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Conditional Item Infit MSQ

Source: R/conditional_infit.R
RMiteminfit.Rd

Computes conditional infit mean-square (MSQ) statistics for each item using iarm::out_infit(), enriched with item locations relative to the sample mean person location.

Usage

RMitemInfit(data, cutoff = NULL, output = "kable", sort)

Arguments

data

A data.frame or matrix of item responses. Items must be scored starting at 0 (non-negative integers). Missing values (NA) are allowed, but at least one complete case (row with no NA) must be present.

cutoff

Optional. Default NULL (no cutoff applied, behaviour is identical to the current version). Can be:

  • The return value of RMitemInfitCutoff (a list with $item_cutoffs): the data.frame is extracted automatically and the number of simulation iterations, cutoff_method, and hdci_width are included in the kable caption.

  • The $item_cutoffs data.frame from RMitemInfitCutoff directly: must have columns Item, infit_low, and infit_high. When provided, adds columns Infit_low, Infit_high, and Flagged (logical; TRUE when Infit_MSQ falls outside the credible range) 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", and "Relative location", and a caption showing the number of complete cases. When cutoff is provided, columns "Infit low", "Infit high", and "Flagged" are also included, and the caption notes the simulation-based cutoffs.

  • If output = "dataframe": a data.frame with columns Item, Infit_MSQ, and Relative_location. When cutoff is provided, columns Infit_low, Infit_high, and Flagged are also included (inserted after Infit_MSQ, before Relative_location).

Details

Infit MSQ is a weighted fit statistic that emphasises deviations near the item location. Values close to 1.0 indicate good fit. Values substantially above 1.0 suggest underfit (unexpected responses), while values substantially below 1.0 suggest overfit (overly predictable responses). The definition of "substantially" depends on several factors such as sample size, and needs to be determined by simulation using RMitemInfitCutoff. There is no general rule-of-thumb value that is correct.

Conditional infit MSQ statistics are computed via iarm::out_infit(), which uses the conditional distribution of the sufficient statistics (Müller, 2020). Only complete cases (rows without any NA) are used in the conditional fit calculation.

For dichotomous data (maximum score = 1), a Rasch model is fitted via eRm::RM(). Item locations are the negative beta parameters. Person locations are estimated via eRm::person.parameter().

For polytomous data (maximum score > 1), a Partial Credit Model is fitted via eRm::PCM(). Item average locations are taken from the "Location" column of the threshold parameter table returned by eRm::thresholds(); if that column is absent, row means of the threshold columns are used instead. Person locations are estimated via eRm::person.parameter().

Relative item location is defined as the item's average location minus the sample mean person location, providing a measure of item targeting.

The iarm package must be installed (it is 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

RMitemInfitCutoff

Examples

# \donttest{
# Simulate binary item response data (5 items, 40 persons)
set.seed(42)
sim_data <- as.data.frame(
  matrix(sample(0:1, 40 * 5, replace = TRUE), nrow = 40, ncol = 5)
)
colnames(sim_data) <- paste0("Item", 1:5)

# Default kable output
RMitemInfit(sim_data)
#> 
#> 
#> Table: MSQ values based on conditional estimation (n = 40 complete cases).
#> 
#> |Item  | Infit MSQ| Relative location|
#> |:-----|---------:|-----------------:|
#> |Item1 |     1.049|             -0.03|
#> |Item2 |     0.929|             -0.54|
#> |Item3 |     0.828|             -0.23|
#> |Item4 |     1.216|              0.26|
#> |Item5 |     0.931|             -0.76|

# Sorted by infit MSQ descending
RMitemInfit(sim_data, sort = "infit")
#> 
#> 
#> Table: MSQ values based on conditional estimation (n = 40 complete cases).
#> 
#> |Item  | Infit MSQ| Relative location|
#> |:-----|---------:|-----------------:|
#> |Item4 |     1.216|              0.26|
#> |Item1 |     1.049|             -0.03|
#> |Item5 |     0.931|             -0.76|
#> |Item2 |     0.929|             -0.54|
#> |Item3 |     0.828|             -0.23|

# Return as data.frame for further processing
df <- RMitemInfit(sim_data, output = "dataframe")
# }
# \donttest{
# Simulation-based cutoffs (100 Monte-Carlo iterations)
cutoff_res <- RMitemInfitCutoff(sim_data, iterations = 100, parallel = FALSE,
                            seed = 42)
RMitemInfit(sim_data, cutoff = cutoff_res)
#> 
#> 
#> Table: MSQ values based on conditional estimation (n = 40 complete cases). Cutoff values based on 99 simulation iterations (99.9% HDCI).
#> 
#> |Item  | Infit MSQ| Infit low| Infit high|Flagged | Relative location|
#> |:-----|---------:|---------:|----------:|:-------|-----------------:|
#> |Item1 |     1.049|     0.576|      1.489|FALSE   |             -0.03|
#> |Item2 |     0.929|     0.660|      1.537|FALSE   |             -0.54|
#> |Item3 |     0.828|     0.547|      1.374|FALSE   |             -0.23|
#> |Item4 |     1.216|     0.699|      1.349|FALSE   |              0.26|
#> |Item5 |     0.931|     0.689|      1.315|FALSE   |             -0.76|
RMitemInfit(sim_data, cutoff = cutoff_res, output = "dataframe")
#>    Item Infit_MSQ Infit_low Infit_high Flagged Relative_location
#> 1 Item1     1.049     0.576      1.489   FALSE             -0.03
#> 2 Item2     0.929     0.660      1.537   FALSE             -0.54
#> 3 Item3     0.828     0.547      1.374   FALSE             -0.23
#> 4 Item4     1.216     0.699      1.349   FALSE              0.26
#> 5 Item5     0.931     0.689      1.315   FALSE             -0.76
# }