I am using `brms`

to fit a bayesian multilevel meta-analysis, including a moderator model with a 3-level moderator variable (i.e., Object, Body, Face). ex_data.csv (6.4 KB)

```
str(df)
tibble [135 × 5] (S3: tbl_df/tbl/data.frame)
study_index : int [1:135] 1 1 1 1 2 3 3 3 3 3 ...
es_num : int [1:135] 1 2 3 4 5 6 7 8 9 10 ...
yi : num [1:135] 1.849 0.395 0.845 1.2 1.337 ...
sei : num [1:135] 0.44 0.277 0.311 0.35 0.16 ...
stimuli_type: Factor w/ 3 levels "object","body",..: 2 2 2 3 2 2 2 3 3 1 ...
```

To fit the moderator model, I used the following code. Note - I actually used different simulation parameters (i.e., 20,000 iterations, tree depth =15)

```
fit <- brm(yi | se(sei) ~ 0 + Intercept + stimuli_type + (1|study_index) + (1|es_num),
data = df,
prior = c(prior(normal(0, 1), class = b),prior(cauchy(0,.3), class = sd)),
sample_prior = "yes")
```

Which results in summary output that looks like this:

```
> summary(fit)
Family: gaussian
Links: mu = identity; sigma = identity
Formula: yi | se(sei) ~ 0 + Intercept + stimuli_type + (1 | study_index) + (1 | es_num)
Data: df (Number of observations: 135)
Samples: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup samples = 4000
Group-Level Effects:
~es_num (Number of levels: 135)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.47 0.05 0.38 0.58 1.00 548 1618
~study_index (Number of levels: 36)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.20 0.09 0.02 0.39 1.01 279 366
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.26 0.14 -0.01 0.53 1.00 850 1550
stimuli_typebody 0.45 0.14 0.18 0.74 1.00 898 1424
stimuli_typeface 0.79 0.18 0.44 1.15 1.00 1163 1907
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.00 0.00 0.00 0.00 1.00 4000 4000
Samples were drawn 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).
```

To visualize the posterior distributions of this model, I used the `tidybayes`

package:

```
fit_draws <- spread_draws(fit, `b_.*` ,regex = TRUE) %>%
mutate(Object = b_Intercept,
Body = b_Intercept + b_stimuli_typebody,
Face = b_Intercept + b_stimuli_typeface) %>%
dplyr::select(-c(b_Intercept, b_stimuli_typeface, b_stimuli_typebody)) %>%
pivot_longer(cols = -c(.chain,.iteration,.draw)) %>% arrange(name,.draw)
fit_draws$name <- factor(fit_draws$name,levels = c("Object", "Body", "Face"))
ggplot(fit_draws, aes(fill = name, x = value, color = name)) +
stat_slab(alpha = .5)
```

To test different hypotheses about these, I used the `hypothesis`

function to first evaluate if they were all above zero:

```
hypothesis(fit, "Intercept > 0") # Object greater than 0?
hypothesis(fit, "Intercept + stimuli_typebody > 0") # Body greater than 0?
hypothesis(fit, "Intercept + stimuli_typeface > 0") # face greater than 0?
```

and then compared them to each other using:

```
hypothesis(fit, "Intercept + stimuli_typebody > Intercept") # Body greater than Object?
hypothesis(fit, "Intercept + stimuli_typeface > Intercept + stimuli_typebody") # Face greater than body?
hypothesis(fit, "Intercept + stimuli_typeface > Intercept") # face greater than Object?
```

Is this the appropriate way to compare levels of this moderator variable to each other? If not, how would I compare these to each other (i.e., pairwise comparisons)? The reason I ask is because there is some overlap in these distributions, but the output from the `hypothesis`

functions show that the posterior probability is .99 for `hypothesis(fit, "Intercept + stimuli_typeface > Intercept + stimuli_typebody")`

; however, according the visualization, it would not appear that 99 percent of the face (blue) distribution is greater than the body distribution (green).

Your help is much appreciated!