Hello! In the course of my master’s degree in psychology we currently conducting a word recognition experiment online. The conditions are varied within-subjects. All participants have to pass both conditions, control and experimental condition on the first date (T1). On the first date the participants are receiving a treatment which is expected to improve the recognition performance in the experimental condition associated recognition task.

One week later the participants have to undergo control and experimental condition again (T2). We want to evaluate whether the treatment effect continues from T1 to T2, specifically that the recognition performance is still larger in the experimental condition.

I’m gonna use the Brms package to specifiy and calculate an ordinal probit model with heteroscedastic error.

**The Variables are defined as follows:**

## Variables of the Model

item = factor variable with 2 levels [new;old]

condition = factor variable with 2 levels [K;E]

time2 = numeric with [0 = T1; 1= T2]

old = numeric with [0 = new; 1 = old]

**But I am unsure about:**

- The Interaction of condition x item is the difference (change in the probability of the categories likewise shift of the thresholds) in detection from old vs new items in the experimental group vs the control group for T1, isn’t it? This Interaction takes just the data from T1 and not the whole from T1 + T2(?).
- I used the discrimination parameter to allow the standart deviation of the old (previous learned items) items differ from 1. Do I have to include more discrimination parameters for condition and time?
- The Interaction (condition x time2 x item) is the difference of the detection from T1 to T2. Does a non significant coefficient of this interaction term imply an enduring effect of the treatment after 1 week for the case that the (condition x item) interaction was significant?
- What is modeled with | i | in this case? Is the benefit of this a more accurate estimation of the coefficients?

The Model I used:

```
uvsdt <- brm(
bf(Response ~ 1 + item * condition * time2 + (1 + item * condition * time2 | i | ID_T1T2 ),
disc ~ 0 + old + (0 + old | i | ID_T1T2 )),
data = data_hypnomemory, family = cumulative("probit"),
iter = 2500, inits = 0
)
```