

Multilevel model + multiple groups 

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Herb Marsh posted on Thursday, November 08, 2012  6:36 pm



In BFLPE multicountgry studies (eg PISA2007 studies) used twolevel model (students & schools) w country as a multiplegroups. contextual effect is difference in the effects of achievement (Ach) on Academic Selfconcept (ASC) for L2 (school ) and L1 (student ), defined with model constraints. along w complete/partial invariance of factor loadings . I want to treat country as L3 (random effects) rather than a multiple group (fixed effect). At least initially, all I want is the L3 variance components  the extent to which the contextual effects at L2 vary for different countries. This is easy to do in a MLwiN/HLM framework w manifest vars, but I want latent vars. I cannot see how to get simple estimates of countrytocountry variation in L2 estimates in an Mplus framework (further complicated as contextual effect estimate derived in model constraint) Eventually, I will want estimates (& CIs) for each countries and some country L3 covariates. I tried %within% ... s  mscW on MAchP1W; %between TIDCLASX7% ... SS  mscB1 on MAchP1B1;! %between IDCNTRX3% s; ss; but got: ** ERROR in MODEL command The following random slope is not allowed for TYPE=THREELEVEL. Problem with: SS  MSCB1 ON MACHP1B1 


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Herb Marsh posted on Monday, November 12, 2012  11:54 pm



MODEL: %within% MSCW by MSCp1@.659 MSCn2 MSCn3 MSCp4 (14); s  mscW on MACH; %between TIDCLASX7% s; MSCB1 by MSCp1@.659 MSCn2 MSCn3 MSCp4 (14); SS  mscB1 on MACHl2; %between IDCNTRX3% s; ss; OUTPUT: In this model there is significant variation in SS (i.e., the mscB1 on MACHl2 regression) across the Level3 groups. How do I save or plot the values of this regression for each group (e.g., construct a caterpillar plot) What are the implications of treating the L3 grouping variable (country) as an additional level vs. a grouping variable in a multigroup analysis 


You can request saving factor scores for s and ss. You bring up the classic random versus fixed mode modeling question, where the issue is mainly if the inference is to a population or this particular set of groups. Mplus Version 7 has both of these approaches to analysis of many groups as discussed in our Version 7 videos from the August Utrecht workshops. You are adding an interesting wrinkle to this by considering the choice on level 3, so the multiplegroup (fixed mode) approach is already a twolevel analysis. 


I should add that the random mode approach to the analysis of many groups follows a Bayesian idea of measurement parameters being random variables that come from a common population. Providing references to work by de Jong and Fox, this is discussed in the paper Asparouhov & Muthen (2012). General random effect latent variable modeling: Random subjects, items, contexts, and parameters. which is posted under Technical Appendices for Mplus Version 7. 

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