- [[mixed-effects models centering]] Different ways of centering predictor variables in MLM can produce different intercept and slope estimates, especially when cluster means (country means in our case) correlate highly with the intercepts, and when the data are imbalanced. Different centering schemes have different interpretations: 1. y ~ b0 + b1 x_grand_mean_center (b1: confounds within- [level 1] and between-cluster [level 2] effects) 2. y ~ b0 + b1 x_within_cluster_center (b1: within-cluster effects; no between-cluster effects estimated by this model) 3. y ~ b0 + b1 x_within_cluster_center + b2 cluster_mean_centered (b1: within-cluster effects; b2: between-cluster effects) 4. y ~ b0 + b1 x_grand_mean_center + b2 cluster_mean_centered (b1: within-cluster effects; b2: between-cluster minus within-cluster effects, aka "contextual effects" e.g., what happens if participant z moves from to a country that's 1 unit higher in the predictor) Also, the interpretations for models 1 and 4 are the same if we use b1 x_raw_score in models instead of b1 x_grand_mean_center. ![[s20220412_221642.png]]