Dear community,

I am new to splines and I had to utilise it for my master’s thesis.

I’m fitting the following bivariate tensor splines using the brms package in R:

```
Family: cumulative
Links: mu = logit; disc = identity
Formula: P_friendliness ~ t2(AV, AS) + (1 + AV + AS | Group)
Data: Final_AV_AS (Number of observations: 796)
Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 2000
Smooth Terms:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sds(t2AVAS_1) 1.38 1.21 0.05 4.41 1.00 1300 1005
sds(t2AVAS_2) 1.66 1.43 0.07 5.34 1.00 1624 1463
sds(t2AVAS_3) 1.66 1.44 0.07 5.28 1.00 1560 1161
Group-Level Effects:
~Group (Number of levels: 6)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 1.23 0.52 0.59 2.46 1.00 807 1206
sd(AV) 0.43 0.29 0.04 1.15 1.00 811 730
sd(AS) 0.24 0.22 0.01 0.82 1.00 1175 1115
cor(Intercept,AV) -0.07 0.43 -0.83 0.74 1.00 1984 1409
cor(Intercept,AS) -0.08 0.48 -0.89 0.85 1.00 2297 1357
cor(AV,AS) -0.18 0.51 -0.94 0.82 1.00 1799 1331
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1] -3.50 0.53 -4.52 -2.38 1.00 815 1113
Intercept[2] -1.67 0.51 -2.66 -0.62 1.00 770 1116
Intercept[3] 0.44 0.51 -0.52 1.50 1.00 756 1228
Intercept[4] 2.89 0.52 1.88 3.98 1.00 783 1208
t2AVAS_1 0.39 0.24 -0.07 0.86 1.00 1553 1534
t2AVAS_2 -0.81 0.29 -1.37 -0.21 1.00 1404 1014
t2AVAS_3 0.07 0.25 -0.49 0.52 1.00 1940 1632
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
disc 1.00 0.00 1.00 1.00 NA NA NA
Draws were sampled using sampling(NUTS). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
```

I am not sure how to interpret the population-level effects table.

Additionally, I obtained this plot:

I can infer the relationship between my predictors and the outcome variable from the plot. However, how can I know whether this relationship is indeed supported by the data? Should i refer to the stats in the population-level effects table?

Thanks in advance :)