effects) because we have removed all between group variation from \(X\).

The visualization below helps us think about centering and why it matters.