Fit a Bayesian Rasch (1PL) IRT Model

Fits a Rasch model using CmdStan. The model is: logit(P(correct)) = alpha_j + delta - beta_k

Usage

rasch_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,
  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) means Normal(0, 1).
prior_alpha_sd: Prior SD for student ability deviations. Default 1.5 means alpha ~ Normal(0, 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 (one per item). Per-item prior means for difficulty. Overrides prior_beta.
prior_beta_sd: Numeric vector of length K (one per item). Per-item prior SDs for difficulty. Overrides prior_beta.
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_fit.

Examples

if (FALSE) { # \dontrun{
sim <- rasch_simulate(J = 200, K = 10, seed = 42)

# Default priors (same for all items)
fit <- rasch_fit(sim$data, seed = 123)

# Per-item priors: item 3 is known to be hard
K <- ncol(sim$data)
b_mean <- rep(0, K)
b_mean[3] <- 2.0
fit <- rasch_fit(sim$data, prior_beta_mean = b_mean, seed = 123)
} # }