simIPD: Simulated CAT Data for Item Parameter Drift (IPD) Detection

In irtQ: Unidimensional Item Response Theory Modeling

Simulated CAT Data for Item Parameter Drift (IPD) Detection

Description

A simulated dataset designed to illustrate the use of the ripd function for detecting item parameter drift (IPD) in computerized adaptive testing (CAT). The dataset represents one replication of a CAT-based IPD simulation study in which 5% of a 360-item pool (18 items) had both their discrimination (a) and difficulty (b) parameters drift downward by 0.5, under a 30-item adaptive test where all focal group examinees were exposed to the drifted items (100% exposure rate).

The data reflect a workflow of IPD detection using the residual-based IPD (RIPD) framework (Lim & Han, in press): a focal group of examinees takes a CAT using a drifted item pool, and a synthetic reference group is created by re-running the CAT with the focal group's ability estimates as true abilities but with the original (non-drifted) item parameters. RIPD statistics are then used to detect which items have drifted between the two groups.

Usage

simIPD

Format

A named list with eight elements:

item_par

A data frame with 360 rows and 6 columns containing the original (pre-drift) item parameters in irtQ format (columns: id, cats, model, par.1, par.2, par.3). All items follow the 3PLM.

key_item

An integer vector of length 90 giving the row indices (in item_par) of the key items - items selected by a preliminary CAT simulation as highly exposed and therefore most relevant for IPD analysis.

item.skip

An integer vector of length 270 giving the row indices of non-key items that should be excluded from RIPD analysis (i.e., the complement of key_item in 1:360). Pass this vector to the item.skip argument of ripd().

ipd_item

An integer vector of length 18 giving the row indices of items that were subjected to IPD manipulation. These 18 items (5% of the 360-item pool) had both their discrimination (a) and difficulty (b) parameters decreased by 0.5. All 18 items are members of key_item.

foc_resp

An integer matrix of dimensions 3000 x 360 containing the focal group CAT response data. Each row is one examinee; each column corresponds to an item in item_par. Because CAT administers only 30 items per examinee, approximately 92% of entries are NA. Responses were generated using the drifted item parameters (all focal examinees were exposed to IPD items; exposure rate = 100%).

foc_score

A numeric vector of length 3000 containing the focal group final maximum likelihood (ML) theta estimates obtained from the CAT.

ref_resp

An integer matrix of dimensions 3000 x 360 containing the synthetic reference group CAT response data (same sparsity structure as foc_resp). The reference group was constructed by: (1) using foc_score as true ability values (1F scaling, i.e., the reference group has the same size as the focal group); (2) generating item responses from the original (non-drifted) item parameters; and (3) running an independent CAT simulation. This synthetic reference group mirrors the construction described in Lim & Han (in press).

ref_score

A numeric vector of length 3000 containing the synthetic reference group final ML theta estimates.

Details

Simulation conditions:

• Item pool: 360 three-parameter logistic model (3PLM) items

• Test length: 30 items per examinee

• Item selection: Maximum Fisher Information (MFI) with target exposure rate 0.30

• Focal group: n = 3{,}000; true abilities drawn from N(0, 1)

• Reference group: n = 3{,}000 (1F); true abilities = foc_score

• IPD items: 18 (5% of 360), randomly drawn from key_item

• IPD manipulation: both a and b decreased by 0.50

• Interim scoring: EAP; final scoring: ML

• Scaling constant: D = 1.7

• Random seed: 2024

Note on reference group size: A 1F reference group (same size as the focal group) is used here for compactness. In practice, larger synthetic reference groups (e.g., 3F - 8F) are recommended to improve RIPD detection power (Lim & Han, in press). A larger reference group can be created by replicating the focal theta estimates: e.g., rep(foc_score, times = 3) for a 3F group, then re-running the CAT simulation with the original item parameters.

References

Lim, H., & Han, K. T. (in press). IRT residual-based approach to detecting item parameter drift in CAT. Journal of Educational and Behavioral Statistics.

See Also

ripd, pcd2, simCAT_DC, simCAT_MX

Examples

data(simIPD)
str(simIPD, max.level = 1)

# Item parameter data frame (first 6 rows)
head(simIPD$item_par)

# Focal group response matrix (sparse)
dim(simIPD$foc_resp)
mean(is.na(simIPD$foc_resp))  # ~0.92 (92% NA due to CAT)

irtQ documentation built on July 27, 2026, 9:08 a.m.