Dear community,

I am completely new to Bayesian stats and read through several tutorials and a few posts here on the forum but I cannot find a conclusive answer to what I need to do if I want to get standardized effect sizes from an ordinal brms regression. I followed the tutorial of Bürkner & Vuorre but also they did not describe how to get a standardized effect size…

model parameters:

Rating = ordered 7-point Likert scale

condition = visual or imagery

stimuls_type = art or face

a random effect for each participant = ID

a random effect for each stimulus = image_id

(I got this model by creating several beforehand and comparing them with the loo, this model was the winner)

```
bay_moving_cond_stim_id_id <- brm(Rating ~ Condition + stimulus_type + (1|ID)+ (1|image_id) , data=moving_long, family=cumulative("probit", threshold = "flexible"), chains = 5,
iter = 3000, warmup = 1000, cores = 10)
```

The result:

```
Family: cumulative
Links: mu = probit; disc = identity
Formula: Rating ~ Condition + stimulus_type + (1 | ID) + (1 | image_id)
Data: moving_long (Number of observations: 2553)
Draws: 5 chains, each with iter = 3000; warmup = 1000; thin = 1;
total post-warmup draws = 10000
Group-Level Effects:
~ID (Number of levels: 34)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.60 0.08 0.47 0.79 1.00 1937 3233
~image_id (Number of levels: 40)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(Intercept) 0.31 0.04 0.23 0.40 1.00 3297 4063
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept[1] -2.26 0.14 -2.53 -1.99 1.00 1598 3043
Intercept[2] -1.33 0.13 -1.59 -1.06 1.00 1504 2881
Intercept[3] -0.60 0.13 -0.85 -0.34 1.00 1509 2642
Intercept[4] -0.14 0.13 -0.39 0.12 1.00 1500 2833
Intercept[5] 0.75 0.13 0.49 1.01 1.00 1510 2677
Intercept[6] 1.79 0.14 1.52 2.07 1.00 1640 3412
Conditionimagery_moving_rating -0.29 0.04 -0.37 -0.20 1.00 15886 6802
stimulus_typeface -0.56 0.11 -0.77 -0.35 1.00 2844 4346
```

So I do get that a change from visual to moving (condition) results in a decrease of the ratings. I also do get that since the beta CI does not cross zero ‘it should be a real effect’ right?

I’d say intuitively from frequentist perspective (if it would be standardized) this is a small effect… Is this true for Bayesian as well?

Also do I need to create a Bayes Factor for this model or so to ‘convince’ a reviewer that this model shows that there is an effect in the data (compared to H0)?

I really appreciate any help!

Thanks for reading this far and have a great day!

Cheers,

Max