02 — Longitudinal traces and simple growth models

ImportantAI-generated — not for publication

The code and prose in this chapter were written by Claude Code (an AI coding agent) under human direction. They have not been line-by-line verified by a human and must not be published or cited as-is.

WarningPreliminary & unvetted analysis

These are exploratory analyses of preliminary, in-progress LEVANTE data. Results have not been reviewed or validated and require checking by the LEVANTE Data Coordinating Center before any use.

NoteNow on corrected data (v1.2)

Re-run on levante_data_latest v1.2, which fixes the IRT column-order scoring bug. The spurious within-child declines seen in earlier (v1.0) renders are gone: all within-child slopes are now positive (e.g. Math ≈ 0.6 θ/yr, Vocab/EF/reasoning ≈ 0.1–0.4). Any text below that frames a task as “declining” reflects the old buggy data and is superseded by the corrected figures.

Note2026-08 data update: rural Colombia’s second wave

The 2026-08 snapshot adds Caquetá/Boyacá as a fourth longitudinal dataset (~213 repeat kids at a ~9.6-month gap, concentrated in ROAR + Math). Its within-child growth is clean and — notably — almost exactly matches the cross-sectional age gradient: Math 0.45 θ/yr within vs 0.45 across, ROAR-Word 0.47 vs 0.49, ROAR-Phoneme 0.28 vs 0.28, ROAR-Sentence 0.22 vs 0.23. Math repeats are CAT→CAT (no mode transition), making this the cleanest within-child growth replication in the project so far.

2026-08-31: Leipzig’s third wave began arriving (39 children re-tested on the full battery Aug 29–30, already scored in the draft snapshot) — the first ≥3-timepoint children in the project. They appear in the Leipzig spaghetti below as three-point trajectories (max within-child span now 24 months); per-child growth-curve models become identifiable once this wave completes.

Purpose

00 inventoried what data we have; 01 audited per-(site, task) data integrity and produced a verdict table at data/task_site_verdict.rds. This notebook focuses on the datasets that actually have repeat assessments and asks:

  1. Do individual children show consistent growth in IRT ability scores across waves?
  2. Are within-individual growth rates broadly consistent with the cross-sectional age gradient in that dataset?

We restrict attention to the four datasets with meaningful longitudinal signal as of the 2026-08 per-site snapshot:

  • Germany — Leipzig (mpieva-de): ~3- and 7-month retest, ~226 kids.
  • Colombia — Bogotá (uniandes-co-bogota): ~15-month gap, ~420 kids.
  • Colombia — Caquetá/Boyacá (uniandes-co-rural): new in the 2026-08 update — a ~9.6-month-gap second wave, ~213 repeat kids. Repeats are concentrated in ROAR (pa/swr/sre) and Math (~170–210 pairs each; Math is cleanly CAT→CAT); the other core tasks are still cross-sectional here.
  • Canada — Ontario (western-ca): ~12-month gap, still only ~10–21 repeat kids per task, so it falls below the ≥ 30-per-task threshold for the mixed models and mainly appears in the spaghetti/cross-sectional views.
source(here::here("common.R"))
library(lme4)
library(broom.mixed)
library(ggrepel)

scores_all <- read_rds(here("data", "scores_all_sites.rds"))

Restrict to longitudinal datasets

long_datasets <- c("pilot_mpieva_de_main",
                   "pilot_uniandes_co_bogota",
                   "pilot_uniandes_co_rural",
                   "pilot_western_ca_main")

scores <- scores_all |>
  filter(dataset %in% long_datasets,
         !is.na(score), !is.na(age))

scores |>
  count(dataset_label, task_label) |>
  pivot_wider(names_from = dataset_label, values_from = n,
              values_fill = 0L) |>
  knitr::kable()
task_label Colombia — Bogotá Colombia — Caquetá/Boyacá Germany — Leipzig Canada — Ontario
Hearts and Flowers 435 491 564 398
Math 908 1182 534 370
Memory 344 485 539 361
Pattern Matching 327 468 506 299
ROAR-Phoneme 578 1162 0 292
ROAR-Sentence 769 936 198 126
ROAR-Word 787 1007 203 140
Same and Different 204 230 542 267
Sentence Understanding 454 601 439 346
Shape Rotation 410 536 474 345
Stories (ToM) 190 304 525 254
Vocabulary 336 651 524 348

Adaptive vs non-adaptive scores

Pilot data mixes non-adaptive and computer-adaptive (CAT) administrations of the same task. Under v1.0’s scoring bug this produced large spurious step jumps across the mode boundary; on v1.2 (fixed) the residual mode shift is small (< 0.75 logits — see 01), attributable to mild ceiling on the easy non-adaptive forms plus EAP shrinkage. We still flag the mode split below so within-mode vs across-mode comparisons stay visible.

scores |>
  group_by(dataset_label, task_label, adaptive) |>
  summarise(n_runs = n_distinct(run_id), .groups = "drop") |>
  pivot_wider(names_from = adaptive, values_from = n_runs, values_fill = 0L,
              names_prefix = "adaptive_") |>
  knitr::kable()
dataset_label task_label adaptive_FALSE adaptive_TRUE
Colombia — Bogotá Hearts and Flowers 435 0
Colombia — Bogotá Math 331 577
Colombia — Bogotá Memory 344 0
Colombia — Bogotá Pattern Matching 81 246
Colombia — Bogotá ROAR-Phoneme 578 0
Colombia — Bogotá ROAR-Sentence 769 0
Colombia — Bogotá ROAR-Word 787 0
Colombia — Bogotá Same and Different 166 38
Colombia — Bogotá Sentence Understanding 177 277
Colombia — Bogotá Shape Rotation 338 72
Colombia — Bogotá Stories (ToM) 151 39
Colombia — Bogotá Vocabulary 63 273
Colombia — Caquetá/Boyacá Hearts and Flowers 491 0
Colombia — Caquetá/Boyacá Math 220 962
Colombia — Caquetá/Boyacá Memory 485 0
Colombia — Caquetá/Boyacá Pattern Matching 23 445
Colombia — Caquetá/Boyacá ROAR-Phoneme 1162 0
Colombia — Caquetá/Boyacá ROAR-Sentence 936 0
Colombia — Caquetá/Boyacá ROAR-Word 1007 0
Colombia — Caquetá/Boyacá Same and Different 20 210
Colombia — Caquetá/Boyacá Sentence Understanding 53 548
Colombia — Caquetá/Boyacá Shape Rotation 0 536
Colombia — Caquetá/Boyacá Stories (ToM) 91 213
Colombia — Caquetá/Boyacá Vocabulary 76 575
Germany — Leipzig Hearts and Flowers 564 0
Germany — Leipzig Math 430 104
Germany — Leipzig Memory 539 0
Germany — Leipzig Pattern Matching 434 72
Germany — Leipzig ROAR-Sentence 198 0
Germany — Leipzig ROAR-Word 203 0
Germany — Leipzig Same and Different 434 108
Germany — Leipzig Sentence Understanding 192 247
Germany — Leipzig Shape Rotation 189 285
Germany — Leipzig Stories (ToM) 495 30
Germany — Leipzig Vocabulary 196 328
Canada — Ontario Hearts and Flowers 398 0
Canada — Ontario Math 69 301
Canada — Ontario Memory 361 0
Canada — Ontario Pattern Matching 69 230
Canada — Ontario ROAR-Phoneme 292 0
Canada — Ontario ROAR-Sentence 126 0
Canada — Ontario ROAR-Word 134 6
Canada — Ontario Same and Different 39 228
Canada — Ontario Sentence Understanding 27 319
Canada — Ontario Shape Rotation 67 278
Canada — Ontario Stories (ToM) 201 53
Canada — Ontario Vocabulary 19 329

Spaghetti plots

Every child with ≥ 2 runs on a given task, one line per child, raw IRT score. Children with ≥ 3 timepoints (new with Leipzig’s third wave) are highlighted in orange; task panels with fewer than 10 repeat children are suppressed.

repeats <- scores |>
  group_by(dataset, user_id, task_id) |>
  filter(n_distinct(run_id) > 1) |>
  ungroup() |>
  arrange(dataset, user_id, task_id, age)

glue("Repeat (dataset, child, task) cells: {n_distinct(paste(repeats$dataset, repeats$user_id, repeats$task_id))}")
Repeat (dataset, child, task) cells: 4313
spaghetti <- function(ds, title) {
  d <- repeats |>
    filter(dataset == ds) |>
    group_by(task_id) |> filter(n_distinct(user_id) >= 10) |> ungroup() |>
    group_by(user_id, task_id) |>
    mutate(waves = if_else(n_distinct(run_id) >= 3, "3+ timepoints", "2 timepoints")) |>
    ungroup()
  ggplot(d, aes(x = age, y = score, group = user_id)) +
    geom_line(data = d |> filter(waves == "2 timepoints"),
              aes(color = waves), alpha = 0.25, linewidth = 0.35) +
    geom_line(data = d |> filter(waves == "3+ timepoints"),
              aes(color = waves), alpha = 0.9, linewidth = 0.6) +
    facet_wrap(vars(task_category, task_label), scales = "free_y") +
    scale_color_manual(values = c(`2 timepoints` = "grey45",
                                  `3+ timepoints` = "#cb4b16"), name = NULL) +
    guides(color = guide_legend(override.aes = list(alpha = 1, linewidth = 1))) +
    labs(title = title, x = "Age (years)", y = "IRT ability") +
    theme(legend.position = "bottom")
}
spaghetti("pilot_mpieva_de_main",
          "Germany — Leipzig spaghetti (3-wave children in orange)")

spaghetti("pilot_uniandes_co_bogota", "Colombia — Bogotá spaghetti")

spaghetti("pilot_uniandes_co_rural",
          "Colombia — Caquetá/Boyacá spaghetti (new in 2026-08; sparse panels suppressed)")

(Rural’s few ≥3-run children include short-gap repeat administrations — the near-vertical orange segments; treat those individual trajectories with care. Leipzig’s orange three-wave children, by contrast, are the designed third wave.)

spaghetti("pilot_western_ca_main", "Canada — Ontario spaghetti")

Simple growth models per (dataset, task)

For each (dataset, task), fit

score ~ age_c + (1 | user_id)

with age_c = age − mean(age). With mostly 2 timepoints the random-slope variance is unidentifiable, so we read the fixed effect of age_c as the average within-individual slope. Per-child heterogeneity is examined separately below.

Where both adaptive and non-adaptive versions are present we include adaptive as a fixed effect.

fit_growth <- function(df) {
  df <- df |> mutate(age_c = age - mean(age, na.rm = TRUE))
  has_both_adaptive <- length(unique(na.omit(df$adaptive))) > 1
  fm <- if (has_both_adaptive) {
    score ~ age_c + adaptive + (1 | user_id)
  } else {
    score ~ age_c + (1 | user_id)
  }
  tryCatch(
    lmer(fm, data = df, REML = TRUE,
         control = lmerControl(optimizer = "bobyqa",
                               optCtrl = list(maxfun = 2e5))),
    error = function(e) {
      message(glue("  fit failed: {conditionMessage(e)}"))
      NULL
    }
  )
}

growth_data <- scores |>
  group_by(dataset, task_id) |>
  filter(n_distinct(user_id[duplicated(user_id) | duplicated(user_id, fromLast = TRUE)]) >= 30) |>
  ungroup()

growth_fits <- growth_data |>
  group_by(dataset, dataset_label, task_id, task_label, task_category) |>
  nest() |>
  mutate(fit = map(data, fit_growth)) |>
  filter(!map_lgl(fit, is.null))

glue("Fitted {nrow(growth_fits)} (dataset, task) growth models.")
Fitted 28 (dataset, task) growth models.
within_slopes <- growth_fits |>
  mutate(coef_tbl = map(fit, \(m) broom.mixed::tidy(m, effects = "fixed",
                                                    conf.int = TRUE))) |>
  select(dataset_label, task_label, task_category, coef_tbl) |>
  unnest(coef_tbl) |>
  filter(term == "age_c") |>
  select(dataset_label, task_label, task_category,
         within_slope = estimate, within_slope_se = std.error,
         within_ci_lo = conf.low, within_ci_hi = conf.high)

knitr::kable(within_slopes, digits = 3)
dataset task_id dataset_label task_label task_category within_slope within_slope_se within_ci_lo within_ci_hi
pilot_mpieva_de_main hearts-and-flowers Germany — Leipzig Hearts and Flowers Executive function 0.660 0.046 0.569 0.751
pilot_mpieva_de_main egma-math Germany — Leipzig Math Math 0.608 0.036 0.537 0.679
pilot_mpieva_de_main matrix-reasoning Germany — Leipzig Pattern Matching Reasoning 0.352 0.035 0.284 0.420
pilot_mpieva_de_main memory-game Germany — Leipzig Memory Executive function 0.197 0.015 0.167 0.226
pilot_mpieva_de_main mental-rotation Germany — Leipzig Shape Rotation Spatial cognition 0.217 0.021 0.176 0.258
pilot_mpieva_de_main same-different-selection Germany — Leipzig Same and Different Executive function 0.129 0.027 0.076 0.182
pilot_mpieva_de_main theory-of-mind Germany — Leipzig Stories (ToM) Social cognition 0.119 0.016 0.088 0.150
pilot_mpieva_de_main trog Germany — Leipzig Sentence Understanding Language 0.140 0.018 0.105 0.176
pilot_mpieva_de_main vocab Germany — Leipzig Vocabulary Language 0.260 0.016 0.230 0.290
pilot_mpieva_de_main sre Germany — Leipzig ROAR-Sentence Reading 0.364 0.037 0.292 0.437
pilot_mpieva_de_main swr Germany — Leipzig ROAR-Word Reading 0.311 0.060 0.194 0.428
pilot_uniandes_co_bogota hearts-and-flowers Colombia — Bogotá Hearts and Flowers Executive function 0.483 0.037 0.410 0.555
pilot_uniandes_co_bogota egma-math Colombia — Bogotá Math Math 0.561 0.023 0.515 0.606
pilot_uniandes_co_bogota memory-game Colombia — Bogotá Memory Executive function 0.260 0.023 0.215 0.305
pilot_uniandes_co_bogota sre Colombia — Bogotá ROAR-Sentence Reading 0.346 0.017 0.313 0.380
pilot_uniandes_co_bogota pa Colombia — Bogotá ROAR-Phoneme Reading 0.391 0.036 0.321 0.462
pilot_uniandes_co_bogota swr Colombia — Bogotá ROAR-Word Reading 0.560 0.031 0.500 0.621
pilot_uniandes_co_bogota trog Colombia — Bogotá Sentence Understanding Language 0.264 0.021 0.222 0.305
pilot_uniandes_co_bogota mental-rotation Colombia — Bogotá Shape Rotation Spatial cognition 0.345 0.028 0.291 0.399
pilot_uniandes_co_rural egma-math Colombia — Caquetá/Boyacá Math Math 0.472 0.022 0.428 0.516
pilot_uniandes_co_rural swr Colombia — Caquetá/Boyacá ROAR-Word Reading 0.511 0.028 0.455 0.566
pilot_uniandes_co_rural sre Colombia — Caquetá/Boyacá ROAR-Sentence Reading 0.236 0.016 0.206 0.267
pilot_uniandes_co_rural pa Colombia — Caquetá/Boyacá ROAR-Phoneme Reading 0.287 0.021 0.246 0.327
pilot_western_ca_main hearts-and-flowers Canada — Ontario Hearts and Flowers Executive function 0.349 0.048 0.254 0.443
pilot_western_ca_main egma-math Canada — Ontario Math Math 0.727 0.040 0.648 0.806
pilot_western_ca_main matrix-reasoning Canada — Ontario Pattern Matching Reasoning 0.430 0.036 0.360 0.500
pilot_western_ca_main memory-game Canada — Ontario Memory Executive function 0.270 0.021 0.229 0.311
pilot_western_ca_main mental-rotation Canada — Ontario Shape Rotation Spatial cognition 0.327 0.031 0.266 0.388

Cross-sectional age gradients for comparison

OLS slope of score on age within each (dataset, task), using each child’s first observation.

cross_slopes <- scores |>
  group_by(dataset, user_id, task_id) |>
  arrange(age) |>
  slice(1) |>
  ungroup() |>
  group_by(dataset, dataset_label, task_id, task_label, task_category) |>
  filter(n() >= 30) |>
  summarise(
    cross_slope = coef(lm(score ~ age))[2],
    cross_n     = n(),
    .groups = "drop"
  )

slope_compare <- within_slopes |>
  inner_join(cross_slopes, by = c("dataset_label", "task_label",
                                   "task_category"))

knitr::kable(slope_compare, digits = 3)
dataset.x task_id.x dataset_label task_label task_category within_slope within_slope_se within_ci_lo within_ci_hi dataset.y task_id.y cross_slope cross_n
pilot_mpieva_de_main hearts-and-flowers Germany — Leipzig Hearts and Flowers Executive function 0.660 0.046 0.569 0.751 pilot_mpieva_de_main hearts-and-flowers 0.699 337
pilot_mpieva_de_main egma-math Germany — Leipzig Math Math 0.608 0.036 0.537 0.679 pilot_mpieva_de_main egma-math 0.665 310
pilot_mpieva_de_main matrix-reasoning Germany — Leipzig Pattern Matching Reasoning 0.352 0.035 0.284 0.420 pilot_mpieva_de_main matrix-reasoning 0.411 310
pilot_mpieva_de_main memory-game Germany — Leipzig Memory Executive function 0.197 0.015 0.167 0.226 pilot_mpieva_de_main memory-game 0.175 325
pilot_mpieva_de_main mental-rotation Germany — Leipzig Shape Rotation Spatial cognition 0.217 0.021 0.176 0.258 pilot_mpieva_de_main mental-rotation 0.227 292
pilot_mpieva_de_main same-different-selection Germany — Leipzig Same and Different Executive function 0.129 0.027 0.076 0.182 pilot_mpieva_de_main same-different-selection 0.128 331
pilot_mpieva_de_main theory-of-mind Germany — Leipzig Stories (ToM) Social cognition 0.119 0.016 0.088 0.150 pilot_mpieva_de_main theory-of-mind 0.146 314
pilot_mpieva_de_main trog Germany — Leipzig Sentence Understanding Language 0.140 0.018 0.105 0.176 pilot_mpieva_de_main trog 0.153 276
pilot_mpieva_de_main vocab Germany — Leipzig Vocabulary Language 0.260 0.016 0.230 0.290 pilot_mpieva_de_main vocab 0.272 296
pilot_mpieva_de_main sre Germany — Leipzig ROAR-Sentence Reading 0.364 0.037 0.292 0.437 pilot_mpieva_de_main sre 0.323 162
pilot_mpieva_de_main swr Germany — Leipzig ROAR-Word Reading 0.311 0.060 0.194 0.428 pilot_mpieva_de_main swr 0.322 164
pilot_uniandes_co_bogota hearts-and-flowers Colombia — Bogotá Hearts and Flowers Executive function 0.483 0.037 0.410 0.555 pilot_uniandes_co_bogota hearts-and-flowers 0.489 383
pilot_uniandes_co_bogota egma-math Colombia — Bogotá Math Math 0.561 0.023 0.515 0.606 pilot_uniandes_co_bogota egma-math 0.532 621
pilot_uniandes_co_bogota memory-game Colombia — Bogotá Memory Executive function 0.260 0.023 0.215 0.305 pilot_uniandes_co_bogota memory-game 0.252 312
pilot_uniandes_co_bogota sre Colombia — Bogotá ROAR-Sentence Reading 0.346 0.017 0.313 0.380 pilot_uniandes_co_bogota sre 0.328 553
pilot_uniandes_co_bogota pa Colombia — Bogotá ROAR-Phoneme Reading 0.391 0.036 0.321 0.462 pilot_uniandes_co_bogota pa 0.414 521
pilot_uniandes_co_bogota swr Colombia — Bogotá ROAR-Word Reading 0.560 0.031 0.500 0.621 pilot_uniandes_co_bogota swr 0.590 570
pilot_uniandes_co_bogota trog Colombia — Bogotá Sentence Understanding Language 0.264 0.021 0.222 0.305 pilot_uniandes_co_bogota trog 0.254 379
pilot_uniandes_co_bogota mental-rotation Colombia — Bogotá Shape Rotation Spatial cognition 0.345 0.028 0.291 0.399 pilot_uniandes_co_bogota mental-rotation 0.338 360
pilot_uniandes_co_rural egma-math Colombia — Caquetá/Boyacá Math Math 0.472 0.022 0.428 0.516 pilot_uniandes_co_rural egma-math 0.463 868
pilot_uniandes_co_rural swr Colombia — Caquetá/Boyacá ROAR-Word Reading 0.511 0.028 0.455 0.566 pilot_uniandes_co_rural swr 0.477 703
pilot_uniandes_co_rural sre Colombia — Caquetá/Boyacá ROAR-Sentence Reading 0.236 0.016 0.206 0.267 pilot_uniandes_co_rural sre 0.223 666
pilot_uniandes_co_rural pa Colombia — Caquetá/Boyacá ROAR-Phoneme Reading 0.287 0.021 0.246 0.327 pilot_uniandes_co_rural pa 0.288 842
pilot_western_ca_main hearts-and-flowers Canada — Ontario Hearts and Flowers Executive function 0.349 0.048 0.254 0.443 pilot_western_ca_main hearts-and-flowers 0.348 354
pilot_western_ca_main egma-math Canada — Ontario Math Math 0.727 0.040 0.648 0.806 pilot_western_ca_main egma-math 0.721 333
pilot_western_ca_main matrix-reasoning Canada — Ontario Pattern Matching Reasoning 0.430 0.036 0.360 0.500 pilot_western_ca_main matrix-reasoning 0.434 263
pilot_western_ca_main memory-game Canada — Ontario Memory Executive function 0.270 0.021 0.229 0.311 pilot_western_ca_main memory-game 0.278 322
pilot_western_ca_main mental-rotation Canada — Ontario Shape Rotation Spatial cognition 0.327 0.031 0.266 0.388 pilot_western_ca_main mental-rotation 0.333 308 
slope_compare |>
  ggplot(aes(x = cross_slope, y = within_slope, color = task_category)) +
  geom_abline(slope = 1, intercept = 0, lty = 3, color = "grey50") +
  geom_hline(yintercept = 0, lty = 3, color = "grey80") +
  geom_vline(xintercept = 0, lty = 3, color = "grey80") +
  geom_errorbar(aes(ymin = within_ci_lo, ymax = within_ci_hi),
                alpha = 0.5, width = 0) +
  geom_point(size = 2.5) +
  geom_text_repel(aes(label = task_label), size = 3,
                  show.legend = FALSE, max.overlaps = 30) +
  facet_wrap(~dataset_label) +
  scale_colour_task() +
  labs(x = "Cross-sectional slope (per year)",
       y = "Within-child slope (per year)",
       title = "Within-child growth vs cross-sectional age gradient",
       subtitle = "Dotted line = identity",
       color = NULL) +
  theme(legend.position = "bottom")

Fitted trajectories

Population-mean model curves overlaid on raw spaghetti, faceted by task.

predict_band <- function(fit, df) {
  if (is.null(fit)) return(NULL)
  age_grid <- seq(min(df$age, na.rm = TRUE),
                  max(df$age, na.rm = TRUE), length.out = 40)
  age_mean <- mean(df$age, na.rm = TRUE)
  newd <- tibble(age = age_grid, age_c = age_grid - age_mean)
  if ("adaptive" %in% all.vars(formula(fit))) newd$adaptive <- FALSE
  newd$score <- predict(fit, newdata = newd, re.form = NA,
                        allow.new.levels = TRUE)
  newd |> select(age, score)
}

fitted_lines <- growth_fits |>
  mutate(pred = map2(fit, data, predict_band)) |>
  select(dataset_label, task_label, task_category, pred) |>
  unnest(pred)

ggplot() +
  geom_line(data = repeats,
            aes(x = age, y = score, group = user_id),
            alpha = 0.15, color = "grey40") +
  geom_line(data = fitted_lines,
            aes(x = age, y = score, color = dataset_label),
            linewidth = 1) +
  facet_wrap(vars(task_category, task_label), scales = "free_y") +
  scale_color_brewer(palette = "Set1", name = NULL) +
  labs(title = "Fitted growth trajectories on top of raw spaghetti",
       x = "Age (years)", y = "IRT ability") +
  theme(legend.position = "bottom")

Child-level slopes

Per-child OLS slopes for kids with ≥ 2 runs (rise / run when N = 2).

child_slopes <- repeats |>
  group_by(dataset, dataset_label, task_id, task_label, task_category, user_id) |>
  filter(n_distinct(run_id) >= 2, diff(range(age)) > 0.1) |>
  summarise(
    n_runs    = n_distinct(run_id),
    age_mean  = mean(age),
    age_span  = diff(range(age)),
    slope     = coef(lm(score ~ age))[2],
    .groups = "drop"
  ) |>
  filter(is.finite(slope))

child_slopes |>
  group_by(dataset_label, task_label) |>
  filter(n() >= 30) |>
  ungroup() |>
  ggplot(aes(x = slope, fill = dataset_label)) +
  geom_histogram(bins = 30, alpha = 0.7, position = "identity") +
  geom_vline(xintercept = 0, lty = 3) +
  facet_wrap(vars(task_category, task_label), scales = "free") +
  scale_fill_brewer(palette = "Set1", name = NULL) +
  labs(title = "Per-child OLS slopes (per year)",
       x = "Slope of score on age",
       y = "Children") +
  theme(legend.position = "bottom")

child_slopes |>
  group_by(dataset_label, task_label) |>
  summarise(n = n(), mean_slope = mean(slope), sd_slope = sd(slope),
            .groups = "drop") |>
  filter(n >= 30) |>
  arrange(dataset_label, task_label) |>
  knitr::kable(digits = 3)
dataset_label task_label n mean_slope sd_slope
Colombia — Bogotá Hearts and Flowers 52 0.614 1.484
Colombia — Bogotá Math 287 0.693 0.818
Colombia — Bogotá Memory 32 0.371 0.724
Colombia — Bogotá ROAR-Phoneme 56 -0.078 1.994
Colombia — Bogotá ROAR-Sentence 215 0.410 0.684
Colombia — Bogotá ROAR-Word 216 0.489 1.457
Colombia — Bogotá Sentence Understanding 75 0.494 0.650
Colombia — Bogotá Shape Rotation 50 0.609 0.729
Colombia — Caquetá/Boyacá Math 297 1.064 1.540
Colombia — Caquetá/Boyacá ROAR-Phoneme 307 0.514 1.686
Colombia — Caquetá/Boyacá ROAR-Sentence 263 0.301 0.836
Colombia — Caquetá/Boyacá ROAR-Word 295 0.821 1.750
Germany — Leipzig Hearts and Flowers 207 1.749 8.785
Germany — Leipzig Math 201 -0.217 4.071
Germany — Leipzig Memory 194 0.491 2.037
Germany — Leipzig Pattern Matching 182 -0.809 4.932
Germany — Leipzig ROAR-Sentence 34 0.438 1.632
Germany — Leipzig ROAR-Word 37 -0.996 4.505
Germany — Leipzig Same and Different 196 0.825 4.389
Germany — Leipzig Sentence Understanding 147 -0.084 2.338
Germany — Leipzig Shape Rotation 168 0.400 3.319
Germany — Leipzig Stories (ToM) 187 -0.328 2.626
Germany — Leipzig Vocabulary 201 0.306 3.200
Canada — Ontario Hearts and Flowers 38 1.281 2.301
Canada — Ontario Math 31 1.309 1.773
Canada — Ontario Memory 33 0.354 0.746
Canada — Ontario Pattern Matching 30 0.594 2.003
Canada — Ontario Shape Rotation 33 0.667 1.393

Save outputs

write_rds(within_slopes,  here("data", "growth_within_slopes.rds"))
write_rds(slope_compare,  here("data", "growth_slope_comparison.rds"))
write_rds(child_slopes,   here("data", "growth_child_slopes.rds"))

glue("Saved within-slope and per-child slope tables to data/.")
Saved within-slope and per-child slope tables to data/.

Open questions for 02

  • The CO-bog 1-year gap means most kids only have 2 timepoints. That’s enough to estimate a slope per child, but the per-individual SE is large. The latent-growth approach in 02 pools across tasks/constructs.
  • mpieva-de’s 3- and 7-month gaps give a within-year change estimate that should be small in absolute terms; per-child OLS slopes there are noisy.
  • Tasks with adaptive/non-adaptive mixing (vocab in mpieva-de especially) might bias estimates; flagged again in 02.