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Dear Bengt and Linda, I wish to run this 3multiple random coefficient modell. Level1 Y = P0 + P1*(v1) + P2*(v2) + P3*(v1*v2) + E Level2 P0 = B00 + R0 P1 = B10 + R1 P2 = B20 + R2 P3 = B30 + R3 Level3 B00 = G000 + U00 B10 = G100 + U10 B20 = G200 + U20 B30 = G300 + U30  ANALYSIS: TYPE = THREELEVEL RANDOM; MODEL: %WITHIN% P1  Y on v1; ! Rand slpe L2 P2  Y on v2; ! Rand slpe L2 P3  Y on v1xv2; ! Random slope for interaction L2 %BETWEEN team%; ! Level 2 Y with P1 P2 P3; !corr betw random slope & random intecept is allowed on L2. %BETWEEN WS%; ! Level 3 B10  Y on v1; ! Rand slpe L3 B20  Y on v2; ! Rand slpe L3 B30  Y on v1xv2; ! Rand slpe for interaction L3 Y with B10 B 20 B30; !corr between random slope & random intecept is allowed on L3 OUTPUT: sampstat tech1 tech2; Is it correct? Are also intercepts random on level 2 and level 3? Sincererly 


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, P1P3 also vary on this highest level  that variation corresponds to your B10B30. 


Thank you very much! Is this revision 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 L2 P2  y on v2; ! Rand slpe L2 P3  y on v1xv2; ! Rand slpe L2 %BETWEEN team% ! Level 2 P1; ! Rand slpe L3 P2; ! Rand slpe L3 P3; ! Rand slpe L3 y with P1 P2 P3; ! covariance betw. random intercept and random slope L2 %BETWEEN WS% ! Level 3 y with P1 P2 P3; ! covariance betw. random intercept and random slope L3 OUTPUT: sampstat tech1 tech2; Sincerely 


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 OUTPUT: sampstat tech1 tech2; Sincerely 


Looks about right except you need 2 cluster variables. Run it and see what you get. 


Thank you. I also ran the model. But I still have a question: Where are 2 cluster variables needed/is this command not enough (see also above)?: cluster = WS team; ! Level 3: WS; Level 2: team 


You are right  that is enough. 


Thank you! 


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 mplusinput) 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, 617630, 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 Level1variables (see my model above), Ryu´s (2015) recommendation (for 2levelmodels) on how to center can therefore be transferred to 3levelmodels, right? 


a) Yes. You can use Define in the same run to grandmean center some variables and groupmean center others. Revised b) That's right. 


Thank you! My threelevelmodel includes two Level1variables (v1, v2) an their interaction. I have another questions. Could you please help me with this or give a reference? a) Interactions (between Level1variables) 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 1model: y as function of grandmeancentered (deviation of level 1 score from the grand mean) v1, v2, and the product of these centered variables. „» Level 2model: intercept as function of group meancentered (deviation of level2 team mean from the level3 workshop mean) v1, v2, and the product of these centered variables. „» Level 3model: intercept as function of grandmeancentered (deviation of level 3workshop mean from the grand mean) v1, v2 and the product of these centered variables. Sincerely 


a) Have a look at 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, 617630, DOI: 10.1080/10705511.2014.936491 view abstract contact first author b) Yes. c) Check the article. 

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