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Hi everyone, I am conducting a threelevel model in which students are nested within school nested within countries. My actual interest is on how systemlevel variables (L3) are correlated with variables on studentlevel (L1). However, I cannot neglect the fact that they are clustered within schools. To not ignore the schoollevel, I computed a threelevel model. The model runs perfectly, but the results are not what I would have expected. I consulted a specialist on this and he told me that the result is often observed in case you allow a random intercept at the schoollevel. He suggested to not include the random intercept at the schoollevel. I tried this, but I get an error message. MODEL: %WITHIN% u PV_M_N on ESCS; PV_M_N on lang; escs with lang; %Between school_N% [pv_M_N]; %BETWEEN cnt_n% PV_M_N on AGE_TRA; PV_M_N on HDI_M; U on HDI_M; U on age_tra; output: sampstat standardized; *** ERROR in MODEL command The means of variables allowed above the BETWEEN SCHOOL_N level exist only on the BETWEEN CNT_N level. Variable used: PV_M_N Many thanks in advance, Emilie Franck 


You don't want to say %Between school_N% [pv_M_N]; Instead fix the variance to zero %Between school_N% pv_M_N@0; 


Thank you very much for the quick response. I already read this online but was not sure if in this case the clustering at schoollevel was still taken into account. In this case I have two more questions: 1) If I am not really interested in the level 2 (schoollevel in this case), but I do want to take into account the clustering, should I also put the random slope@0 on that level? Or would you strongly advice not to? 2) what happens with the variance on level 2? One of my colleagues was wondering if the variance would just be 'reflected' in the other levels in case I put the random intercept and/or the random slope@0. Could you advice an article that explains this a bit more  the consequences and to understand it a bit more in depth? Many thanks in advance, Kind Regards, Emilie 


Dear Prof. Muthen, My apologies for my second post. I just have tried out some other steps and have another question on this topic. In the example I dicussed above, I was only interested in the crosslevel correlation between L1 and L3. In a second model I would have analyzed the L2L3 correlation. However, I am trying to fit a full threelevel model with both crosslevel interactions between L1 and L3 and between L2 and L3. My model looks like this: %WITHIN% u PV_M_N on ESCS; PV_M_N on lang; escs with lang; %Between school_N% Y PV_M_N on M_ESCS; %BETWEEN cnt_n% PV_M_N on AGE_TRA; PV_M_N on HDI_M; U on HDI_M; U on age_tra; Y on HDI_M; Y on AGe_tra; HDI_M with age_tra; The problem I am having with this model is that I actually do not want to include another random slope Y. When I run the analysis, I can see that the random slope U has both variance at country and schoollevel. I was wondering if it is possible to use only that 1 random slope U to make crosslevel interactions between both L1L3 and L2L3. I am not sure if this is possible at all. In case it isnt, I might put U@0 in this model Many thanks in advance, Emilie Franck 


If you don't want to estimate the variance of a variable on a certain level, you fix it at zero. But you then have to move the mean to be estimated on the level where the variance is not fixed at zero; otherwise, the algorithm for finding the solution won't work. But if the variance is in fact not zero on a certain level, fixing it at zero leads to a misspecification that can influence many parts of the model. 


Dear Bengt Muthen, Many thanks for your quick response. I had a meeting with some colleagues and their was some discussion about the syntax of our 3level model. The model is: %WITHIN% u PV_M_N on ESCS; %Between school_N% Y PV_M_N on ESCS; %BETWEEN cnt_n% PV_M_N on AGE_TRA; PV_M_N on HDI_M; U on HDI_M; U on age_tra; Y on HDI_M; Y on AGe_tra; We are interested in both crosslevel interactions between Level 1 and Level 3  and Level 2 and Level 3. However, we have some questions about the interpretation and did not find an answer in the users guide. Q1) How should we interpret the results of our L1L3 crosslevel interactions? For instance if we find a negative coefficient between AGE_TRA and U should we then interpret it as " the higher AGE_TRA the lower the correlation between PV_M_N and ESCS? Q2) In case this is true, what should we do with the variance of our random slope U that appears on Level 2? We don't do anything with the variance of random slope U on that level and we were wondering is this changes the interpretation of our crosslevel interaction? Should we fix it at 0 given that we do not use it and given that we Estimate a new random slope Y which reflects (contentwise) exactly the same? We would really appreciate your input on this. Many thanks in advance, Emilie franck 


Q1: Replace "the lower the correlation..." with "the lower the regression slope..." Q2: Check if the L2 variance of u is zero. It is of course up to you, but if Y is much the same thing, then why not use U on L2 rather than Y? 


Dear Bengt Muthen, I really appreciate all your responses. Thank you for Q1. With regards to Q2: that was also what I was trying to figure out  whether or not this is possible in Mplus. How should I do this? Because as far as I understand I need to make a distinction between the random slope U at L1 and the random slope U at level 2 to make crosslevel interactions (L1L3 and L2L3 interactions). Should we rename Random slope U at level 2? Or can we define this in a specific way? Many thanks in advance! Kind Regards, Emilie Franck 


With 3level modeling, Mplus allows random slopes to have random slopes too. See the UG ex 9.22 where s is a random slope that has a random slope ss on level 2. 


Dear Bengt Muthen, many thanks again for the quick reply. I already saw this and tried it out, but I got an error. The model is: %WITHIN% u PV_M_N on ESCS; %Between school_N% Y PV_M_N on U; %BETWEEN cnt_n% PV_M_N on AGE_TRA; PV_M_N on HDI_M; U on HDI_M; U on age_tra; Y on HDI_M; Y on AGe_tra; ERROR: The following random slope is not allowed for TYPE=THREELEVEL or TYPE=CROSSCLASSIFIED. Problem with: Y  PV_M_N ON U However, I saw that in the UG, a different dependent variable at level 2 is used. In case I do want to make it work, should I aggregate the mathematics scores of students (PV_M_N) to schoollevel and use that variable as dependent? Many thanks again for your time, Kind regards, Emilie Franck 


Please send the output with the error to Support so we can better diagnose this. 

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