Hello. I am trying to find if there is an interaction between time (called delay in the model) and the number of repetitions that the participants were exposed to the material they had to memorise, but three different methods are giving me different results and I want to know if I did something wrong or which one should I trust.

This is my model:

```
modexp3 <- brm(
stringent ~ 1 + delay + repetitions
+ delay:repetitions
+ ( 1 + delay | id )
+ ( 1 + delay + repetitions | item ),
data = df,
family = bernoulli(),
iter = 4000,
file = "modexp3"
)
```

The output of summary(modexp3) says that there is evidence for one of the interactions and no evidence for the other (see the last two lines)

```
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 1.23 0.38 0.50 1.98 1.00 1543 3153
delay1day -1.78 0.29 -2.37 -1.23 1.00 4059 4832
delay3days -2.96 0.41 -3.83 -2.19 1.00 2895 4049
repetitions2repetitions -1.68 0.49 -2.67 -0.76 1.00 1496 3159
delay1day:repetitions2repetitions -1.05 0.48 -2.07 -0.16 1.00 3821 4512
delay3days:repetitions2repetitions -0.99 0.63 -2.34 0.15 1.00 3000 2829
```

Then I manually computed the mean, SD and CIs like this:

```
my_samples <- posterior_samples(modexp3)
a <- my_samples$b_Intercept
b <- my_samples$b_Intercept + my_samples$b_delay1day
c <- my_samples$b_Intercept + my_samples$b_delay3days
d <- my_samples$b_Intercept + my_samples$b_repetitions2repetitions
e <- my_samples$b_Intercept + my_samples$b_delay1day + my_samples$b_repetitions2repetitions +
my_samples$`b_delay1day:repetitions2repetitions`
f <- my_samples$b_Intercept + my_samples$b_delay3days + my_samples$b_repetitions2repetitions +
my_samples$`b_delay3days:repetitions2repetitions`
```

immediate vs one day, 4 vs 2 repetitions

```
fourrepimm.fourrepday <- a - b
tworepimm.tworepday <- d - e
first_slopes <- fourrepimm.fourrepday - tworepimm.tworepday
meanfirst <- round(mean(first_slopes),2)
sdfirst <- round(sd(first_slopes),2)
cifirst <- round(quantile(first_slopes, probs = c(0.025, 0.975)),2)
```

immediate vs 3 days, 4 vs 2 repetitions

```
fourrepimm.fourrep3days <- a - c
tworepimm.tworep3days <- d - f
second_slopes <- fourrepimm.fourrep3days - tworepimm.tworep3days
meansecond <- round(mean(second_slopes),2)
sdsecond <- round(sd(second_slopes),2)
cisecond <- round(quantile(second_slopes, probs = c(0.025, 0.975)),2)
```

one day vs 3 days, 4 vs 2 repetitions

```
fourrepday.fourrep3days <- b - c
tworepday.tworep3days <- e - f
third_slopes <- fourrepday.fourrep3days - tworepday.tworep3days
meanthird <- round(mean(third_slopes),2)
sdthird <- round(sd(third_slopes),2)
cithird <- round(quantile(third_slopes, probs = c(0.025, 0.975)),2)
```

And the results were:

meanfirst

[1] -1.05

sdfirst

[1] 0.48

cifirst

2.5% 97.5%

-2.07 -0.16

meansecond

[1] -0.99

sdsecond

[1] 0.63

cisecond

2.5% 97.5%

-2.34 0.15

meanthird

[1] 0.06

sdthird

[1] 0.68

cithird

2.5% 97.5%

-1.30 1.37

Finally, I learned how to do the same using hypothesis() thanks to this answer here in the forum

```
h <- c("delay1day < 0", # evidence delay1day is less than immediate for the 4 repetitions
"delay3days < 0",# evidence delay3days is less than immediate for the 4 repetitions
"delay3days - delay1day < 0",# evidence delay3days is less than delay1day for the 4 repetitions
"delay1day + delay1day:repetitions2repetitions < 0",# evidence delay1day is less than immediate for the 2 repetitions
"delay3days + delay3days:repetitions2repetitions < 0",# evidence delay3days is less than immediate for the 2 repetitions
"(delay3days + delay3days:repetitions2repetitions) - (delay1day + delay1day:repetitions2repetitions) < 0",# evidence delay3days is less than delay1day for the 2 repetitions
"repetitions2repetitions < 0",# evidence repetitions2repetitions is less than 4 repetitions at immediate
"repetitions2repetitions + delay1day:repetitions2repetitions < 0",# evidence repetitions2repetitions is less than 4 repetitions at delay1day
"repetitions2repetitions + delay3days:repetitions2repetitions < 0",# evidence repetitions2repetitions is less than 4 repetitions at delay3days
"delay1day:repetitions2repetitions < 0",# evidence slope between delay1day and immediate is steeper for repetitions2repetitions than repetitions4repetitions
"delay3days:repetitions2repetitions < 0",# evidence slope between delay3days and immediate is steeper for repetitions2repetitions than repetitions4repetitions
"delay3days:repetitions2repetitions - delay1day:repetitions2repetitions < 0"# evidence slope between delay3days and delay1day is steeper for repetitions2repetitions than repetitions4repetitions
)
hypothesis(modexp3, h)
```

And these are the results for the last three which are the interactions:

```
10 (delay1day:repeti... < 0 -1.05 0.48 -1.87 -0.30 95.39 0.99 *
11 (delay3days:repet... < 0 -0.99 0.63 -2.07 -0.02 20.45 0.95 *
12 (delay3days:repet... < 0 0.06 0.68 -1.04 1.16 0.84 0.46
```

As you can see there is one of the three interactions that appears and disappears depending on the method I use :(

- Operating System: Windows 10
- brms Version: 2.12.0