I have data with an outcome measured by four different methods a different timepoints in a group of individuals. One outcome is considered gold standard and so I’m interested in how the other outcomes correlate with it after multivariate modelling.

What I’m confused about is whether or not I should include group level modelling or not, and if I do, how does that change the interpretation of the residual correlation? To illustrate I include two different modesl and output (sorry cannot share the data for reproducible example)

```
fit1 <- brm(
mvbind(outA, outB, outC, outD) ~ centre + days_from_baseline + (days_from_baseline | uin) ,
data = df2, chains = 4, cores = 4)
fit2 <- brm(
mvbind(outA, outB, outC, outD) ~ centre + days_from_baseline + (days_from_baseline | p | uin) ,
data = df2, chains = 4, cores = 4)
> summary(fit1)$rescor_pars
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
rescor(outA,outB) 0.9534558 0.004181592 0.9446059 0.9609188 1.001909 2614 2993
rescor(outA,outC) 0.8686476 0.017175859 0.8324190 0.8992108 1.002068 1261 2092
rescor(outB,outC) 0.8572975 0.017809584 0.8199478 0.8880892 1.001311 1344 2242
rescor(outA,outD) 0.9070788 0.010486762 0.8848478 0.9261268 1.001920 1451 2412
rescor(outB,outD) 0.9087151 0.010564702 0.8861320 0.9277103 1.003154 1342 2752
rescor(outC,outD) 0.8413673 0.019031188 0.8006894 0.8760983 1.000012 1518 2512
> summary(fit2)$rescor_pars
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
rescor(outA,outB) 0.45600262 0.04868140 0.358168835 0.5492583 1.000698 1669 2241
rescor(outA,outC) 0.15993739 0.06086832 0.040071641 0.2793375 1.001684 2730 3197
rescor(outB,outC) 0.12594397 0.06094139 0.005829229 0.2452957 1.002860 2169 3038
rescor(outA,outD) 0.19459390 0.06270912 0.075989452 0.3189153 1.000178 2270 2965
rescor(outB,outD) 0.27492125 0.05871985 0.155382198 0.3853291 1.001018 2042 3233
rescor(outC,outD) 0.08333154 0.06564745 -0.045100800 0.2104020 1.003709 1471 2681
```

I note also that fit1 gives a BulkESS warning, fit2 does not.

However, my difficulty is intepreting these coefficients. For example in fit1 outA and outB have 0.95 residual correlation conditional on the model. I understand that - these two methods are very similar and I expect alot of correlation in these metrics. For fit2 however, outA and outB have 0.46 residual correlation conditional on model2. If the `(days_from_baseline | p | uin)`

specification has included correlation within groups across outcomes - what does this 0.46 residual correlation now represent ?

I also plot the fit for each outcome for both models:

fit1 - not sure why outcomeB is horizontal given its highly correlated with outcome A

fit2 - makes more sense