library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
✔ dplyr     1.1.4          ✔ readr     2.1.5     
✔ forcats   1.0.0          ✔ stringr   1.5.1     
✔ ggplot2   3.5.1.9000     ✔ tibble    3.2.1     
✔ lubridate 1.9.4          ✔ tidyr     1.3.1     
✔ purrr     1.0.4          
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
ℹ Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errors

library(here)

here() starts at /Users/visuallearninglab/Documents/vedi_survey/vedi

Data loading

center_vars <- function(data) {
  return(data |>
           mutate(visual_frequency_centered = scale(Frequency_numeric_val),
         total_count_centered = scale(TotalCount_numeric_val),
         interaction_count_centered = scale(InteractionCount_numeric_val),
         formats_seen_centered = scale(FormatsSeen_numeric_val),
         babiness_centered = scale(babiness_mean),
         age_centered = scale(childAge)))
}

combined_normed <- read_csv(file.path(here('data','main', 'processed'),"processed-responses.csv"))

Rows: 3403 Columns: 23
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr   (6): object, globalID, category, childSiblingAges, feedback, age_half
dbl  (15): aoa, sessionID, Frequency_normalized_val, TotalCount_normalized_v...
dttm  (2): startTimestamp, endTimestamp

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

combined_normed_summary <- read_csv(file.path(here('data','main', 'processed'),"processed-responses-summarized.csv")) |>
  arrange(object)

Rows: 49 Columns: 16
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr  (2): object, category
dbl (14): aoa, Frequency_normalized_val, TotalCount_normalized_val, Interact...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

# can't use this directly since there are multiple elements with the same AoA dependent variable value, can't add item-level random effects
centered_vars <- combined_normed |>
  filter(!is.na(InteractionCount_numeric_val) & sessionID == 1) |>
  mutate(
    InteractionCount_numeric_val = ifelse(InteractionCount_numeric_val > 0, log(InteractionCount_numeric_val), 0),
    TotalCount_numeric_val = ifelse(TotalCount_numeric_val > 0, log(TotalCount_numeric_val), 0)
  ) |>
  # we are adding new centered vars here but not using the centered vars in later analyses
  center_vars()

# can use this but it does not include anything age-related and we are just predicting object
centered_summarized_vars <- combined_normed_summary |>
  center_vars()

Helpers

make_mat <- function(df, col_name) {
  d_wide <- df |> 
  select(object, globalID, {{col_name}}) |> 
  pivot_wider(names_from = object, values_from = {{col_name}}) |> 
    #todo: can't assume all participants completed survey
  mutate(across(-globalID, ~replace_na(., 0)))
  d_mat <- d_wide %>%
  select(-globalID) %>% 
  data.frame %>%
  data.matrix
  colnames(d_mat) <- sort(unique(df$object))
  rownames(d_mat) <- d_wide$globalID
  # Requires no empty rows - `personfit` doesn't work with `removeEmptyRows=TRUE` even though the model fit will work that way. 
  d_mat <- d_mat[complete.cases(d_mat),]
  return(d_mat)
}

make_discrim_diff_plot <- function(df, input_title) {
  ggplot(df, aes(x = b, y = a, label = item_name)) +
  geom_point(aes(color=category), size=4, alpha=0.6) +
  ggrepel::geom_label_repel() +
  labs(
    title = input_title,
    x = "Difficulty",
    y = "Discrimination"
  ) +
  theme_minimal()
}

run_grm <- function(df, combined_normed_summary) {
  model_1dim <- mirt(df, 1, itemtype = "graded")
  coefs_1dim <- coef(model_1dim, simplify = TRUE, IRTpars = TRUE)$items
  # Get difficulty parameters
  difficulty_1dim <- gen.difficulty(model_1dim)
  # Calculate column means
  col_means <- colMeans(df)
  # Create a single tibble with all information
  output_tibble <- tibble(
    item_name = rownames(coefs_1dim),
   a = coefs_1dim[, "a"],                 # Discrimination parameter (slope)
    b = difficulty_1dim,     # Difficulty parameter
    mean = col_means
  ) |> left_join(combined_normed_summary |> select(object, category), by=c("item_name" = "object"))
  return(output_tibble)
}

Fitting IRT models

library(mirt) # requires package loading, not just referencing. 

Loading required package: stats4

Loading required package: lattice

d_mat_count <- make_mat(centered_vars, "TotalCount_numeric_val")

d_mat_freq <- make_mat(centered_vars, "Frequency_numeric_val")

d_mat_formats <- make_mat(centered_vars, "FormatsSeen_numeric_val")

#df <- data.frame(
#  Item = names(loadings),
#  Loading = loadings,
#  Difficulty = difficulty
#)

# Plot
#ggplot(df, aes(x = Difficulty, y = Loading, label = Item)) +
#  geom_point() +
#  geom_text(vjust = -0.5, size = 3) +
#  labs(
#    title = "Item Loadings vs. Difficulty",
#    x = "Difficulty (Mean Log Count)",
#    y = "Factor Loading (Discrimination)"
#  ) +
#  theme_minimal()

Frequency

model_1dim <- mirt(d_mat_freq, 1, itemtype = "graded")

"beach" re-mapped to ensure all categories have a distance of 1

"bird" re-mapped to ensure all categories have a distance of 1

"block" re-mapped to ensure all categories have a distance of 1

"book" re-mapped to ensure all categories have a distance of 1

"bus" re-mapped to ensure all categories have a distance of 1

"car" re-mapped to ensure all categories have a distance of 1

"elephant" re-mapped to ensure all categories have a distance of 1

"firetruck" re-mapped to ensure all categories have a distance of 1

"hand" re-mapped to ensure all categories have a distance of 1

"motorcycle" re-mapped to ensure all categories have a distance of 1

"penguin" re-mapped to ensure all categories have a distance of 1

"pool" re-mapped to ensure all categories have a distance of 1

"radio" re-mapped to ensure all categories have a distance of 1

"scissors" re-mapped to ensure all categories have a distance of 1

"slide" re-mapped to ensure all categories have a distance of 1

"spoon" re-mapped to ensure all categories have a distance of 1

"stroller" re-mapped to ensure all categories have a distance of 1

"train" re-mapped to ensure all categories have a distance of 1

"watch" re-mapped to ensure all categories have a distance of 1

Iteration: 1, Log-Lik: -3674.022, Max-Change: 0.96209
Iteration: 2, Log-Lik: -3635.790, Max-Change: 0.47086
Iteration: 3, Log-Lik: -3630.917, Max-Change: 0.20774
Iteration: 4, Log-Lik: -3629.710, Max-Change: 0.19630
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Iteration: 25, Log-Lik: -3628.220, Max-Change: 0.00009

coefs_1dim <- coef(model_1dim, simplify = TRUE, IRTpars = TRUE)$items

# Get difficulty parameters
difficulty_1dim <- gen.difficulty(model_1dim)

# Calculate column means
col_means <- colMeans(d_mat_freq)

# Create a single tibble with all information
freq_tibble <- tibble(
  item_name = rownames(coefs_1dim),
  a = coefs_1dim[, "a"],                 # Discrimination parameter (slope)
  b = difficulty_1dim,     # Difficulty parameter
  mean = col_means
) |> left_join(combined_normed_summary |> select(object, category), by=c("item_name" = "object"))

make_discrim_diff_plot(freq_tibble, "Frequency IRT")

Warning: ggrepel: 10 unlabeled data points (too many overlaps). Consider
increasing max.overlaps

Plotting ‘watch’ which has high discrimination and medium difficulty

plot(model_1dim, type = "trace", which.items = c(49, 4))

anova(model_1dim) #, model_2dim

                AIC    SABIC       HQ      BIC   logLik
model_1dim 7794.439 7502.921 8010.334 8348.698 -3628.22

Total Count

using bootCRM to look at total count. Noting here that this analysis still involves first making all counts greater than a 100 equivalent to a 100

library(EstCRM)

Loading required package: Hmisc

Attaching package: 'Hmisc'

The following objects are masked from 'package:dplyr':

    src, summarize

The following objects are masked from 'package:base':

    format.pval, units

estcrm_input <- as.data.frame(d_mat_count)
m <- ncol(estcrm_input)
# 4.605170 = ln(100)
model <- EstCRMitem(estcrm_input, rep(4.60518, m), rep(0, m))

Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced
Warning in sqrt(diag(solve(Hess))): NaNs produced

count_params <- as_tibble(model$param) |>
  mutate(item_name = rownames(coefs_1dim)) |> left_join(combined_normed_summary |> select(object, category), by=c("item_name" = "object"))
make_discrim_diff_plot(count_params, "Total count IRT")

Ball and book are still learning towards the least difficult portion which makes sense but other than that I really need to re-think this, making sure that I’m not counting interaction counts as 0 if no encounter.

Also looking at factor analysis

library(psych)

Attaching package: 'psych'

The following object is masked from 'package:Hmisc':

    describe

The following objects are masked from 'package:ggplot2':

    %+%, alpha

# One factor: similar to unidimensional IRT
fa_result <- fa(d_mat_count, nfactors = 1, rotate = "none", fm = "ml")

# View loadings (like discrimination in IRT)
loadings <- fa_result$loadings
names(loadings) <- colnames(d_mat_count)
# 'difficulty'
difficulty <- colMeans(d_mat_count)
# Factor scores (person ability estimates)
theta_hat <- fa_result$scores

Formats

formats_tibble <- run_grm(d_mat_count, combined_normed_summary)

"bear" re-mapped to ensure all categories have a distance of 1

"cat" re-mapped to ensure all categories have a distance of 1

"computer" re-mapped to ensure all categories have a distance of 1

"park" re-mapped to ensure all categories have a distance of 1

Iteration: 1, Log-Lik: -2316.220, Max-Change: 4.03548
Iteration: 2, Log-Lik: -2258.378, Max-Change: 1.36117
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make_discrim_diff_plot(formats_tibble, "Formats IRT")

Warning: ggrepel: 10 unlabeled data points (too many overlaps). Consider
increasing max.overlaps