Go-to modeling method for factorial experimental designs (with >2 levels)

In an experiment, two groups of patients (treatment vs. control) learn over the course of 4 sessions a memory strategy (2 x 4 design). A multilevel binomial regression appears as a reasonable model. However, I found in the literature that specifying equal priors across factor levels for factors with > 2 levels is not trivial.

We have hypotheses about both the main effect of the factor session and the sub-interactions in the treatment x session interaction (e.g. treatment_session4 x control_session3).

I found 3 modeling options in the literature:

• using orthonormal contrast coding (Orthonormal Contrast Matrices for Bayesian Estimation â€” contr.orthonorm â€˘ bayestestR): this does only work for the overall effects and not for the sub-interactions (as noted in the vignette)

• using the index variable approach illustrated in McElreaths rethinking: however, we would like to dissociate the main effects and the interaction (â€śinteraction effect controlling for the general learning effect across the sessionsâ€ť). I only found either an interaction or main effect model for such cases in the book.

• the procedure recommended in: How to properly compare interacting levels - #6 by Solomon
However, the credibility intervals grow very large (due to overparametrization?) so that no effects exist anymore, even though the effects are descriptively pretty large. (results printed below)

My question is: what is the standard/a reasonable option for modeling this 4x2 design? None of them seemed to really work for our data.

Code for option 3:

``````library(brms)
library(tidyverse)

wup <- 1000
itr <- 4000
chain <- 3
seeds <- 123
core <- 3

df <- data.frame(structure(list(VP = structure(c(1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 4L, 5L,
5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 5L, 6L, 6L, 6L, 6L, 6L,
6L, 6L, 6L, 6L, 6L, 6L, 6L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L, 7L,
7L, 7L, 7L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 8L, 9L,
9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 9L, 10L, 10L, 10L, 10L,
10L, 10L, 10L, 10L, 10L, 11L, 11L, 11L, 11L, 11L, 11L, 11L, 11L,
11L, 11L, 11L, 11L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L, 12L,
12L, 12L, 12L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L, 13L,
13L, 13L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 14L, 15L, 15L,
15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 15L, 16L, 16L, 16L,
16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 16L, 17L, 17L, 17L, 17L,
17L, 17L, 17L, 17L, 17L, 18L, 18L, 18L, 18L, 18L, 18L, 18L, 18L,
18L, 18L, 18L, 18L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L, 19L,
20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 20L, 21L,
21L, 21L, 21L, 21L, 21L, 21L, 21L, 21L, 22L, 22L, 22L, 22L, 22L,
22L, 22L, 22L, 22L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L, 23L,
23L, 23L, 23L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L, 24L,
24L, 24L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 25L, 26L, 26L,
26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 26L, 27L, 27L, 27L,
27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 27L, 28L, 28L, 28L, 28L,
28L, 28L, 28L, 28L, 28L, 29L, 29L, 29L, 29L, 29L, 29L, 29L, 29L,
29L, 29L, 29L, 29L, 30L, 30L, 30L, 30L, 30L, 30L, 30L, 30L, 30L,
30L, 30L, 30L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L, 31L,
31L, 31L, 32L, 32L, 32L, 32L, 32L, 32L, 32L, 32L, 32L, 32L, 32L,
32L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 33L, 33L,
34L, 34L, 34L, 34L, 34L, 34L, 34L, 34L, 34L, 34L, 34L, 34L, 35L,
35L, 35L, 35L, 35L, 35L, 35L, 35L, 35L, 35L, 35L, 35L, 36L, 36L,
36L, 36L, 36L, 36L, 36L, 36L, 36L, 37L, 37L, 37L, 37L, 37L, 37L,
37L, 37L, 37L, 37L, 37L, 37L, 38L, 38L, 38L, 38L, 38L, 38L, 38L,
38L, 38L, 39L, 39L, 39L, 39L, 39L, 39L, 39L, 39L, 39L, 39L, 39L,
39L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L, 40L,
41L, 41L, 41L, 41L, 41L, 41L, 41L, 41L, 41L, 41L, 41L, 41L, 42L,
42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 42L, 43L, 43L,
43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 43L, 44L, 44L, 44L,
44L, 44L, 44L, 44L, 44L, 44L, 44L, 44L, 44L, 45L, 45L, 45L, 45L,
45L, 45L, 45L, 45L, 45L, 45L, 45L, 45L, 46L, 46L, 46L, 46L, 46L,
46L, 46L, 46L, 46L, 46L, 46L, 46L, 47L, 47L, 47L, 47L, 47L, 47L,
47L, 47L, 47L, 47L, 47L, 47L, 48L, 48L, 48L, 48L, 48L, 48L, 48L,
48L, 48L, 48L, 48L, 48L), .Label = c("1", "2", "3", "4", "5",
"6", "7", "8", "9", "10", "11", "12", "13", "14", "15", "16",
"17", "18", "19", "20", "21", "22", "23", "24", "25", "26", "27",
"28", "29", "30", "31", "32", "33", "34", "35", "36", "37", "38",
"39", "40", "41", "42", "43", "44", "45", "46", "47", "48"), class = "factor"),
session = structure(c(1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L,
1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L,
2L, 2L, 2L, 3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L,
3L, 3L, 3L, 4L, 4L, 4L, 1L, 1L, 1L, 2L, 2L, 2L, 3L, 3L, 3L,
4L, 4L, 4L), .Label = c("1", "2", "3", "4"), class = "factor"),
img_50group = structure(c(1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L,
1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L,
1L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 2L,
2L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 2L, 1L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 2L, 2L, 2L,
1L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L,
1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
1L, 1L, 2L, 2L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L,
1L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L,
1L, 1L, 1L, 1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L,
2L, 1L, 1L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L,
2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 1L, 2L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 1L,
2L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L,
2L, 1L, 1L, 2L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 2L, 2L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
1L, 1L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 1L, 2L, 2L,
2L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L,
1L, 1L, 2L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 1L, 1L, 1L,
2L, 2L, 2L, 1L, 1L, 1L, 2L, 2L, 1L, 2L, 1L, 2L, 2L, 1L, 1L,
1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L,
1L, 2L, 2L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 2L, 2L, 1L, 2L, 1L,
1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 2L, 1L, 1L, 2L,
2L, 2L, 2L, 1L, 2L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L,
1L, 1L, 2L, 2L, 1L, 1L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L,
1L, 2L, 2L, 2L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 2L, 1L, 1L, 1L,
2L, 2L, 1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 1L, 1L,
2L, 1L, 1L, 1L, 1L, 1L, 2L, 2L, 1L, 1L, 2L, 1L, 2L, 1L, 2L,
2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 2L, 1L, 1L, 2L, 2L, 1L, 1L,
1L, 1L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 2L, 1L, 1L, 1L, 1L,
1L, 1L, 1L, 1L), .Label = c("cont", "treat"), class = "factor"),
items = c(1, 2, 2, 5, 4, 4, 6, 4, 5, 5, 5, 5, 2, 2, 2, 3,
2, 4, 6, 3, 4, 7, 5, 6, 4, 7, 5, 3, 1, 2, 3, 4, 2, 5, 3,
5, 7, 7, 5, 2, 3, 3, 4, 2, 4, 5, 4, 3, 4, 6, 5, 2, 1, 2,
4, 4, 3, 5, 5, 5, 5, 5, 6, 2, 2, 1, 3, 4, 4, 4, 5, 4, 7,
6, 5, 2, 4, 4, 4, 5, 4, 6, 5, 4, 7, 4, 6, 2, 2, 4, 5, 3,
4, 3, 4, 4, 5, 6, 5, 2, 2, 3, 2, 5, 2, 5, 4, 6, 1, 1, 2,
3, 2, 3, 4, 4, 6, 5, 6, 4, 1, 2, 4, 2, 3, 5, 4, 4, 5, 5,
5, 6, 4, 3, 1, 5, 3, 3, 4, 4, 3, 5, 6, 5, 3, 3, 4, 4, 4,
5, 6, 6, 7, 3, 2, 2, 3, 3, 3, 5, 4, 4, 6, 7, 7, 2, 1, 2,
4, 4, 3, 3, 5, 4, 5, 6, 6, 4, 3, 4, 5, 4, 5, 5, 5, 4, 2,
4, 2, 4, 3, 5, 6, 5, 6, 6, 5, 6, 1, 1, 1, 4, 3, 4, 5, 4,
4, 4, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 5, 3, 3, 3, 4, 2, 2,
4, 4, 3, 3, 3, 3, 5, 5, 5, 4, 5, 6, 1, 3, 3, 3, 2, 5, 5,
4, 3, 4, 5, 5, 4, 2, 2, 2, 4, 5, 5, 4, 4, 6, 5, 6, 1, 2,
3, 3, 3, 4, 4, 4, 6, 4, 3, 1, 3, 4, 3, 4, 4, 6, 5, 5, 6,
3, 3, 2, 4, 3, 5, 5, 4, 5, 6, 6, 6, 4, 5, 4, 4, 5, 4, 5,
4, 4, 2, 2, 2, 4, 3, 2, 3, 5, 3, 6, 4, 7, 3, 3, 2, 4, 5,
3, 5, 4, 5, 5, 5, 5, 1, 2, 2, 3, 3, 3, 5, 3, 5, 6, 7, 7,
3, 2, 1, 5, 4, 3, 3, 4, 6, 4, 5, 6, 4, 1, 3, 3, 4, 3, 6,
6, 5, 6, 6, 5, 3, 3, 2, 4, 2, 4, 5, 4, 5, 4, 5, 7, 3, 1,
3, 4, 4, 5, 5, 4, 5, 6, 6, 6, 3, 3, 3, 5, 6, 4, 4, 7, 5,
3, 3, 1, 4, 4, 3, 5, 3, 4, 7, 6, 5, 4, 3, 3, 5, 5, 3, 5,
4, 5, 3, 3, 1, 4, 4, 3, 4, 4, 5, 6, 6, 7, 3, 2, 1, 4, 4,
5, 5, 3, 5, 4, 5, 7, 2, 3, 2, 4, 4, 3, 3, 5, 4, 7, 6, 6,
4, 3, 3, 4, 3, 3, 6, 6, 6, 5, 4, 5, 3, 2, 2, 5, 4, 4, 4,
4, 4, 5, 5, 4, 2, 2, 3, 3, 4, 4, 3, 5, 3, 6, 5, 6, 2, 2,
2, 3, 2, 3, 6, 3, 4, 6, 5, 7, 1, 3, 3, 4, 4, 5, 5, 4, 5,
6, 5, 6, 3, 4, 3, 3, 4, 3, 3, 4, 3, 6, 5, 5, 3, 3, 3, 4,
3, 3, 4, 3, 4, 5, 5, 4), maxitems = c(8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
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8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8,
8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8)), row.names = c(NA,
-537L), class = "data.frame"))

df %>% group_by(session, img_50group) %>% summarise(m = mean(items))
#> A tibble: 8 x 3
#> Groups:   session [4]
#>  session img_50group     m
#>  <fct>   <fct>       <dbl>
#>1 1       cont         1.88
#>2 1       treat        3.1
#>3 2       cont         3.10
#>4 2       treat        4.06
#>5 3       cont         3.96
#>6 3       treat        4.95
#>7 4       cont         4.92
#>8 4       treat        6

# from https://discourse.mc-stan.org/t/how-to-properly-compare-interacting-levels/20457/5
fit_index <- brm(data = df,
family = binomial,
bf(
items | trials(maxitems) ~ 0 + a + g + s + i,
g ~ 0 + img_50group,
s ~ 0 + session,
a ~ 0 + (1 | VP),
i ~ (0 + img_50group) : (0 + session),
nl = TRUE
),
prior = c(prior(exponential(1), class = sd, group = VP, nlpar = a),
prior(normal(0, 0.5), nlpar = g),
prior(normal(0, 0.5), nlpar = s),
prior(normal(0, 0.5), nlpar = i)),
warmup = wup,
iter = itr,
chains = chain,
seed = seeds,
cores = core)
#> Compiling Stan program...
#> Start sampling

summary(fit_index)
#>  Family: binomial
#> Formula: items | trials(maxitems) ~ 0 + a + g + s + i
#>          g ~ 0 + img_50group
#>          s ~ 0 + session
#>          a ~ 0 + (1 | VP)
#>          i ~ (0 + img_50group):(0 + session)
#>    Data: df (Number of observations: 537)
#>   Draws: 3 chains, each with iter = 4000; warmup = 1000; thin = 1;
#>          total post-warmup draws = 9000
#>
#> Group-Level Effects:
#> ~VP (Number of levels: 48)
#>                 Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
#> sd(a_Intercept)     0.03      0.02     0.00     0.09 1.00     5433     3083
#>
#> Population-Level Effects:
#>                             Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
#> g_img_50groupcont              -0.24      0.28    -0.77     0.32 1.00     4680
#> g_img_50grouptreat              0.23      0.29    -0.32     0.80 1.00     4298
#> s_session1                     -0.54      0.33    -1.19     0.10 1.00     4888
#> s_session2                     -0.14      0.33    -0.77     0.51 1.00     5161
#> s_session3                      0.16      0.33    -0.50     0.81 1.00     4643
#> s_session4                      0.52      0.33    -0.13     1.17 1.00     4696
#> i_img_50groupcont:session1     -0.39      0.34    -1.05     0.28 1.00     5014
#> i_img_50grouptreat:session1    -0.14      0.34    -0.80     0.53 1.00     4879
#> i_img_50groupcont:session2     -0.08      0.33    -0.74     0.58 1.00     5756
#> i_img_50grouptreat:session2    -0.06      0.34    -0.73     0.61 1.00     5080
#> i_img_50groupcont:session3      0.06      0.34    -0.59     0.72 1.00     4803
#> i_img_50grouptreat:session3     0.09      0.34    -0.58     0.77 1.00     4861
#> i_img_50groupcont:session4      0.18      0.34    -0.48     0.84 1.00     5311
#> i_img_50grouptreat:session4     0.34      0.34    -0.34     1.02 1.00     5165
#>                             Tail_ESS
#> g_img_50groupcont               5534
#> g_img_50grouptreat              5366
#> s_session1                      5550
#> s_session2                      5410
#> s_session3                      5131
#> s_session4                      5581
#> i_img_50groupcont:session1      5761
#> i_img_50grouptreat:session1     5740
#> i_img_50groupcont:session2      6031
#> i_img_50grouptreat:session2     5803
#> i_img_50groupcont:session3      5809
#> i_img_50grouptreat:session3     6092
#> i_img_50groupcont:session4      6356
#> i_img_50grouptreat:session4     6170
#>
#> Draws were sampled 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).
``````

Created on 2022-07-05 by the reprex package (v2.0.1)

``````