sim.data.FCGDINA: Simulate Forced-Choice GDINA Data
In ForceChoice: Forced-Choice Modeling Based on Item Response Theory and Cognitive Diagnostic Models

sim.data.FCGDINA

R Documentation

Simulate Forced-Choice GDINA Data

Description

Generates forced-choice response data from a cognitive diagnostic item model. The item-level model may be DINA, DINO, ACDM, or GDINA. The resulting statement endorsement probabilities are transformed into forced-choice response probabilities for "RANK", "MOLE", or "PICK" blocks using the same sequential Luce–Plackett mechanism used by sim.data.FCMIRT and sim.data.FCGGUM.

Usage

sim.data.FCGDINA(
  N.person = 1000,
  N.block = 10,
  I.block = 2,
  D = 3,
  model = "GDINA",
  fc.type = "RANK",
  control = NULL
)

Arguments

`N.person`	Number of persons.
`N.block`	Number of forced-choice blocks.
`I.block`	Number of items per block when `control$block.items` is not supplied. Must be at least 2.
`D`	Number of latent attributes. If `control$Q.matrix` is supplied, `D` is reset to `ncol(control$Q.matrix)`.
`model`	CDM item model: `"DINA"`, `"DINO"`, `"ACDM"`, or `"GDINA"`.
`fc.type`	Forced-choice response type: `"RANK"`, `"MOLE"`, or `"PICK"`. A scalar value is recycled to all blocks; a vector of length `B` may be supplied for mixed block formats.
`control`	Optional named list controlling the data-generating process. Supported entries are described below.

Value

An object of class "data.FCGDINA", a list containing:

data: N \times B character matrix of forced-choice responses, such as "1>3>2" for ranking blocks.
response: N \times B integer matrix of 1-based pattern indices matching patterns.
alpha: N \times D binary matrix of true latent attribute profiles.
gs: I \times 2 matrix of item probability bounds P0 and P1.
delta.list: List of true CDM delta vectors, one per statement.
design.matrix.list: List of CDM design matrices used to map delta parameters to item endorsement probabilities.
Q.matrix: I \times D Q-matrix.
block.items: List of statement indices per forced-choice block.
model: CDM item model used for simulation.
patterns: List of observed response-pattern matrices per block.
patterns.total: List of full-ranking pattern matrices per block.
prob.item: N \times I matrix of item-level endorsement probabilities for sampled persons.
prob.states: I \times 2^D matrix of item endorsement probabilities for every attribute pattern.
prob: N \times \sum_b P_b matrix of forced-choice response-pattern probabilities.
N.person, N.block, I.block, D, I.states, fc.type: Final data-generating dimensions and response type.
call, arguments: Matched call and effective simulation arguments.

Data-Generating Process

The simulation proceeds in four steps:

Generate or validate the Q-matrix and forced-choice block structure.
Generate latent attribute profiles \boldsymbol{\alpha}_n.
Generate item-level CDM endorsement probabilities using guessing and slipping-style bounds P0 and P1; then recover the corresponding CDM delta parameters from the design matrix.
Convert item endorsement probabilities into block-level forced-choice pattern probabilities and sample observed responses.

Attribute profiles can be generated from a higher-order latent trait model, a thresholded multivariate normal model, a uniform distribution over all attribute patterns, or supplied directly through control$alpha.

Control List

Q.matrix: Optional I \times D binary Q-matrix. If omitted, a Q-matrix is generated by sim.data.Q.CDM().
block.items: Optional list of item indices per block. If omitted, blocks are formed sequentially using N.block and I.block.
single: Logical passed to sim.data.Q.CDM() when Q.matrix is generated internally. Default TRUE.
alpha: Optional N \times D binary matrix of true attribute profiles. If supplied, latent attributes are not generated.
distribution: Latent attribute distribution when alpha is not supplied. Options are "horder" (default; alias "higher.order"), "mvnorm", and "uniform".
delta1, delta0, theta: Higher-order discrimination, threshold, and person trait values used when distribution = "horder". Defaults are generated from log-normal, normal, and standard normal distributions.
Corr, threshold: Correlation matrix and thresholds used when distribution = "mvnorm".
gs: Optional I \times 2 matrix with columns P0 and P1; P0 is the lower endorsement probability and P1 is the upper endorsement probability for each statement. Defaults are sampled from U(0, .2) and U(.8, 1).
mono.constraint: Logical; whether to enforce monotonic item probabilities for GDINA item generation. Default TRUE.

References

de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76(2), 179–199. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/s11336-011-9207-7")}

Examples

set.seed(123)
sim <- sim.data.FCGDINA(N.person = 20, N.block = 3, I.block = 2,
                        D = 2, model = "DINA", fc.type = "RANK")

str(sim$data)
head(sim$response)
head(sim$alpha)
sim$Q.matrix

# Mixed response formats across blocks.
sim.mix <- sim.data.FCGDINA(
  N.person = 12, N.block = 3, I.block = 3, D = 2,
  model = "GDINA", fc.type = c("RANK", "MOLE", "PICK")
)
vapply(sim.mix$patterns, nrow, integer(1))

ForceChoice documentation built on Sept. 13, 2026, 1:06 a.m.