Item Restscore Analysis — RMitemRestscore • easyRasch2

Computes observed and model-expected item-restscore correlations using iarm::item_restscore(), and enriches the output with the absolute difference between observed and expected values, item average locations, and item locations relative to the sample mean person location.

Usage

RMitemRestscore(data, output = "kable", sort, p.adj = "BH")

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.
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 = "diff", rows are sorted by the absolute magnitude of Difference in descending order, so that both over- and underfitting items appear near the top.
p.adj: Character string specifying the p-value adjustment method passed to iarm::item_restscore(). Default "BH" (Benjamini-Hochberg). See stats::p.adjust() for available methods.

Value

If output = "kable": a knitr_kable object (plain text table via format = "pipe") with columns for item name, observed and expected restscore correlations, the signed difference (observed minus expected), adjusted p-value, significance level, item location, and item location relative to the sample mean person location.
If output = "dataframe": a data.frame with columns Item, Observed, Expected, Difference, p_adjusted, Significance, Location, and Relative_location.

The Difference column is signed (observed minus expected): positive values indicate that the item correlates more strongly with the rest-score than the Rasch model predicts (over-discrimination / overfit, often associated with local dependence), and negative values indicate weaker-than-expected association (under-discrimination / underfit, often associated with multidimensionality or noise).

Details

Item-restscore correlations using Goodman-Kruskal's gamma (Kreiner, 2011) measure the association between a person's score on a single item and their total score on the remaining items (the "restscore"). Under a correctly fitting Rasch model, observed and model-expected correlations should agree closely.

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 the row-means of the threshold parameter table returned by eRm::thresholds(). 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

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{
# Simulate binary item response data (8 items, 200 persons)
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)

# Default kable output
RMitemRestscore(sim_data)
#> 
#> 
#> 
#> |Item  | Observed value| Expected value| Difference| Adj. p-value (BH)|p-value sign. | Location| Rel. location|
#> |:-----|--------------:|--------------:|----------:|-----------------:|:-------------|--------:|-------------:|
#> |Item1 |           0.00|           0.01|      -0.01|             0.955|              |    -0.20|         -0.23|
#> |Item2 |           0.00|           0.01|      -0.01|             0.955|              |     0.16|          0.13|
#> |Item3 |          -0.01|           0.01|      -0.02|             0.955|              |     0.02|         -0.01|
#> |Item4 |          -0.05|           0.01|      -0.06|             0.955|              |    -0.02|         -0.05|
#> |Item5 |           0.07|           0.01|       0.06|             0.955|              |     0.12|          0.09|
#> |Item6 |          -0.04|           0.01|      -0.05|             0.955|              |    -0.06|         -0.09|
#> |Item7 |           0.15|           0.01|       0.14|             0.955|              |    -0.02|         -0.05|
#> |Item8 |          -0.01|           0.01|      -0.02|             0.955|              |     0.00|         -0.03|

# Sorted by absolute difference
RMitemRestscore(sim_data, sort = "diff")
#> 
#> 
#> 
#> |Item  | Observed value| Expected value| Difference| Adj. p-value (BH)|p-value sign. | Location| Rel. location|
#> |:-----|--------------:|--------------:|----------:|-----------------:|:-------------|--------:|-------------:|
#> |Item7 |           0.15|           0.01|       0.14|             0.955|              |    -0.02|         -0.05|
#> |Item4 |          -0.05|           0.01|      -0.06|             0.955|              |    -0.02|         -0.05|
#> |Item5 |           0.07|           0.01|       0.06|             0.955|              |     0.12|          0.09|
#> |Item6 |          -0.04|           0.01|      -0.05|             0.955|              |    -0.06|         -0.09|
#> |Item3 |          -0.01|           0.01|      -0.02|             0.955|              |     0.02|         -0.01|
#> |Item8 |          -0.01|           0.01|      -0.02|             0.955|              |     0.00|         -0.03|
#> |Item1 |           0.00|           0.01|      -0.01|             0.955|              |    -0.20|         -0.23|
#> |Item2 |           0.00|           0.01|      -0.01|             0.955|              |     0.16|          0.13|

# Return as data.frame for further processing
df <- RMitemRestscore(sim_data, output = "dataframe")
#> 
# }