Conditional Item Infit MSQ for Multiply Imputed Data

Extends RMitemInfit to work with multiply imputed datasets produced by the mice package. Computes conditional infit MSQ on each imputed dataset and pools the results using Rubin's rules.

Usage

RMitemInfitMI(mids_object, cutoff = NULL, output = "kable", sort)

Arguments

mids_object

A mids object (multiply imputed dataset) as returned by mice::mice(). Each completed dataset must contain only the item response columns to be analysed (i.e., no ID or grouping variables). Items must be scored starting at 0 (non-negative integers).

cutoff

Optional. Default NULL (no cutoff applied). Can be:

• The return value of RMitemInfitCutoff or RMitemInfitCutoffMI (a list with $item_cutoffs): the data.frame is extracted automatically and metadata is included in the kable caption.

• The $item_cutoffs data.frame directly: must have columns Item, infit_low, and infit_high. When provided, adds columns Infit_low, Infit_high, and Flagged to the result. Flagged is a character column labelling the misfit direction: "overfit" (pooled infit below the range), "underfit" (above), or "" (within range).

output

Character string controlling the return value. Either "kable" (default) for a formatted knitr::kable() table, or "dataframe" for the underlying data.frame.

sort

Optional character string. When sort = "infit", rows are sorted by Infit_MSQ in descending order before output.

Value

• If output = "kable": a knitr_kable object (plain text table via format = "pipe") with columns "Item", "Infit MSQ", "Infit SE", "Relative location", and a caption noting the number of imputations and complete cases. When cutoff is provided, columns "Infit low", "Infit high", and "Flagged" are also included.

• If output = "dataframe": a data.frame with columns Item, Infit_MSQ, Infit_SE, and Relative_location. When cutoff is provided, columns Infit_low, Infit_high, and Flagged are also included (inserted after Infit_SE, before Relative_location). Flagged is a character column ("overfit" / "underfit" / ""), not the previous logical.

Details

For each of the m imputed datasets, the function:

1. Fits a Rasch model by CML via psychotools::pcmodel() (a dichotomous item is a 2-category partial credit model), consistent with RMitemInfit and the rest of the package.

2. Computes conditional infit MSQ and its standard error via iarm::out_infit().

3. Computes item locations (mean of the grand-mean-centred CML Andrich thresholds) and the mean WLE person location.

The per-imputation estimates are then pooled using Rubin's rules:

Pooled MSQ

The mean of the m infit MSQ point estimates.

Within-imputation variance

The mean of the m squared standard errors.

Between-imputation variance

The sample variance of the m point estimates.

Total variance

Within + (1 + 1/m) * Between.

Pooled SE

The square root of the total variance.

Relative item location is the mean of per-imputation relative locations (item location minus sample mean person location).

Caveat on the pooled SE. The within-imputation variance is the squared conditional infit SE from iarm::out_infit(). Müller (2020) showed that this asymptotic SE is an unreliable measure of uncertainty for the conditional infit statistic; Rubin's pooled SE inherits that limitation, so the Infit_SE/Infit SE column should be read as an approximate indication of imputation-related variability rather than a trustworthy inferential standard error. For item misfit decisions, prefer the simulation-based cutoffs from RMitemInfitCutoffMI.

Imputed datasets that cause model convergence failures are dropped with a warning. If all imputations fail, the function stops with an error. At least two successful imputations are required to estimate between-imputation variance.

The mice and iarm packages must be installed (they are in Suggests, not Imports).

References

Müller, M. (2020). Item fit statistics for Rasch analysis: Can we trust them? Journal of Statistical Distributions and Applications, 7(5). doi:10.1186/s40488-020-00108-7

See also

RMitemInfit, RMitemInfitCutoffMI

Examples

# \donttest{
if (requireNamespace("mice", quietly = TRUE) &&
    requireNamespace("iarm", quietly = TRUE) &&
    requireNamespace("ggdist", quietly = TRUE)) {
  # Create example data with ~10% MCAR missingness
  set.seed(42)
  mat <- matrix(sample(0:1, 200 * 8, replace = TRUE), nrow = 200, ncol = 8)
  mat[sample(length(mat), round(0.10 * length(mat)))] <- NA
  sim_data <- as.data.frame(mat)
  colnames(sim_data) <- paste0("Item", 1:8)

  # mice's ordinal method (`polr`) requires the items to be ordered
  # factors, so code them as such before imputing. RMitemInfitMI()
  # converts the completed factors back to numeric internally.
  sim_data[] <- lapply(sim_data, function(x) factor(x, ordered = TRUE))

  # Impute (use more imputations, e.g. m = 5+, in real analyses)
  imp <- mice::mice(sim_data, m = 2, method = "polr", seed = 123,
                    printFlag = FALSE)

  # Pooled infit table (no cutoffs)
  RMitemInfitMI(imp)

  # With simulation-based cutoffs
  # (use more iterations, e.g. 250+, in real analyses)
  cutoff_mi <- RMitemInfitCutoffMI(imp, iterations = 50, parallel = FALSE,
                                seed = 42)
  RMitemInfitMI(imp, cutoff = cutoff_mi)

  # As data.frame
  df <- RMitemInfitMI(imp, cutoff = cutoff_mi, output = "dataframe")
}
# }