I am using `brms`

package in R. I have two models, an interaction and a simple model, that roughly have similar distributions of data by a factor of 3 levels (TrialRep) `model1 <- brm(Inter_div_abs~TrialRep + (1|ID/AbsSuj), data=totaldf1, family=student)`

, and an interaction with grouping factor in the second model (TrialRep*Group) `model2 <- brm(Inter_div_abs~TrialRep*Group + (1|ID/AbsSuj), data=totaldf2, family=student)`

. I would expect the population-effect estimates in both models to be around the same scale, but this is not the case. When I plot the `conditional_effects`

I have the following results:

In the y axis scale it is obvious something is not well. I post also the summary of both models:

This is population effects for `model1`

(TrialRep)

```
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 1.46 0.13 1.20 1.73 1.00 11034 21440
TrialRep2 -1.03 0.07 -1.18 -0.90 1.00 57843 51081
TrialRep3 -1.15 0.07 -1.29 -1.01 1.00 56529 50206
```

And this is population effects for `model2`

(interaction TrialRep*Group)

```
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 3.77 0.20 3.39 4.16 1.00 11466 20753
TrialRep2 -1.83 0.06 -1.94 -1.72 1.00 58790 57464
TrialRep3 -2.21 0.06 -2.33 -2.10 1.00 58552 56927
GroupI -0.08 0.28 -0.63 0.46 1.00 10058 18532
TrialRep2:GroupI 0.98 0.08 0.82 1.14 1.00 60255 58130
TrialRep3:GroupI 1.04 0.08 0.88 1.20 1.00 60912 57605
```

If I do the simple model from a frequentist approach, I get the following summary:

```
> m <- lmer(Inter_div_abs~ TrialRep + (1|ID/AbsSuj), data=totaldf)
> m
Linear mixed model fit by REML ['lmerModLmerTest']
Formula: Inter_div_abs ~ TrialRep + (1 | ID/AbsSuj)
Data: totaldf
REML criterion at convergence: 63112.62
Random effects:
Groups Name Std.Dev.
AbsSuj:ID (Intercept) 0.0000
ID (Intercept) 0.9875
Residual 4.6132
Number of obs: 10694, groups: AbsSuj:ID, 36; ID, 18
Fixed Effects:
(Intercept) TrialRep2 TrialRep3
5.872 -3.458 -4.570
optimizer (nloptwrap) convergence code: 0 (OK) ; 0 optimizer warnings; 1 lme4 warnings
```

Here, the fixed effects make sense now, they are closer to what I would expect. I am attaching the code I’m using so it can be reproducible and I am uploading the data I am working with. I have been struggling to figure out why this discrepancy is happening between a bayesian/frequentist approach, I also don’t understand why this is not happening with the interaction model.

totaldata2reduced.csv (142.2 KB)

```
totaldf <- read.csv("totaldata2reduced.csv")
names<-c('TrialRep','Trial','AbsSuj','ID')
totaldf[,names] <- lapply(totaldf[,names],factor)
q <- quantile(totaldf$Inter_div_abs, probs = 0.99)
#mu <- quantile(totaldf$Inter_div_abs, probs = 0.5)
for(i in 1:nrow(totaldf)){#if outlier, p50=0
tmp <- totaldf$Inter_div_abs[i]
totaldf$Inter_div_abs[i] <- ifelse(totaldf$Inter_div_abs[i]>q,NA,tmp)
}
bprior2 <- get_prior(Inter_div_abs~ (1|TrialRep) + (1|ID/AbsSuj), data=totaldf)
bprior2$prior[1] <- "student_t(3, 2, 3)"
bprior2$prior[2] <- "student_t(3, 0, 3)"
total_bayesian_mlm2 <- brm(Inter_div_abs~ TrialRep + (1|ID/AbsSuj), data=totaldf, family=student,
prior=bprior2, chains=4, cores=4, iter=20000, warmup=2000, init='0', control=list(adapt_delta=0.9, max_treedepth = 10))
```

Thanks in advance, any insight or guidance will be highly appreciated.