tirt (version 0.2.0)

sim_irt: Simulate Item Response Theory Data

Description

Simulate item responses data. Support both dichotomous and polytomous responses. Provide an easy implementation with a few default settings.

Usage

sim_irt(
  n_people = 1000,
  item_structure = list(),
  theta = NULL,
  theta_mean = 0,
  theta_sd = 1
)

Value

A list containing:

resp

data.frame of responses (rows=people, cols=items)

true_params

data.frame of true item parameters

theta

vector of true latent traits

Arguments

n_people

Integer. Number of students.

item_structure

List of lists defining item blocks.

theta

Numeric vector (Optional). If provided, these exact ability values are used.

theta_mean

Numeric. Mean of latent trait (used if theta is NULL).

theta_sd

Numeric. SD of latent trait (used if theta is NULL).

Examples

  # 1. Define the Test Blueprint
  # We want:
  # - 10 items using 2PL (medium difficulty)
  # - 5 items using 3PL (difficult, with guessing)
  # - 5 items using GPCM (4-point Likert scale)
  # - 5 items using GRM (5-point Likert scale)

  my_test_structure <- list(
    # Block 1: 2PL
    list(model = "2PL", n_items = 10, a = c(0.8, 1.2), b = c(-1, 1)),

    # Block 2: 3PL (Harder items, b from 1 to 2.5, fixing guessing at 0.2)
    list(model = "3PL", n_items = 5, a = c(1.0, 1.5), b = c(1.0, 2.5), c = 0.2),

    # Block 3: GPCM (Polytomous, 4 categories 0-3)
    list(model = "GPCM", n_items = 5, categories = 4, a = c(0.7, 1.3), b = c(-1, 1)),

    # Block 4: GRM (Polytomous, 5 categories 0-4)
    list(model = "GRM", n_items = 5, categories = 5, a = c(1.0, 2.0))
  )

  # 2. Run the Simulation
  # Define N and a specific Theta vector
  N <- 2000
  theta_vec <- rnorm(N, 0, 2)

  sim_data <- sim_irt(
    n_people = N,
    theta = theta_vec,
    item_structure = my_test_structure
  )

  # 3. Inspect the Output
  # The Response Matrix
  head(sim_data$resp)

  # The True Parameters (Useful for recovery studies)
  # Note how it aligns a, b, and threshold parameters (step_1, step_2...)
  head(sim_data$true_params)