TestDesign (version 1.2.4)

p_1pl: Calculate item response probability

Description

p_* and array_p_* are functions to calculate item response probability.

Usage

p_1pl(x, b)
p_2pl(x, a, b)
p_3pl(x, a, b, c)
p_pc(x, b)
p_gpc(x, a, b)
p_gr(x, a, b)
array_p_1pl(x, b)
array_p_2pl(x, a, b)
array_p_3pl(x, a, b, c)
array_p_pc(x, b)
array_p_gpc(x, a, b)
array_p_gr(x, a, b)

Arguments

x

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

b

the *b*-parameter.

a

the *a*-parameter.

c

the *c*-parameter.

Details

p_* functions accept a single theta value, and array_p_* functions accept multiple theta values.

Currently supports unidimensional models.

• p_1pl, array_p_1pl: 1PL models

• p_2pl, array_p_2pl: 2PL models

• p_3pl, array_p_3pl: 3PL models

• p_pc, array_p_pc: PC (partial credit) models

• p_gpc, array_p_gpc: GPC (generalized partial credit) models

• p_gr, array_p_gr: GR (graded response) 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 {
x <- 0.5

p_1pl(x, 1)
p_2pl(x, 1, 2)
p_3pl(x, 1, 2, 0.25)
p_pc(x, c(0, 1))
p_gpc(x, 2, c(0, 1))
p_gr(x, 2, c(0, 2))

x <- matrix(seq(0.1, 0.5, 0.1)) # column vector in matrix form

array_p_1pl(x, 1)
array_p_2pl(x, 1, 2)
array_p_3pl(x, 1, 2, 0.25)
array_p_pc(x, c(0, 1))
array_p_gpc(x, 2, c(0, 1))
array_p_gr(x, 2, c(0, 2))

# }