Simulation-Based Infit MSQ Cutoff Determination

Uses parametric bootstrap simulation to determine appropriate cutoff values for RMitemInfit. This function simulates data from a correctly fitting Rasch model that mimics your data and returns per-item empirical cutoffs.

Usage

RMitemInfitCutoff(
  data,
  iterations = 400,
  parallel = TRUE,
  n_cores = NULL,
  verbose = FALSE,
  seed = NULL,
  cutoff_method = "hdci",
  hdci_width = 0.95,
  dgp = c("resample", "conditional")
)

Arguments

data

A data.frame or matrix of item responses. Items must be scored starting at 0 (non-negative integers). Only complete cases (rows without any NA) are used.

iterations

Integer. Number of simulation iterations (default 400).

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 (single core) processing.

verbose

Logical. Show a progress bar (default FALSE).

seed

Integer or NULL. Random seed for reproducibility. See easyRasch2-reproducibility for what this guarantees and how it interacts with parallel.

cutoff_method

Character string specifying how cutoff intervals are computed. Either "hdci" (default) for the Highest Density Interval via ggdist::hdci(), or "quantile" for the 2.5th/97.5th percentiles via stats::quantile().

hdci_width

Numeric. Width of the HDCI when cutoff_method = "hdci". Default is 0.95 (95% HDCI). Ignored when cutoff_method = "quantile".

The interval is a description of where a fitting item's statistic is expected to fall, not a decision rule. Flagging every item outside a width-w interval tests all k items at once, so the family-wise error rate is 1 - w^k, which is 37% for a 95% interval over nine items. Decisions should come from the corrected p-value instead (RMitemInfit with p_value = NULL and the full object returned here). The default was 0.999 up to and including version 1.1.1, which needs roughly 5000 iterations before the interval reaches its stated width; 0.95 reaches it by about 1000, so the band shown to readers means close to what it says (Johansson, 2026).

dgp

Character. Data-generating process for the parametric bootstrap. "resample" (default) resamples WLE person locations with replacement and simulates responses under the model (a marginal null). "conditional" simulates each respondent's pattern from the exact Rasch conditional distribution given their observed total score, item parameters fixed (a conditional null). Because the conditional infit/outfit statistic is itself conditional on the total score, "conditional" is its naturally matched null. Experimental.

Value

A list with components:

results

data.frame with columns iteration, Item, InfitMSQ, OutfitMSQ (one row per item per successful iteration).

item_cutoffs

data.frame with per-item cutoff summaries: Item, infit_low, infit_high, outfit_low, outfit_high. Bounds are computed using the method specified by cutoff_method.

actual_iterations

Number of successful iterations. Everything downstream rests on this rather than on iterations, so it is the number to report.

requested_iterations

The iterations argument, kept so callers can tell how many simulated datasets were discarded.

sample_n

Number of complete cases used.

sample_n_total

Number of respondents in the raw input data, before the complete-case filter.

sample_has_na

Logical. Whether the raw input data contained any missing values.

sample_summary

Summary statistics of estimated person parameters.

item_names

Character vector of item names from data.

cutoff_method

The method used to compute cutoffs ("hdci" or "quantile").

hdci_width

The HDCI width used (only meaningful when cutoff_method = "hdci").

dgp

The data-generating process used ("resample" or "conditional").

Details

The generating model is CML item parameters (via psychotools) with WLE person locations. For each iteration a dataset is simulated under the chosen dgp, the model is refitted by CML (psychotools::pcmodel(), which handles dichotomous and polytomous data and is accepted by iarm), and conditional infit and outfit MSQ are computed via iarm::out_infit(). The distribution of these statistics across iterations provides empirical critical values per item. Failed iterations (e.g., degenerate simulated data) are silently discarded.

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

Johansson, M. (2025). Detecting item misfit in Rasch models. Educational Methods & Psychometrics, 3(18). doi:10.61186/emp.2025.5

Johansson, M. (2026). Simulation-based cutoffs for conditional item fit in Rasch models: Iterations, multiplicity correction, and decision stability. PsyArXiv. doi:10.31234/osf.io/7pqz4_v2

See also

RMitemInfit

Examples

# \donttest{
if (requireNamespace("iarm", quietly = TRUE) &&
    requireNamespace("ggdist", quietly = TRUE)) {
  set.seed(42)
  sim_data <- as.data.frame(
    matrix(sample(0:1, 200 * 10, replace = TRUE), nrow = 200, ncol = 10)
  )
  colnames(sim_data) <- paste0("Item", 1:10)

  # Run 100 iterations sequentially for a quick demo
  cutoff_res <- RMitemInfitCutoff(sim_data, iterations = 100,
                                  parallel = FALSE, seed = 42)
  cutoff_res$item_cutoffs

  # Use the cutoffs in RMitemInfit()
  RMitemInfit(sim_data)
}
#> 
#> 
#> Table: MSQ values based on conditional estimation. n = 200 respondents.
#> 
#> |Item   | Infit MSQ| Relative location|
#> |:------|---------:|-----------------:|
#> |Item1  |     1.008|             -0.22|
#> |Item2  |     0.999|              0.14|
#> |Item3  |     0.994|              0.00|
#> |Item4  |     1.055|             -0.04|
#> |Item5  |     1.004|              0.10|
#> |Item6  |     1.032|             -0.08|
#> |Item7  |     0.943|             -0.04|
#> |Item8  |     0.988|             -0.02|
#> |Item9  |     0.933|              0.12|
#> |Item10 |     1.044|              0.38|
# }