Exploratory reduced Reparameterized Unified Model (ErRUM)

Obtains samples from posterior distribution for the Exploratory reduced Reparameterized Unified Model (ErRUM).

errum(
  y,
  k = 3,
  burnin = 1000,
  chain_length = 10000,
  verbose = FALSE,
  X = matrix(1, nrow = ncol(y)),
  v0 = 4,
  v1 = 2,
  cv0 = 0.1,
  cv1 = 10,
  bnu = 16
)

Arguments

y

Binary responses to assessments in matrix form with dimensions \(N \times J\).

k

Number of Attribute Levels as a positive integer.

burnin

Number of Observations to discard on the chain.

chain_length

Length of the MCMC chain

verbose

Display estimation progress updates.

X, v0, v1, cv0, cv1, bnu

Additional tuning parameters

Value

An errum object that has:

• PISTAR

• RSTAR

• PIs

• QS

• m_Delta

• Delta_biject

• M2

• M1

• NUS

See also

simcdm::attribute_bijection(), simcdm::sim_rrum_items()

Examples

# Setup Simulation Parameters
N = 5
K = 3
J = 30
# Note:
# Sample size has been reduced to create a minimally
# viable example that can be run during CRAN's automatic check.
# Please make sure to have a larger sample size of around 3,000.

# Sample true attribute profiles
Z         = matrix(rnorm(N * K), N, K)
Sig       = matrix(.5, K, K)
diag(Sig) = 1
theta     = Z %*% chol(Sig)

thvals    = matrix(qnorm((1:K) / (K + 1)),
                   N, K, byrow = TRUE)

Alphas    = 1 * (theta > thvals)

# Defining matrix of possible attribute profiles
As = as.matrix(expand.grid(c(0, 1), c(0, 1), c(0, 1)))
Q = rbind(As[rep(c(2, 3, 5), 4),],
          As[rep(c(4, 6, 7), 4),],
          As[rep(8, 6),])

# Use simulation functions available in simcdm
if (requireNamespace("simcdm", quietly = TRUE)) {

a = As %*% simcdm::attribute_bijection(K)
As = As[a + 1,]

# Setting item parameters
pistar = rep(.9, J)
rstar = matrix(.6, J, K) * Q

# Simulate data under rRUM model
Y = simcdm::sim_rrum_items(Q, rstar, pistar, Alphas)

# Estimation Settings
chainLength = 10000  # Run with 20000
burnin = chainLength / 2

# Gibbs Estimation
model = errum(Y, K, burnin, chainLength)
}
#> Beginning the estimation procedure...