Have a look at UG ex 9.20 and in particular how Y appears on all 3 levels. This shows that you don't specify random slopes on your highest level ("WS"). Instead, P1-P3 also vary on this highest level - that variation corresponds to your B10-B30.
I think a saw a mistake. Here is a another revision, is it correct?
Variable: Names = WS team y v1 v2; cluster = WS team; ! Level 3: WS; Level 2: team WITHIN = v1 v2 DEFINE: v1xv2 = v1*v2; ANALYSIS: TYPE = THREELEVEL RANDOM MODEL: %WITHIN% P1 | y on v1; ! Rand slpe P2 | y on v2; ! Rand slpe P3 | y on v1xv2; ! Rand slpe
%BETWEEN team% ! Level 2 P1; ! Rand slpe L2 P2; ! Rand slpe L2 P3; ! Rand slpe L2 y with P1 P2 P3; ! covariance betw. random intercept and random slope L2
%BETWEEN WS% ! Level 3 P1; ! Rand slpe L3 P2; ! Rand slpe L3 P3; ! Rand slpe L3 y with P1 P2 P3; ! covariance betw. random intercept and random slope L3
I still have a question about centering: According to Ryu (2015), the centering depends on the Level. „...when the interaction involves two Level 1 variables …grand mean centering is recommended to obtain unbiased estimates for Level 2 model. Cluster mean centering is recommended to obtain unbiased estimates for the Level 1 model.“
a) Can you do different centerings with Mplus (within the same mplus-input) using the command Define: center ? b) Do you know (or do you know a reference) how to center for the level 3 model (grand mean or cluster mean?) if level 1 predictors and their interaction is involved?
Ehri Ryu (2015) The Role of Centering for Interaction of Level 1 Variables in Multilevel Structural Equation Models, Structural Equation Modeling: A Multidisciplinary Journal, 22:4, 617-630, DOI: 10.1080/10705511.2014.936491 Sincerely and thank you
I would revise my question b) Of course for the model on level 3 (highest Level) you can only use grand mean centering. If interactions involves two Level-1-variables (see my model above), Ryu´s (2015) recommendation (for 2-level-models) on how to center can therefore be transferred to 3-level-models, right?
My three-level-model includes two Level-1-variables (v1, v2) an their interaction. I have another questions. Could you please help me with this or give a reference?
a) Interactions (between Level-1-variables) can also have contextual effects, right?
b) Is it possible to test contextual effects for all three variables v1, v2, and their interaction v1Xv2 in one an the same model? So you can test contextual effects between L1 and L2, L2 and L3, and L1 and L3?
c) Would you consider this approach to be correct? „» Level 1-model: y as function of grand-mean-centered (deviation of level 1 score from the grand mean) v1, v2, and the product of these centered variables. „» Level 2-model: intercept as function of group -mean-centered (deviation of level-2 team mean from the level-3 workshop mean) v1, v2, and the product of these centered variables. „» Level 3-model: intercept as function of grand-mean-centered (deviation of level 3-workshop mean from the grand mean) v1, v2 and the product of these centered variables.
Ryu, E. (2015). The role of centering for interaction of level 1 variables in multilevel structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 22:4, 617-630, DOI: 10.1080/10705511.2014.936491 view abstract contact first author