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.

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).

Details

For each of the m imputed datasets, the function:

1. Fits a Rasch model (eRm::RM() for dichotomous data or eRm::PCM() for polytomous data).

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

3. Computes item and person locations.

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).

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).

See also

RMitemInfit, RMitemInfitCutoffMI

Examples

# \donttest{
if (requireNamespace("mice", quietly = TRUE)) {
  # Create example data with missing values
  set.seed(42)
  sim_data <- as.data.frame(
    matrix(sample(0:1, 200 * 8, replace = TRUE), nrow = 200, ncol = 8)
  )
  colnames(sim_data) <- paste0("Item", 1:8)
  sim_data[sample(length(sim_data), 0.10 * length(sim_data))] <- NA

  # 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")
}
# }