guess (version 0.7.0)

simulate_lca: Simulation Functions for LCA Models

Description

Functions to generate simulated pre/post test data from known LCA parameters for validation and parameter recovery studies. Simulate Pre-Post Test Data (No DK Model)

Usage

simulate_lca(
  n,
  n_items = 1,
  gg = 0.35,
  gk = 0.3,
  kk = 0.35,
  gamma = 0.25,
  difficulty = NULL,
  base_rate = 0.25,
  seed = NULL,
  return_classes = FALSE
)

Value

List with components:

pre

Data frame of pre-test responses (0/1 for each item)

post

Data frame of post-test responses (0/1 for each item)

true_class

(If return_classes=TRUE) Factor with levels "gg", "gk", "kk"

learned

(If return_classes=TRUE) Logical vector: TRUE if individual is in gk class

Arguments

n

Integer. Number of individuals to simulate.

n_items

Integer. Number of test items. Default 1.

gg

Numeric. Proportion in guess->guess state (stable ignorance). Default 0.35.

gk

Numeric. Proportion in guess->know state (LEARNED). Default 0.30.

kk

Numeric. Proportion in know->know state (stable knowledge). Default 0.35.

gamma

Numeric. Probability of guessing correctly. Can be scalar (same for all items) or vector of length n_items. Default 0.25.

difficulty

Numeric vector. Optional difficulty-link scores. If provided, gamma is computed as base_rate + (1 - base_rate) * plogis(-difficulty). Higher difficulty = harder item (lower gamma). Ignored if NULL.

base_rate

Numeric. Minimum guessing probability (random chance). Used when difficulty is specified. Default 0.25 (1/4 for 4-choice items).

seed

Optional integer. Random seed for reproducibility.

return_classes

Logical. If TRUE, also return true latent class assignments. Default FALSE for backward compatibility.

Details

Generates simulated pre/post test data from a latent class model with known parameters. Useful for parameter recovery validation studies.

The model simulates three latent classes: - **gg (guess->guess)**: Don't know at both times. Responses are random guesses. - **gk (guess->know)**: Learned between tests. Random guess pre, correct post. - **kk (know->know)**: Know at both times. Correct responses at both times.

Parameters must satisfy: gg + gk + kk = 1 (constraint enforced automatically).

When difficulty is specified, gamma values are derived using a logistic transformation: gamma_i = base_rate + (1 - base_rate) * plogis(-difficulty_i). This means: - difficulty = 0: gamma = base_rate + 0.5 * (1 - base_rate) (middle) - difficulty -> +Inf: gamma -> base_rate (hard item, random guessing) - difficulty -> -Inf: gamma -> 1 (easy item, always correct)

Examples

# Simulate data with 30% learning
sim <- simulate_lca(n = 500, gg = 0.35, gk = 0.30, kk = 0.35, gamma = 0.25, seed = 123)
fit <- item_lca_fit(sim$pre, sim$post)
fit$params["gk", ] # Should be close to 0.30

# Multi-item simulation
sim_multi <- simulate_lca(n = 500, n_items = 3, seed = 456)

# Item-specific gamma (vector)
sim_vec <- simulate_lca(n = 500, n_items = 3, gamma = c(0.2, 0.25, 0.3), seed = 789)

# Difficulty-link scores
sim_irt <- simulate_lca(n = 500, n_items = 3, difficulty = c(1, 0, -1), seed = 101)

# Return true class assignments for validation
sim_classes <- simulate_lca(n = 500, gk = 0.30, seed = 123, return_classes = TRUE)
table(sim_classes$true_class)
mean(sim_classes$learned) # Should be close to 0.30