Fit a 2PL IRT Model — twopl

Fits a two-parameter logistic IRT model using CmdStan. The model is: logit(P(correct)) = a_k * (alpha_j + delta - beta_k)

Usage

twopl_fit(
  data,
  prior_delta = c(0, 1),
  prior_alpha_sd = 1.5,
  prior_beta = c(0, 1.5),
  prior_beta_mean = NULL,
  prior_beta_sd = NULL,
  prior_a = c(0, 0.5),
  prior_a_meanlog = NULL,
  prior_a_sdlog = NULL,
  chains = 4,
  parallel_chains = 4,
  iter_warmup = 1000,
  iter_sampling = 1000,
  seed = NULL,
  ...
)

Arguments

data: A matrix or data frame of binary (0/1) responses. Rows = students, Columns = questions. NA is allowed.
prior_delta: Prior for mean ability: c(mean, sd). Default c(0, 1).
prior_alpha_sd: Prior SD for student ability deviations. Default 1.5.
prior_beta: Prior for item difficulties when all items share the same prior: c(mean, sd). Default c(0, 1.5). Ignored if prior_beta_mean or prior_beta_sd is provided.
prior_beta_mean: Numeric vector of length K. Per-item prior means for difficulty. Overrides prior_beta.
prior_beta_sd: Numeric vector of length K. Per-item prior SDs for difficulty. Overrides prior_beta.
prior_a: Prior for discrimination when all items share the same prior (lognormal): c(meanlog, sdlog). Default c(0, 0.5). Ignored if prior_a_meanlog or prior_a_sdlog is provided.
prior_a_meanlog: Numeric vector of length K. Per-item prior meanlog for discrimination. Overrides prior_a.
prior_a_sdlog: Numeric vector of length K. Per-item prior sdlog for discrimination. Overrides prior_a.
chains: Number of MCMC chains. Default 4.
parallel_chains: Chains to run in parallel. Default 4.
iter_warmup: Warmup iterations per chain. Default 1000.
iter_sampling: Sampling iterations per chain. Default 1000.
seed: Random seed for reproducibility.
...: Extra arguments passed to cmdstanr's sample() method.

Value

An object of class birt_2pl_fit.

Examples

if (FALSE) { # \dontrun{
sim <- rasch_simulate(J = 300, K = 10, seed = 42)

# Default priors
fit2 <- twopl_fit(sim$data, seed = 123)

# Per-item: item 5 is known to be poorly discriminating
K <- ncol(sim$data)
a_meanlog <- rep(0, K)
a_sdlog <- rep(0.5, K)
a_meanlog[5] <- -0.5   # prior centered below 1.0
a_sdlog[5] <- 0.3      # tighter prior
fit2 <- twopl_fit(sim$data,
  prior_a_meanlog = a_meanlog,
  prior_a_sdlog = a_sdlog,
  seed = 123
)
} # }