theta_EAP function

(C++) Calculate a theta estimate using EAP (expected a posteriori) method

theta_EAP() and theta_EAP_matrix() are functions for calculating a theta estimate using EAP (expected a posteriori) method.

theta_EAP(theta_grid, item_parm, resp, ncat, model, prior, prior_parm)

theta_EAP_matrix(theta_grid, item_parm, resp, ncat, model, prior, prior_parm)

Arguments

• theta_grid: theta quadrature points.

• item_parm: a matrix containing item parameters.

• resp: responses on each item. Must be a vector for theta_EAP(), and a matrix for theta_EAP_matrix(). Each row should represent an examinee.

• 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_EAP() and theta_EAP_matrix() are designed for multiple items.

theta_EAP() is designed for one examinee, and theta_EAP_matrix() is designed for multiple examinees.

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)

# simulate response
item_parm <- as.data.frame(item_parm)
item_parm <- cbind(101:106, 1:6, item_parm)
pool <- loadItemPool(item_parm)
true_theta <- seq(-3, 3, 1)
resp <- simResp(pool, true_theta)

theta_grid <- matrix(seq(-3, 3, .1), , 1)

theta_EAP(theta_grid, pool@ipar, resp[1, ], ncat, model, 1, c(1, 2))
theta_EAP_matrix(theta_grid, pool@ipar, resp, ncat, model, 1, c(1, 2))