Two Parameter Choice IRT Model MCMC

Performs an MCMC routine for a two parameter IRT Model using Choice Data

TwoPLChoicemcmc(
  unique_subject_ids,
  subject_ids,
  choices_nk,
  fixed_effects,
  B,
  rv_effects_design,
  gamma,
  beta,
  zeta_rv,
  Sigma_zeta_inv,
  Y,
  theta0,
  a0,
  b0,
  mu_xi0,
  Sig_xi0
)

Arguments

unique_subject_ids

A vector with length \(N \times 1\) containing unique subject IDs.

subject_ids

A vector with length \(NK \times 1\) containing subject IDs.

choices_nk

A vector with length \(NK \times 1\) containing subject choices.

fixed_effects

A matrix with dimensions \(NK \times P_1\) containing fixed effect design matrix without theta.

B

A \(V\) dimensional column vector relating \(\theta_i\) and \(\zeta_i\).

rv_effects_design

A matrix with dimensions \(NK \times V\) containing random effect variables.

gamma

A vector with dimensions \(P \times 1\) containing fixed parameter estimates, where \(P = P_1 + P_2\)

beta

A vector with dimensions \(P_2\) containing random parameter estimates.

zeta_rv

A matrix with dimensions \(N \times V\) containing random parameter estimates.

Sigma_zeta_inv

A matrix with dimensions \(P_2 \times P_2\).

Y

A matrix of dimensions \(N \times J\) for Dichotomous item responses

theta0

A vector of length \(N \times 1\) for latent theta.

a0

A vector of length \(J\) for item discriminations.

b0

A vector of length \(J\) for item locations.

mu_xi0

A vector of dimension 2 (i.e. c(0,1)) that is a prior for item parameter means.

Sig_xi0

A matrix of dimension 2x2 (i.e. diag(2)) that is a prior for item parameter vc matrix.

Value

A list that contains:

ai1

A vector of length J

bi1

A vector of length J

theta1

A vector of length N

Z_c

A matrix of length NK

Wzeta_0

A matrix of length NK

See also

cIRT(), rmvnorm(), and riwishart()

Author

Steven Andrew Culpepper and James Joseph Balamuta

Examples

if (FALSE) {
# Call with the following data:
TwoPLChoicemcmc(cogDAT, theta0, a0, b0, mu_xi0, Sig_xi0)
}