TestDesign (version 1.2.4)

theta_EB: Calculate theta estimates using EB (Empirical Bayes) method

Description

theta_EB_single and theta_EB are functions to calculate theta estimates 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

initial estimate of theta.

theta_prop

SD of the proposal distribution.

item_parm

a matrix containing item parameters. Each row represents each item.

resp

a vector (or a value if for one item) containing responses on each item.

ncat

a vector (or a value if for one item) containing the number of response categories of each item.

model

a vector (or a value if for one item) 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.

References

Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research.

Lord, F. M. (1952). A theory of test scores (Psychometric Monograph No. 7). Richmond, VA: Psychometric Corporation.

Birnbaum, A. (1957). Efficient design and use of tests of mental ability for various decision-making problems (Series Report No. 58-16. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). On the estimation of mental ability (Series Report No. 15. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1958). Further considerations of efficiency in tests of a mental ability (Series Report No. 17. Project No. 7755-23). Randolph Air Force Base, TX: USAF School of Aviation Medicine.

Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (eds.), Statistical Theories of Mental Test Scores, 397<U+2013>479. Reading, MA: Addison-Wesley.

Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149<U+2013>174.

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561<U+2013>573.

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159<U+2013>176.

Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.

Examples

# NOT RUN {
# 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))

# }