sim.data.TIRT: Simulate Data from the Thurstonian IRT (TIRT) Model

In ForceChoice: Forced-Choice Modeling Based on Item Response Theory and Cognitive Diagnostic Models

Simulate Data from the Thurstonian IRT (TIRT) Model

Description

Generates forced-choice pairwise comparison data under the Thurstonian IRT framework. Each statement loads on exactly one latent dimension; pairwise latent differences with probit link determine binary outcomes. Supports RANK, MOLE, and PICK response types. For each pair (i,k), the simulated comparison uses -\gamma_{ik} + \lambda_i q_i'\theta_j - \lambda_k q_k'\theta_j + \epsilon_i - \epsilon_k, with \epsilon_i \sim N(0,\psi_i^2).

Usage

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

Arguments

N.person	Integer; number of persons (default: 1000).
N.block	Integer; number of blocks (default: 10).
I.block	Integer; items per block (default: 2).
D	Integer; number of latent dimensions (default: 3, >= 2).
fc.type	Character; "RANK" (default), "MOLE", or "PICK".
control	Optional list with entries Q.matrix, block.items, lambda, psi2, gamma.matrix, gamma.item, Corr.

Value

An object of class "data.TIRT" containing data, response, theta, par, Q.matrix, block.items, Corr, gamma.matrix, lambda, psi2, pairs.value, and data-generating arguments.

See Also

fit.TIRT, model.TIRT

Examples

set.seed(123)
sim <- sim.data.TIRT(N.person = 20, N.block = 3, I.block = 2,
                     D = 2, fc.type = "RANK")
str(sim$data)
head(sim$response)
dim(sim$Q.matrix)

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