Task Selction in Multi-Domain Training

Author

Zhang, Liang

Published

October 27, 2023

Modified

July 20, 2024

Code 
library(tidyverse)
library(lavaan)
# we need bit64 package to handle large integers
requireNamespace("bit64")

projects <- targets::tar_config_yaml()
targets::tar_load(
  c(fit_origin_highorder, fit_origin_bifactor, dims_origin),
  store = projects$confirm_factors$store
)
targets::tar_load(
  c(indices_of_interest, indices_wider_clean),
  store = projects$prepare_source_data$store
)
dim_label_map <- dims_origin |>
  distinct(dim_label, dim_name) |>
  deframe()
game_name_map <- data.iquizoo::game_info |>
  distinct(game_name_abbr, game_name) |>
  deframe()

# custom functions ----
extract_latent_scores <- function(fit) {
  fit |>
    lavPredict() |>
    unclass() |>
    as_tibble() |>
    relocate(g, .before = 1)
}

visualize_latent_structure <- function(scores, dim_label_map) {
  colors <- c("#4477AA", "#77AADD", "#FFFFFF", "#EE9988", "#BB4444")
  cor_mat <- scores |>
    rename_with(~ dim_label_map[.x], all_of(names(dim_label_map))) |>
    cor()
  new_order <- order(cor_mat[,"g"], decreasing = TRUE)
  cor_mat[new_order, new_order] |>
    corrplot::corrplot(
      method = "color",
      type = "upper",
      tl.col = "black",
      tl.srt = 45,
      tl.cex = 0.8,
      addCoef.col = "black",
      number.cex = 0.8,
      diag = FALSE,
      tl.offset = 0.5,
      col = colorRampPalette(colors)(200)
    )
}

Correlation among Latent Factors

Code 
scores_latent <- list(
  bifactor = fit_origin_bifactor,
  highorder = fit_origin_highorder
) |>
  map(extract_latent_scores)

scores_latent |>
  walk(
    ~ visualize_latent_structure(
      .x,
      dim_label_map
    )
  )

The bifactor model scores.

The 2nd order model scores.

Correlation among latent factors.

The correlation matrix by 2nd order model is more reasonable.

After excluding transfer domains ("Reasoning" and "Episodic Memory"), the most correlated 2 domains with g are "Spatial STM" and "Verbal STM". However, the correlation between them is also very high, which means that we should not include both of them as training domains. Here we include "Spatial STM" as the training domain 1. Two other selected training domains are "Divided Attention" and "Inhibition". Note that "Speed" is not selected as training domain because it is not so reasonable to be included as training domain 2.

Selection Results

Code 
dim_order <- with(
  scores_latent,
  cor(
    select(highorder, g),
    select(highorder, -g)
  )[1, ]
) |>
  sort(decreasing = TRUE) |>
  names()
dim_transfer <- c("Rsn", "EM")
dim_train <- c("SSTM", "Inh", "AttDiv")
corrs_task_dim <- indices_of_interest |>
  left_join(
    scores_latent$highorder |>
      add_column(user_id = indices_wider_clean$user_id),
    by = "user_id"
  ) |>
  summarise(
    across(
      all_of(c("g", dims_origin$dim_label)),
      ~ cor(score_adj, .x, use = "pairwise.complete.obs")
    ),
    .by = c(game_name, index_name)
  ) |>
  inner_join(
    select(dims_origin, game_name, index_name, dim_label, dim_name),
    by = join_by(game_name, index_name)
  ) |>
  select(
    dim_name, game_name, index_name, g, all_of(dim_order)
  )

As a reference, here we list the correlations with all latent factors for all tasks. (Rows with pink background are the transfer domains, rows with green background are the training domains.)

Code 
corrs_task_dim |>
  gt::gt() |>
  gt::fmt_number(
    columns = c("g", all_of(names(dim_label_map))),
    decimals = 2
  ) |>
  gtExtras::gt_highlight_rows(
    rows = dim_name %in% dim_label_map[dim_transfer],
    fill = "#FFCCCC"
  ) |>
  gtExtras::gt_highlight_rows(
    rows = dim_name %in% dim_label_map[dim_train],
    fill = "#CCFFCC"
  ) |>
  gt::tab_header(
    title = "Task Selection Results",
    subtitle = "The most correlated task with g for each dimension/domain."
  ) |>
  gt::opt_interactive(
    use_filters = TRUE,
    use_highlight = TRUE
  )
Task Selection Results
The most correlated task with g for each dimension/domain.
Figure 1

Transfer Tasks

For reasoning, we used nonverbal reasoning task (see the highlighted row in Table 1).

Code 
tasks_transfer <- c("图形推理", "万花筒")
corrs_task_dim |>
  filter(dim_name %in% dim_label_map[dim_transfer]) |>
  arrange(desc(g)) |>
  gt::gt() |>
  gt::fmt_number(
    columns = c("g", all_of(names(dim_label_map))),
    decimals = 2
  ) |>
  gtExtras::gt_highlight_rows(
    rows = game_name %in% tasks_transfer,
    fill = "#FFCCCC",
    bold_target_only = TRUE,
    target_col = c(game_name, Rsn, EM)
  ) |>
  gt::tab_footnote(
    footnote = "The previous version is '词汇学习'.",
    locations = gt::cells_body(
      columns = game_name,
      rows = EM == max(EM)
    )
  ) |>
  gt::opt_footnote_marks("standard")
Table 1: The selected transfer tasks
dim_name game_name index_name g VSTM SSTM Rsn EM Spd Inh AttDiv Shift
Reasoning 三维心理旋转测试A nc 0.63 0.52 0.55 0.81 0.49 0.38 0.43 0.39 0.09
Reasoning 图形折叠 nc 0.61 0.53 0.51 0.80 0.46 0.40 0.38 0.36 0.07
Reasoning 图形推理 nc 0.61 0.53 0.51 0.73 0.49 0.41 0.46 0.33 0.05
Episodic Memory 过目不忘PRO nc 0.58 0.56 0.47 0.50 0.68 0.40 0.45 0.20 0.08
Reasoning 数字推理 nc 0.56 0.50 0.48 0.63 0.44 0.43 0.38 0.27 0.09
Reasoning 平面展开 nc 0.55 0.48 0.50 0.70 0.42 0.31 0.34 0.36 0.03
Reasoning 物体旋转 nc 0.53 0.45 0.44 0.67 0.50 0.29 0.42 0.26 0.02
Reasoning 视角判断 nc 0.53 0.45 0.44 0.67 0.43 0.33 0.38 0.32 0.03
Episodic Memory 万花筒* nc 0.52 0.49 0.41 0.47 0.72 0.32 0.36 0.22 0.10
Episodic Memory 欢乐餐厅PRO nc 0.51 0.53 0.43 0.38 0.66 0.31 0.39 0.18 0.09
Episodic Memory 人工语言-高级 nc 0.50 0.48 0.43 0.43 0.62 0.31 0.37 0.20 0.06
Reasoning 登陆月球（中级） mean_log_err 0.50 0.43 0.43 0.58 0.44 0.33 0.38 0.28 0.08
Episodic Memory 词汇学习 nc 0.45 0.41 0.35 0.39 0.69 0.29 0.33 0.11 0.11
Episodic Memory 事件记忆 nc 0.43 0.39 0.37 0.34 0.61 0.26 0.30 0.16 0.06
Episodic Memory 图片记忆A bps_score 0.42 0.35 0.31 0.42 0.59 0.27 0.39 0.13 0.11
Episodic Memory 连续再认PRO dprime 0.41 0.32 0.32 0.36 0.57 0.25 0.40 0.22 0.09
Reasoning 阅读判断 nc 0.41 0.37 0.30 0.45 0.40 0.28 0.36 0.17 0.09
Episodic Memory 社交达人 fntotal 0.37 0.32 0.26 0.33 0.68 0.21 0.30 0.03 0.03
Episodic Memory 视觉记忆测试 nc 0.36 0.32 0.28 0.35 0.55 0.19 0.29 0.15 0.06
Reasoning 强化学习 pc_test 0.30 0.27 0.24 0.34 0.30 0.21 0.20 0.13 −0.02
* The previous version is '词汇学习'.

Training Tasks (Training Group)

For training tasks, we will consider the correlations with the training domain, the transfer tasks and g. The tasks should be most related to g, and the correlations between the training task and transfer task should also be matched.

But here comes the question of selecting single-domain training tasks. There are two options:

  1. "Divided Atetion": this will match the mean correlations with g.
  2. "Spatial STM": add this as additional group to further justify the effectiveness of multi-domain training (i.e., better than single-domain WM training).
Code 
tasks_train <- c("蝴蝶照相机", "捉虫高级简版", "我是大厨")
tasks_train_1 <- c("小狗回家", "一心二用PRO")
tasks_train_1_alt <- c("打靶场", "位置记忆PRO")
corr_task_transfer <- indices_of_interest |>
  inner_join(
    select(dims_origin, game_name, index_name, dim_label, dim_name),
    by = join_by(game_name, index_name)
  ) |>
  filter(!dim_label %in% dim_transfer) |>
  inner_join(
    indices_of_interest |>
      filter(game_name %in% tasks_transfer) |>
      pivot_wider(
        id_cols = user_id,
        names_from = game_name,
        values_from = score_adj
      ),
    by = "user_id"
  ) |>
  summarise(
    across(
      all_of(tasks_transfer),
      ~ cor(score_adj, .x, use = "pairwise.complete.obs")
    ),
    .by = c(game_name, index_name)
  )

corrs_task_dim |>
  filter(dim_name %in% dim_label_map[dim_train]) |>
  left_join(
    corr_task_transfer,
    by = join_by(game_name, index_name)
  ) |>
  select(
    dim_name, game_name,
    g, SSTM, VSTM, Inh, AttDiv, Rsn, EM,
    all_of(tasks_transfer)
  ) |>
  arrange(desc(g)) |>
  gt::gt() |>
  gt::fmt_number(decimals = 2) |>
  gtExtras::gt_highlight_rows(
    rows = game_name %in% tasks_train,
    fill = "#11FF11"
  ) |>
  gtExtras::gt_highlight_rows(
    rows = game_name %in% tasks_train_1,
    fill = "#88FF88"
  ) |>
  gtExtras::gt_highlight_rows(
    rows = game_name %in% tasks_train_1_alt,
    fill = "#CCFFCC"
  ) |>
  gt::tab_footnote(
    footnote = paste(
      "Although '候鸟迁徙PRO' is most correlated with both g and Inhibition,",
      "it is not selected because it is a multi-domain (`Inh` and `Shift`) task."
    ) |>
      gt::md(),
    locations = gt::cells_body(
      columns = game_name,
      rows = Inh == max(Inh)
    )
  ) |>
  gt::opt_footnote_marks("standard")
Table 2: The selected training tasks (train group). The rows with darker background are from three different domains, the rows with lighter background are single "Divided Atetion" tasks, and the rows with lightest background are single "Spatial STM" tasks.
dim_name game_name g SSTM VSTM Inh AttDiv Rsn EM 图形推理 万花筒
Spatial STM 蝴蝶照相机 0.69 0.81 0.62 0.50 0.51 0.51 0.42 0.35 0.28
Spatial STM 打靶场 0.62 0.71 0.57 0.42 0.42 0.47 0.44 0.31 0.23
Spatial STM 位置记忆PRO 0.59 0.74 0.52 0.37 0.46 0.44 0.32 0.27 0.18
Spatial STM 路径学习 0.53 0.62 0.44 0.38 0.31 0.47 0.44 0.34 0.29
Inhibition 候鸟迁徙PRO* 0.48 0.41 0.39 0.74 0.29 0.36 0.39 0.25 0.22
Spatial STM 萤火虫PRO 0.47 0.55 0.40 0.34 0.37 0.39 0.30 0.24 0.17
Divided Attention 我是大厨 0.42 0.39 0.36 0.31 0.59 0.31 0.25 0.23 0.17
Divided Attention 变戏法 0.40 0.36 0.34 0.33 0.61 0.29 0.20 0.21 0.11
Divided Attention 一心二用PRO 0.39 0.41 0.32 0.24 0.72 0.29 0.10 0.15 0.07
Inhibition 捉虫高级简版 0.39 0.30 0.30 0.64 0.20 0.33 0.33 0.29 0.16
Divided Attention 小狗回家 0.35 0.33 0.30 0.23 0.56 0.32 0.19 0.22 0.16
Inhibition 变色魔块PRO 0.29 0.23 0.24 0.47 0.23 0.16 0.22 0.13 0.12
Divided Attention 连点成画PRO 0.29 0.31 0.23 0.16 0.64 0.21 0.05 0.12 0.04
Inhibition 多彩文字PRO 0.24 0.21 0.20 0.41 0.13 0.15 0.19 0.11 0.11
Inhibition 数感 0.05 0.05 0.06 0.01 −0.01 0.05 0.07 0.08 0.06
* Although ‘候鸟迁徙PRO’ is most correlated with both g and Inhibition, it is not selected because it is a multi-domain (Inh and Shift) task.

Training Tasks (Active Control Group)

For this group, the domain least correlated with g, i.e., Shifting is selected. We choose the 3 most correlated tasks with Shifting as the training task.

Code 
dim_control <- "Shift"
corrs_task_dim |>
  filter(dim_name %in% dim_label_map[dim_control]) |>
  left_join(
    corr_task_transfer,
    by = join_by(game_name, index_name)
  ) |>
  select(
    dim_name, game_name,
    g, Shift, Rsn, EM,
    all_of(tasks_transfer)
  ) |>
  arrange(desc(g)) |>
  gt::gt() |>
  gt::fmt_number(decimals = 2) |>
  gtExtras::gt_highlight_rows(
    rows = dense_rank(desc(Shift)) <= 3,
    fill = "gray"
  )
Table 3: The selected training tasks (control group).
dim_name game_name g Shift Rsn EM 图形推理 万花筒
Shifting 多变计数师 0.34 0.55 0.23 0.27 0.18 0.15
Shifting 卡片分类PRO 0.13 0.43 0.04 0.14 0.04 0.06
Shifting 察颜观色PRO 0.06 0.58 −0.02 0.00 −0.03 0.00
Shifting 候鸟迁徙PRO 0.06 0.54 −0.01 0.02 −0.02 0.02
Shifting 随机应变 0.05 0.60 −0.03 −0.07 −0.07 −0.03

References

Takeuchi, Hikaru, and Ryuta Kawashima. 2012. “Effects of Processing Speed Training on Cognitive Functions and Neural Systems.” Reviews in the Neurosciences 23 (3). https://doi.org/10.1515/revneuro-2012-0035.

Footnotes

  1. Maybe spatial stimuli are better for younger children to understand and remember than verbal ones.↩︎

  2. This is mainly based on intuition, but see (Takeuchi and Kawashima 2012).↩︎