Herb Marsh posted on Thursday, November 08, 2012 - 6:36 pm
In BFLPE multi-countgry studies (eg PISA2007 studies) used two-level model (students & schools) w country as a multiple-groups.
contextual effect is difference in the effects of achievement (Ach) on Academic Self-concept (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 country-to-country 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
Herb Marsh posted on Monday, November 12, 2012 - 11:54 pm
MODEL: %within% MSCW by MSCp1@.659 MSCn2 MSCn3 MSCp4 (1-4); s | mscW on MACH;
%between TIDCLASX7% s; MSCB1 by MSCp1@.659 MSCn2 MSCn3 MSCp4 (1-4); 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 multiple-group (fixed mode) approach is already a two-level 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.
Following Barr’s 2013 recommendations to “keep it maximal”, I am interested in testing a moderation model with multiple random effects as below.
%within% S1| Y on X1; S2| Y on X2; S3| Y on X1X2;
I would also like to examine whether the random slope for the interaction is different across two groups and I attempted to do so using a Wald test in a multigroup model, labeling and constraining S3 across the groups. However, I got the error message that random effects can only be labelled in the general model. Given this, would examining the difference between groups as a cross-level interaction accomplish the same goal? i.e., %between% S3 on Z;
I have not seen any examples of a cross-level interaction of an interaction effect, so I kindly request your opinion of this.