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Dear Mplus Team, I want to test if a L2Variable moderates a contextual (compostional) effect. For the L2Variable (measured by L1ratings) I use the doubly latent approach, for the contextual effect I use manifest aggregation (sampling ratio = 1, thus there is no sampling error) with grandmean centering. My input is... %within% anom_W by a1 a2a4 (13); mathe ON kft anom_W;! kft with anom_W; %between% anom_B by a1 a2a4 (13); INT  anom_B xwith kft_cm; mathe ON kft_cm anom_B INT; Would this be correct, or do I have to include the interaction also at Level 1? Thanks Christoph Weber 


what I have forgotten to add: Is it necessary to include "kft_cm with anom_B" at L2? Am I wright that without this command the effects of kft_cm on mathe is only controlled for INT but not for anom_b, because the covariance between latent und manifest variables is set = 0 by default? 


I want to add a second possibiliy using crosslevel interactions. If the effect of kft (groupmean centered) on mathe varies between classes, and anom explains s, then it follows that there are different contextual effects conditional on anom? Is this correct? %within% anom_W by a1 a2a4 (13); s  mathe ON kft; mathe ON anom_W;! kft with anom_W; %between% anom_B by a1 a2a4 (13); mathe ON kft_cm anom_B ; s ON kft_cm anom_B; s with mathe; kft_cm anom_B with kft_cm anom_B ; 


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Sorry, … a new attempt I want to test if a L2Variable (anom) moderates a contextual (kft on L1 and kft_cm on L2) effect. For the L2Variable (measured by L1ratings) I use the doubly latent approach, for the contextual effect I use manifest aggregation. I think that there are two different possibilities A.) Using grandmean centering for kft, thus the L2effect of kft_cm is the contextual effect and xwith command on L2. %within% anom_W by a1 a2a4 (13); mathe ON kft anom_W;! kft with anom_W; %between% anom_B by a1 a2a4 (13); INT  anom_B xwith kft_cm; mathe ON kft_cm anom_B INT; kft_cm with anom_B; B.) Using groupmean centering for kft, thus the contextual effect is b(between) – b(within) and crosslevel interactions. If the effect of kft on mathe varies between classes, and anom explains s, then it follows that there are different contextual effects conditional on anom? %within% anom_W by a1 a2a4 (13); s  mathe ON kft; mathe ON anom_W;! kft with anom_W; %between% anom_B by a1 a2a4 (13); mathe ON kft_cm anom_B ; s ON kft_cm anom_B; s with mathe; kft_cm with anom_B; What approach is suitable? I would appreciate your advice or any references on this topic… Thanks Christoph 


I think both approaches are ok. You can check if the random slope s in alt. B has substantial variation and it if does that approach would be the choice. You may also want to study what the Raudenbush & Bryk book says about the topic of a random slope in conjunction with contextual effects. 


Thanks a lot, I will have a look at R & B. One follow up question: In alt. B I actually estimate 2 crosslevelinteractions (s on kft and Anom). Is it necessary to estimate both, or should I fix S on Kft at 0, because this interaction has a different meaning and is not related to my research question. Christoph 


I would go with what is significant. 


Dear Dr. Muthén, I havn't found much on this topic in R&B. I have thought about this topic and have come to the following conclusion: Contextual effects are a function of L1 and L2Effects, thus a moderator may operate on L1 (approach B) and/or on L2 (approach A). Then it follows that it is necessary to model both interactions in one model? What do you think about this? I really appreciate your advice! christoph 


I would explore both. 

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