TestDesign (version 1.2.4)

calc_info: Calculate Fisher information (multiple items)

Description

calc_info and calc_info_matrix are functions to calculate Fisher information. These functions are designed for multiple items.

Usage

calc_info(x, item_parm, ncat, model)
calc_info_matrix(x, item_parm, ncat, model)

Arguments

x

the theta value. This must be a column vector in matrix form for array_info_* functions.

item_parm

a matrix containing item parameters. Each row represents 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

Details

calc_info accepts a single theta value, and calc_info_matrix accepts multiple theta values.

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)

# single theta example
x <- 0.5
calc_info(x, item_parm, ncat, model)
# same as
info_1pl(x, 1)
info_2pl(x, 1, 2)
info_3pl(x, 1, 2, 0.25)
info_pc(x, c(0, 1))
info_gpc(x, 2, c(0, 1))
info_gr(x, 2, c(0, 2))

# multiple thetas example
x <- matrix(seq(0.1, 0.5, 0.1)) # column vector in matrix form
calc_info_matrix(x, item_parm, ncat, model)
# same as
array_info_1pl(x, 1)
array_info_2pl(x, 1, 2)
array_info_3pl(x, 1, 2, 0.25)
array_info_pc(x, c(0, 1))
array_info_gpc(x, 2, c(0, 1))
array_info_gr(x, 2, c(0, 2))

# }