theta_EB function

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

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

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))