Hi @FoscoB,

The detailed answers to your questions depend on how you have coded your predictors. For example, you may have coded condition and group with dummy variables (0 = group a, 1 = group b), or you may have used effect coding (e.g. -1 = group a, 1 = group b).

Letâs assume that you have coded group and condition with dummy variables (this is what R modeling functions will do unless you specify otherwise.) Here is some example data in variable `dat`

:

```
> str(dat)
Classes âtbl_dfâ, âtblâ and 'data.frame': 557 obs. of 3 variables:
$ Rating: num 4 4 4 4 4 4 4 4 4 4 ...
$ Group : Factor w/ 2 levels "0","1": 1 1 1 1 1 1 1 1 1 1 ...
$ Cond : Factor w/ 2 levels "0","1": 1 1 2 2 1 1 2 1 2 2 ...
```

I then estimated the model as specified in your example code (varying intercepts for participants are irrelevant for us now, so I donât include them):

```
> fit <- brm(
+ Rating ~ Group * Cond,
+ data = dat,
+ family = cumulative()
+ )
> summary(fit)
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Eff.Sample Rhat
Intercept[1] -1.52 0.18 -1.88 -1.18 3156 1.00
Intercept[2] -0.44 0.15 -0.73 -0.14 3554 1.00
Intercept[3] 1.46 0.17 1.13 1.79 2950 1.00
Group1 0.95 0.22 0.52 1.41 2581 1.00
Cond1 0.35 0.22 -0.10 0.79 2667 1.00
Group1:Cond1 -0.06 0.32 -0.69 0.56 2493 1.00
```

The estimated effects are interpreted as in any regression model where you have dummy coded group and condition. `Group1`

is the effect on the mean of the latent variable (from which the ordinal ratings are assumed to originate) when `Cond`

= 0. `Cond1`

is the effect of condition when `Group`

= 0.

The interaction `Group1:Cond1`

tells you how much the effect of group changes between conditions, or equivalently how much the effect of condition changes between groups. To get the effect of condition for both groups separately, you can use the hypothesis method.

```
> Hypotheses <- c(
+ "Cond-group0" = "Cond1 + Group1:Cond1*0 = 0",
+ "Cond-group1" = "Cond1 + Group1:Cond1*1 = 0"
+ )
> hypothesis(fit, Hypotheses)
Hypothesis Tests for class b:
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
1 Cond-group0 0.35 0.22 -0.10 0.79 NA NA
2 Cond-group1 0.29 0.22 -0.15 0.71 NA NA
---
'CI': 90%-CI for one-sided and 95%-CI for two-sided hypotheses.
'*': For one-sided hypotheses, the posterior probability exceeds 95%;
for two-sided hypotheses, the value tested against lies outside the 95%-CI.
Posterior probabilities of point hypotheses assume equal prior probabilities.
```

(Notice how the first row corresponds to the basic model output.) You can also specify the hypotheses with `> 0`

or `< 0`

to get evidence ratios.

Then, to specifically answer your questions: The estimate and evidence ratio (that effect is positive) for the interaction is given by:

```
> hypothesis(fit, "Group1:Cond1 > 0")
Hypothesis Tests for class b:
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
1 (Group1:Cond1) > 0 -0.06 0.32 -0.59 0.45 0.77 0.44
```

(I would not over-interpret the evidence ratio or posterior probability numbers.)

The main effect of `Cond`

is typically taken to mean the effect of Condition âfor the average groupâ. To get that effect, you need to estimate the model using effect coded `Group`

variable, and then the summary of `Cond1`

would be the âmain effectâ (see `?contr.sum`

). You can also get a main effect from the model with dummy coded variables by asking for the effect of `Cond`

when `Group1:Cond1`

= 0.5

```
> hypothesis(fit, "Cond1 + Group1:Cond1*0.5 = 0")
Hypothesis Tests for class b:
Hypothesis Estimate Est.Error CI.Lower CI.Upper Evid.Ratio Post.Prob Star
1 (Cond1+Group1:Con... = 0 0.32 0.15 0.02 0.62 NA NA *
```

More generally, as others pointed out, you can think of any contrast or transformation of the parameters, and using the posterior samples, you can get the posterior of that contrast / transformation. With the `hypothesis()`

method, all thatâs left for you to do is to write out the equation for the contrast.

Hope that helps.