Bootstrap Item-Restscore Misfit Detection

Non-parametric bootstrap of item-restscore fit using iarm::item_restscore(). For each iteration, a sample of size samplesize is drawn from data with replacement, the appropriate Rasch model is refitted, and item-restscore results are classified as "overfit", "underfit", or "no misfit" based on the BH-adjusted p-value (< .05) and the sign of expected - observed. The function returns the percentage of iterations in which each item is flagged.

Usage

RMitemRestscoreBoot(
  data,
  iterations = 200,
  samplesize = 600,
  parallel = TRUE,
  n_cores = NULL,
  cutoff = 5,
  verbose = FALSE,
  seed = NULL,
  output = "kable"
)

Arguments

data: A data.frame or matrix of item responses. Items must be scored starting at 0 (non-negative integers).
iterations: Integer. Number of bootstrap samples (default 200).
samplesize: Integer. Size of each bootstrap sample (default 600). Must not exceed nrow(data).
parallel: Logical. Use parallel processing via mirai if available (default TRUE).
n_cores: Integer or NULL. Number of parallel workers. When NULL, getOption("mc.cores") is checked first. If neither is set and parallel = TRUE, a warning is issued and execution falls back to sequential processing.
cutoff: Numeric. Items flagged in fewer than this percentage of iterations are excluded from the kable output (default 5). Has no effect when output = "dataframe" or output = "raw".
verbose: Logical. Show a progress bar (default FALSE).
seed: Integer or NULL. Random seed for reproducibility.
output: Either "kable" (default) for a formatted knitr::kable() table, "dataframe" for the per-item summary data.frame, or "raw" for the per-iteration long data.frame (useful for custom plotting).

Value

If output = "kable": a knitr_kable object listing items flagged in more than cutoff% of iterations, with columns Item, Item-restscore result, % of iterations, Conditional MSQ infit, and Relative item location, and a caption noting iteration count, bootstrap size, and number of complete cases.
If output = "dataframe": a data.frame with one row per item × classification combination (Item, item_restscore, n, percent, Infit_MSQ, Relative_location), including "no misfit" rows.
If output = "raw": a long data.frame with one row per item × successful iteration (iteration, Item, item_restscore, diff, diff_abs), where diff = expected - observed.

Details

Useful with large samples, where the asymptotic test underlying RMitemRestscore can flag items that are not practically misfitting; bootstrapping gives a more nuanced view of the probability of an item actually being misfit.

The full-sample model is fitted by CML via psychotools::pcmodel() (a dichotomous item is a 2-category partial credit model), and item locations (mean of the grand-mean-centred CML Andrich thresholds) and the mean WLE person location are computed from it — consistent with RMitemRestscore and the rest of the package. Each bootstrap iteration draws a sample of size samplesize with replacement and refits via psychotools::pcmodel(..., hessian = FALSE) for speed; iarm::item_restscore() accepts the fitted model.

Conditional infit MSQ (computed once on the full sample via iarm::out_infit()) and relative item locations are reported alongside the bootstrap percentages for context. The item-restscore classification and the infit statistic are conditional and engine-invariant; only the relative-item location shifts slightly relative to the previous eRm implementation, because it now uses the WLE person mean (finite at extreme scores) rather than the eRm MLE mean.

Iterations that fail (e.g., due to convergence issues on a degenerate bootstrap sample) are silently discarded; the caption / actual_iterations reflects only successful runs.

Parallel processing is provided by the mirai package (optional). Install it with install.packages("mirai") to enable parallelisation.

The iarm package must be installed (it is in Suggests, not Imports).

References

Kreiner, S. (2011). A Note on Item-Restscore Association in Rasch Models. Applied Psychological Measurement, 35(7), 557-561. doi:10.1177/0146621611410227

Examples

# \donttest{
if (requireNamespace("iarm", quietly = TRUE)) {
set.seed(42)
sim_data <- as.data.frame(
  matrix(sample(0:1, 400 * 8, replace = TRUE), nrow = 400, ncol = 8)
)
colnames(sim_data) <- paste0("Item", 1:8)

# Few iterations for a fast example; use 100+ in real analyses
# Default kable output (only items flagged > cutoff%)
RMitemRestscoreBoot(sim_data, iterations = 50, samplesize = 300,
                parallel = FALSE, seed = 1)

# Per-item summary data.frame (all classifications, including "no misfit")
summary_df <- RMitemRestscoreBoot(sim_data, iterations = 50, samplesize = 300,
                              parallel = FALSE, seed = 1,
                              output = "dataframe")

# Per-iteration long data for custom plotting
raw_df <- RMitemRestscoreBoot(sim_data, iterations = 50, samplesize = 300,
                          parallel = FALSE, seed = 1, output = "raw")

# Distribution of (expected - observed) across iterations, per item
if (requireNamespace("ggplot2", quietly = TRUE)) {
  library(ggplot2)
  ggplot(raw_df, aes(x = Item, y = diff)) +
    geom_hline(yintercept = 0, linetype = "dashed", colour = "grey50") +
    geom_violin(fill = "grey90", colour = NA) +
    geom_jitter(aes(colour = item_restscore),
                width = 0.15, alpha = 0.5, size = 0.8) +
    scale_colour_manual(values = c("overfit"   = "#377eb8",
                                   "underfit"  = "#e41a1c",
                                   "no misfit" = "grey60")) +
    labs(y = "Expected - observed restscore correlation",
         colour = NULL) +
    theme_minimal() +
    theme(axis.text.x = element_text(angle = 45, hjust = 1))
}
}
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