theta_EB: (C++) Calculate a theta estimate using EB (Empirical Bayes)...

In TestDesign: Optimal Test Design Approach to Fixed and Adaptive Test Construction

(C++) Calculate a theta estimate using EB (Empirical Bayes) method

Description

theta_EB_single() and theta_EB() are functions for calculating a theta estimate using EB (Empirical Bayes) method.

Usage

theta_EB(
  nx,
  theta_init,
  theta_prop,
  item_parm,
  resp,
  ncat,
  model,
  prior,
  prior_parm
)

theta_EB_single(
  nx,
  theta_init,
  theta_prop,
  item_parm,
  resp,
  ncat,
  model,
  prior,
  prior_parm
)

Arguments

nx	the number of MCMC draws.
theta_init	the initial estimate to use.
theta_prop	the SD of the proposal distribution.
item_parm	a matrix containing item parameters. Each row should represent an item.
resp	a vector containing responses on each item.
ncat	a vector containing the number of response categories of each item.
model	a vector indicating item models of each item, using 1: 1PL model 2: 2PL model 3: 3PL model 4: PC model 5: GPC model 6: GR model
prior	an integer indicating the type of prior distribution, using 1: normal distribution 2: uniform distribution
prior_parm	a vector containing parameters for the prior distribution.

Details

theta_EB_single() is designed for one item, and theta_EB() is designed for multiple items.

Currently supports unidimensional models.

Examples

# item parameters
item_parm <- matrix(c(
  1, NA,   NA,
  1,  2,   NA,
  1,  2, 0.25,
  0,  1,   NA,
  2,  0,    1,
  2,  0,    2),
  nrow = 6,
  byrow = TRUE
)

ncat  <- c(2, 2, 2, 3, 3, 3)
model <- c(1, 2, 3, 4, 5, 6)
resp  <- c(0, 1, 0, 1, 0, 1)

nx <- 100
theta_init <- 0
theta_prop <- 1.0
set.seed(1)
theta_EB_single(nx, theta_init, theta_prop, item_parm[1, ], resp[1], ncat[1], model[1], 1, c(0, 1))
theta_EB(nx, theta_init, theta_prop, item_parm, resp, ncat, model, 1, c(0, 1))

TestDesign documentation built on Sept. 11, 2024, 7:12 p.m.