mhmc_sc: MHMC Parameter Estimates for Single Chain

In cogirt: Cognitive Testing Using Item Response Theory

MHMC Parameter Estimates for Single Chain

Description

This function uses the Metropolis-Hastings algorithm for a single chain to calculate parameter estimates using the Markov Chain Monte Carlo method. The method implemented follows Patz and Junker (1999). The approach to tuning the scale and covariance matrix follows BDA and SAS 9.2 User Guide, 2nd Ed. "The MCMC Procedure: Tuning the Proposal Distribution".

Usage

mhmc_sc(
  y = y,
  obj_fun = NULL,
  link = NULL,
  est_omega = TRUE,
  est_lambda = TRUE,
  est_zeta = TRUE,
  est_nu = TRUE,
  omega0 = NULL,
  gamma0 = NULL,
  lambda0 = NULL,
  zeta0 = NULL,
  nu0 = NULL,
  kappa0 = NULL,
  omega_mu = NULL,
  omega_sigma2 = NULL,
  lambda_mu = NULL,
  lambda_sigma2 = NULL,
  zeta_mu = NULL,
  zeta_sigma2 = NULL,
  nu_mu = NULL,
  nu_sigma2 = NULL,
  burn = NULL,
  thin = NULL,
  min_tune = NULL,
  tune_int = NULL,
  max_tune = NULL,
  niter = NULL,
  weight = 1,
  verbose = FALSE
)

Arguments

y	Item response matrix (K by IJ).
obj_fun	A function that calculates predictions and log-likelihood values for the selected model (character).
link	Choose between "logit" or "probit" link functions.
est_omega	Determines whether omega is estimated (logical).
est_lambda	Determines whether nu is estimated (logical).
est_zeta	Determines whether zeta is estimated (logical).
est_nu	Determines whether nu is estimated (logical).
omega0	Starting or known values for omega (K by MN).
gamma0	Starting or known values for gamma (JM by MN).
lambda0	Starting or known values for lambda (IJ by JM).
zeta0	Starting or known values for zeta (K by JM).
nu0	Starting or known values for nu (IJ by 1).
kappa0	Starting or known values for kappa (K by IJ).
omega_mu	Mean prior for omega (1 by MN).
omega_sigma2	Covariance prior for omega (MN by MN).
lambda_mu	Mean prior for lambda (1 by JM)
lambda_sigma2	Covariance prior for lambda (JM by JM)
zeta_mu	Mean prior for zeta (1 by JM).
zeta_sigma2	Covariance prior for zeta (JM by JM).
nu_mu	Mean prior for nu (1 by 1).
nu_sigma2	Covariance prior for nu (1 by 1).
burn	Number of iterations at the beginning of an MCMC run to discard (scalar).
thin	Determines every nth observation retained (scalar).
min_tune	Determines when tunning begins (scalar).
tune_int	MHMC tuning interval (scalar).
max_tune	Determines when tunning ends (scalar).
niter	Number of iterations of the MHMC sampler.
weight	Determines the weight of old versus new covariance matrix.
verbose	Print progress of MHMC sampler.

Value

List with elements omega_draws (list of (niter - burn) / thin draws for K by MN omega matrix), lambda_draws (list of (niter - burn) / thin draws for IJ by JM lambda matrix), zeta_draws (list of (niter - burn) / thin draws for K by JM zeta matrix), nu_draws (list of (niter - burn) / thin draws for IJ by 1 nu matrix), cand_o_var (list of K final MN by MN candidate proposal covariance matrices for omega for each examinee), cand_l_var (list of IJ final JM by JM candidate proposal covariance matrices for lambda for each item), cand_z_var (list of final JM by JM candidate proposal covariance matrices for zeta for all examinees), and cand_n_var (list of IJ final scalar candidate proposal variances for nu for all items).

References

Patz, R. J., & Junker, B. W. (1999). A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models. Journal of Educational and Behavioral Statistics, 24(2), 146.

cogirt documentation built on April 3, 2025, 8:14 p.m.