Good evening,

I am using brms() to run the analysis of a longitudinal, multivariate data set (R version 3.6.2, Platform: x86_64-w64-mingw32/x64 (64-bit), brms version 2.12). My research is about which predictor(s) best explain(s) the change observed over the time in the income generation of 66 individuals (3 or 4 time points per individuals).

I compared several models using loo() and ended up with this one (“revenus” = income) :

```
mdSi6__ <- brm(data = DT, family = student(), formula = revenus ~ 1 + capital + cycle*octroi + cycle:signification + (1 + capital + cycle*octroi + cycle*signification | id_client), iter = 4000, warmup = 1000, chains = 4, control = list(adapt_delta = .90, max_treedepth = 20), seed = 1414)
```

With the following output:

```
Family: student
Links: mu = identity; sigma = identity; nu = identity
Formula: revenus ~ 1 + capital + cycle * octroi + cycle:signification + (1 + capital + cycle * octroi + cycle * signification | id_client)
Data: DT (Number of observations: 222)
Samples: 4 chains, each with iter = 4000; warmup = 1000; thin = 1;
total post-warmup samples = 12000
Group-Level Effects:
~id_client (Number of levels: 66)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 685.80 488.48 33.67 1836.61 1.00 3427 4957
sd(capital) 0.59 0.11 0.40 0.82 1.00 2839 4404
sd(cycle) 318.13 237.03 12.45 887.34 1.00 3784 5256
sd(octroi) 0.26 0.19 0.01 0.70 1.00 3427 6176
sd(signification) 79.03 50.11 3.95 189.44 1.00 1414 3396
sd(cycle:octroi) 0.09 0.07 0.00 0.25 1.00 2542 4457
sd(cycle:signification) 42.48 25.77 2.48 97.38 1.00 1362 3598
(I won't display cor, because none is significant)
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
Intercept 1426.62 557.11 330.79 2508.66 1.00 6853
capital 0.96 0.13 0.71 1.22 1.00 4286
cycle -121.83 448.65 -975.28 790.58 1.00 6223
octroi 0.66 0.32 0.04 1.28 1.00 7478
cycle:octroi -0.24 0.11 -0.46 -0.02 1.00 6814
cycle:signification 68.84 24.51 21.21 117.63 1.00 5901
Tail_ESS
Intercept 9216
capital 5551
cycle 8056
octroi 8184
cycle:octroi 7547
cycle:signification 6705
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 1211.48 209.07 816.01 1633.53 1.00 1692 1449
nu 2.37 0.65 1.42 3.91 1.00 2915 2593
```

A basic interpretation of these results is that the intercepts of “capital” and “octroi”, and the slope of “signification” do contribute significantly to “income” improvement.

Well, my question is : can I assume that “capital” and “octroi” are only contributing to the intercept of my outcome variable (eg, improvement at time 0) and that the only variable contributing to the improvement of the later OVER THE TIME is the slope of “signification” ? Thus, concluding that the only positive change factor is “signification” ? Or, does the results claim for a positive contribution of both “capital” and “octroi” intercepts at any time point ?

Thank you for your help !

Best,