Hi,

If standard mixed-effect packages don't handle multiple responses, you can consider 'mcglm' or 'MCMCglmm' approaches or restructure your data for separate models.

That's merely my perspective.

Hi Ádám Fehér In theory this is possible using standard approach. This then falls under the term MvGLMM or multivariate generalized linear mixed model (e.g., https://www.routledge.com/Multivariate-Generalized-Linear-Mixed-Models-Using-R/Berridge-Crouchley/p/book/9781439813263 or https://quantpsych.net/stats_modeling/multivariate-general-linear-models.html#reasons-to-use-multivariate-glms) or MANVO. Brms and MCMCglmm can do so the question becomes, is this really what you want ???Article MANOVA: A Procedure Whose Time Has Passed?

The hierarchial structure of your data can be nicely modelled using glmmTMB or otherwise. Often multiple response variables are quite a condrum considering the underlying relation cannot be easily adressed and considering you pontentially will try an x combination of responses so you eventually end up with a postive result. Thereby leaving out your "failures" and fall to a "winners curse".

It would be more elegant and straight forward to present a good explanation of what response you would expect to observe and which mechnismn would be responsible for that so that the theory of your treatment aligns with the question you ask. "Dumping" all responses on one pile so that some average estimate is "significant" without reasonable interpretation removes the informatative interpretation the model returns for you (and others) and effort you put in the sample design.

Best,

P.S. Lots of people (including me) build such models, perhaps more forcingly so. However, I recieve no joy or meaningfull interpretation from it perse. So, the question is a bit of how such models than contribute to the community.

Wim Kaijser Yes, absolutely, these things also came into my mind when I tried to find the ideal model design. The thing is, that the samples I've tried to visualize in the attached figure are soil samples measured with a multifunctional tool that can provide data about the main nutrient content of the samples. That was why I tried to keep myself to the "oldschool" MANOVA, but its true that many response vars will fall out due to multicollinearity as well.

Previously I started to build this up using this "toy example" : https://stats.stackexchange.com/questions/468506/using-and-interpreting-nested-manova-in-r

But I also realized that these complex structures can give a headache when we need to come up with a straightforward interpretation. (It wasnt an issue us so far because it wasn't a multilevel structure.)

I also like glmmTMB and will check those potential solutions too that you mentioned.

Really appreciate your detailed help and effort!

Best,

Ádám Fehér I would like to second Wim Kaijser 's answer about the use of multivariate analyses. In my research area, psychology, it is very seldom that you have a truly multivariate question. Therefore, it does not make sense to do a multivariate analysis. Nevertheless, I see many MANOVAs, just because you have multiple DVs and your lecturer and textbooks told you to do if you have this situation (and I am pretty sure I was guilty of this behavior, too…). Of course, I cannot tell how it is in your research area.

Just to give two examples from clinical psychology.

1) Imagine you have a treatment (and possible confounders) and you would like to assess the impact of the treatment on several outcome variables, like depression, anxiety, body mass index, checking behavior and some more. Here it does not make any sense imo to do a MAN(C)OVA, since the DVs may be not even correlated with each other, and you cannot tell what the meaning of the artificial variate (DV) will be. It explains the maximum variance between the original DVs, but what does this mean? Typically, you are interested in the treatment effect on each DV separately, i.e. you want to know how the treatment affects each DV, which is an univariate question.

2) Take the example from above, but your DVs are different measures of depression, e.g. measured with different questionnaires, like BDI, PVQ, SCL etc. Now, you may be interested in the treatment effect on depression as such, and you think that an artificial variate representing the “core” of all depression measures gives you the answer. You are not interested in the difference on BDI or SCL itself, just if the treatment affects depression. Here I would say that you have a multivariate question/hypothesis and therefore, a MAN(C)OVA may be appropriate.

As you can see, there is no single answer to your problem. Maybe you want to check Huang (2020) on this topic.

Nevertheless, I also recommend to use the brms package, which allows you for generalized linear mixed models and also multivariate approaches, as well as (truly) non linear models.

Huang, F. L. (2020). MANOVA: A procedure whose time has passed?. Gifted Child Quarterly, 64(1), 56-60.