- I am running brms 2.13.1 on MacOS 10.14.6

Hello folks,

I am quite new to brms (and multi-level modelling), so I apologise in advance for any basic and obvious questions. I would like to gain a clearer understanding of the difference between a multivariate model (with correlated grouping variables) and a univariate model (with covariates). Essentially, I want to know how similar (or not) the conclusions / interpretations can be from these different models. Details on the models are as follows.

Multivariate model:

I have a multivariate model with three dependent variables (DVs). More specifically, I have one primary DV (DV1) and two that help qualify the primary DV. As such, some of the DVs (DVs 2 and 3) can also be considered as covariates in a univariate model – see below. I also have some factors and a bunch of human participants. The DVs/predictors are different rating scales (from 1-5) based on evaluating a set of images. I also have a factorial design, such that the images fall into different categories. Below is an example model (it takes hours to build hence why I have not included a reproducible version). I only include one factor below for simplicity. I have a varying intercept for ‘item’ = the image (or stimulus) and a varying intercept and slope for participant, which is treated as a correlated grouping variable. The model is here:

```
brm(mvbind(DV1, DV2, DV3) ~ 1 + factor +
(1 + factor |a| participant) +
(1|item),
data = data, family = cumulative("probit"),
prior = priors,
iter = 6000, warmup = 1000, cores = 4, chains = 4,
control = list(adapt_delta = 0.99, max_treedepth = 15),
init_r = 0.1)
```

Univariate model:

(I understand that the DV2 and 3 are now predictors, but I wanted to keep the same labelling as above)

```
brm(DV1 ~ 1 + DV2 + DV3 + factor +
(1 + DV2 + DV3 + factor | participant) +
(1|item),
data = data, family = cumulative("probit"),
prior = priors,
iter = 6000, warmup = 1000, cores = 4, chains = 4,
control = list(adapt_delta = 0.99),
init_r = 0.1)
```

Questions:

Essentially, the univariate model makes sense as follows: I’d like to know how much the factor influences DV1 with other ratings (DV1 and DV2) in the model as covariates. Then I could compare models with and without these covariates and see how much the factor influences the outcome across the different models.

For the multivariate model, it is not so clear to me. I understand that the influence of the factor is estimated for all DVs separately. And that there is a correlated grouping variable. And if I had to guess, I’d say that I could not make the same conclusion as the univariate model? But is this correct? I guess I’d like to know if both models are needed if one wants to estimate how much the three DVs are influenced by the factor AND how much the factor influences my primary DV (DV1) with other factors in the model?

A further question – if ratings on a scale from 1-5 are included as predictors, what’s the best way to include them? Should they be monotonic? After reading this, I am a little unclear. https://psyarxiv.com/9qkhj/

Any help would be appreciated.

Regards,

Rich