I think it make sense to fit the same model for all nine outcomes providing your included predictor variables make theoretical sense in each case.

This may be too challenging but you could fit a four level multivariate model when all the 9 outcomes are modelled simultaneously, so level 4 would be classroom , 3: pupils, 2: the outcome variables and level 1 the occasions which are repeated measures on each of the outcome variables; see http://www.bristol.ac.uk/cmm/software/mlwin/mlwin-resources.html#multipleresp

This model allows you to estimate the correlation between the outcomes and you can evaluate if any predictor variable is differently related to each outcome. If you choose to go down this route it is a good idea to have experience with the non-multivariate mixed model and then work to begin with a pair of outcome variables.

I think you can use some directional distribution (multivariate dierctional models), e.g., Matrix-variate Fisher distribution, Von Misses Fisher distribution, or the most fit Matrix-Variate Bingham density based model, which is Antipodal Symetric distribution. Moreover, you can use Bayesian parameric framework (need normalizing constant to be calculated), or simply you may use Logestic regression technique. Also you may use mixture models via Expectation Maximization techniques. In order to know about directional statistic or Aspects of multivariate statistics, you may follow:

Chapter In Directional Statistics

https://books.google.com.au/books?hl=en&lr=&id=TKVfbEvrgu4C&oi=fnd&pg=PP2&dq=multivariate+statistics+muirhead&ots=4xYrrvCZlQ&sig=ukTWxWljCGfePGPVtp-3FkGbupk#v=onepage&q=multivariate%20statistics%20muirhead&f=false

Thank you for your quick answer.

As i just started with multilevel modeling i think the four level variante is too tricky for now.

I was also thinking calculate two models for each variable:

Model 1:

- intervention-groups, time, interaction between intervention-groups and time

- random intercepts for students and classroom

Model 2:

- intervention-groups, time, interaction between intervention-groups and time

- random intercepts for students and classroom

- add covariates of gender and age

What i found by comparing models with lrtest in STATA is that with some variables a random intercept for classroom generates a better fit and with others it doesn't. With one variable the interaction (time*group) generates a better fit and with another variable it doesn't.

However i guess from a theoretical standpoint it makes sense to include the interaction term and the random intercept for classroom.

Would you say it is necessary to use a third model (or rather first) without the random intercept for classroom?

Thank you again for your quick reply!

David

Why not a logistic model for each of the variables? That seems to be the most logical to me. E.g. x=time spent on mindfulness per week, y=some attention measurement.

I would start with the unconditional model with an intercept and time in the fixed part and both the intercept and the parameter for time allowed to vary between children (that is random slopes and intercepts model). This allows each child to have their own trajectory. The covariance is a crucial term; if it is substantial and positive the differences between children are increasing; negative - the differences are decreasing; if zero: (that is little correlation between differential intercept and differential slope) where the child starts from is unrelated to where they end up. This will give you a good idea of what needs to be 'explained'

You can then put in variables (main effects and then interactions) to see what happens to this unexplained variance, and to compare badness of fit.

This is a thorough slow paced systematic introduction to these models:

https://www.pilesofvariance.com/

Longitudinal Analysis: Modeling Within-Person Fluctuation and Change (by Lesa Hoffman)

I am taking it that you have more than two measurement occasions? Not just before and after the intervention.

Thank you for your help! I really appreciate it.

I only have two measurement occasions. I guess this would allow me to simply add the first measurement as a covariant and run a two-level analysis. Is it a problem to run a three-level-model with only two measurement occasions?

I will go through those articles. I also found a helpful chapter in the book 'linear mixed models: a practical guide using statistical software' by Brady et al. (2015), where they go through model selection with a similar structure.

David

You can estimate a multilevel model with just two repeated observations ; think of twin studies.

However, using the before measure as a predictor variable and the after variable as the outcome simplifies the model, as you say, to a two level model of pupils nested in classrooms. You could then interact the intervention dummy with the before score. You are then modelling change.

This manual has an extended example of a similar set up Chapters 1 to 8

http://www.bristol.ac.uk/cmm/media/software/mlwin/downloads/manuals/3-05/manual-web.pdf

This too has similar modelling

Article Evaluation of the primary schools whiteboard expansion project

Thank you a lot again for your answer. It took me a while to do the analysis.

One of the problems with the data is that there are differences in baseline measurements between the control and intervention groups. Now i ran a two-level model with and without interactions and a three-level-model with interactions.

I added prints of the models and a graph.

Intervention groups: Binja, BTP

Outcome: z_k_socomp_pospeer

The two- and three-level-model appear to account differently for the baseline-differences.

Would you say that the two-level-model is to prefer as the model is simpler?

I think i just realized where the difference lies. The three-way-model includes all the participants with at least one measurement (occasion 1 or 2). The two-level model only includes participants with measurement at occasion 2.