Hi everyone,
I am conducting multilevel analyses in Mplus with students (L1) nested in classrooms (L2). I have several predictors at L1 and L2 that predict individual behavior. The output gives me the results for the within and between model. I am wondering now, whether Mplus aggregates automatically my outcome variable for the between model at L2 or whether my L2 variables are predicting individual behavior as my predictors at L1 do.
I thought this is an easy question but I got from colleagues contradicting answers. That’s why I am hoping to get this clarified here.
best wishes,
Sebastian
If you could post your Mplus syntax file that would help. Otherwise, it's impossible to know what specific multilevel model you are estimating.
Thanks for taking the time to look at this!
My L2 predictors are aggregated at the classroom level (L2).
SYNTAX
CLUSTER = DCO_s;
WITHIN ARE
ZEMP ZMDE ZSPB ZSAS DDC_s sex_bi DMB_s_b NZDFA_s ;
BETWEEN ARE
cpf_c RPP_C Grade_7 Grade_8 Grade_9
CIF_C RPT_C RIA_C RIP_C ;
DEFINE:
COUNS = MEAN (RIA_s_1 RIA_s_2 RIA_s_3 RIA_s_4 RIA_s_5);
REIN = MEAN (RIP_s_1 RIP_s_2 RIP_s_3);
CENTER ZSPB ZEMP ZMDE (GROUPMEAN);
CENTER Cpf_c CIF_C RPP_C RPT_C (GRANDMEAN);
ANALYSIS:
TYPE = TWOLEVEL;
MODEL:
%WITHIN%
COUNS REIN ON ZSPB ZSAS ZEMP ZMDE sex_bi DMB_s_b NZDFA_s DDC_s
%BETWEEN%
COUNS REIN ON cpf_c CIF_C RPT_C RPP_C Grade_7 Grade_8 Grade_9 ;
OUTPUT:
STDYX; SAMPSTAT;
What you are predicting in your model at Level 2 are the random intercepts of the two Level-1 regressions (one regression equation for COUNS and one for REIN). That is, the model allows you to account for variability in the Level-1 intercepts across classes by regressing those intercepts on Level-2 predictors. So you are not explaining variability in individual scores on Level 2 but rather variability in the Level-1 intercepts. In terms of equations, it would look like this for a single outcome variable:
Level 1: Y = b0 + b1*X1 + ... + e
Level 2: b0 = g0 + g1*W1 + ... + u
where Y is the outcome variable, b0 is the random intercept, b1, g0 and g1 are fixed effects (constants), X1 is a Level-1 predictor, W1 is a Level-2 predictor, and e and u are error terms.
Again, thank you so much. I have your book but wasn’t able to answer this question.
you wrote: So you are not explaining variability in individual scores on Level 2 but rather variability in the Level-1 intercepts.
but what practical meaning does this have? Do I predict at L2 variability of COUNS and REIN between classes?
I am confused because Mplus reports R2 between and within for the outcome variables and that’s why I thought that Mplus aggregates my outcome variables.
I am really new to multilevel so I need to translate it into to the statement I can make to understand it better.
The implication of this model is that there is variability in the Level-1 intercepts across school classes and that this variability may be explained (in part) by Level-2 predictors. Whether this does or does not have a practical meaning depends on your research question(s). You should think about what it is that you are trying to find out and then choose your model specification accordingly.
As an aside, I should have mentioned in my earlier post that you can of course insert what you have for b0 in the Level-2 equation into the Level-1 equation:
Level 1: Y = b0 + b1*X1 + ... + e
Level 2: b0 = g0 + g1*W1 + ... + u
Combined equation: Y = g0 + g1*W1 + ... + u + b1*X1 + ... + e
In that sense, the Level-2 predictors do predict your individual outcome scores in this model.
The Mplus R^2 for Level 2 reflects the proportion of variability in the intercepts that is accounted for by the Level-2 predictors.
Hi Sebastian, what is your research question? The stats guru of my PhD program taught me that using HLM at L2 you can only predict group means of L1 variables (granted, this was quite a few years ago). Intuitively this made a whole lot of sense to me.
I am not sure what the research question would be for a model that predicts L1 intercept variability (random effect) with L2 variables...
Hi Lars,
Thanks for your comment. Christian already answered my question. I was trying to understand whether my L2 variable predicts my outcome at L2 or L1 if I don't add any specific syntax in Mplus. There are many research questions that come into my mind... For example, in one study I conducted a 2-1-1 multilevel mediation model. More specifically, I investigated whether average classroom climate is associated with individual counter speech via individual self-efficacy. In bullying research there are also many interesting questions where you predict individual behavior by context variables (e.g., at classroom level).
- Badges
- Science topic
- Similar topics
- Filing