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 — contr.orthonorm • 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 (“interaction effect controlling for the general learning effect across the sessions”). 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,
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, 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, 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, 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, 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
#> Links: mu = logit
#> 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)
Please also provide the following information in addition to your question:
* Operating System: windows 10 64 bit
* brms Version: version 2.17.0