e_item {TestDesign} | R Documentation |
(C++) Calculate expected scores
Description
e_*()
and array_e_*()
are C++ functions for calculating expected scores.
Usage
e_1pl(x, b)
e_2pl(x, a, b)
e_m_2pl(x, a, d)
e_3pl(x, a, b, c)
e_m_3pl(x, a, d, c)
e_pc(x, b)
e_gpc(x, a, b)
e_m_gpc(x, a, d)
e_gr(x, a, b)
e_m_gr(x, a, d)
array_e_1pl(x, b)
array_e_2pl(x, a, b)
array_e_3pl(x, a, b, c)
array_e_pc(x, b)
array_e_gpc(x, a, b)
array_e_gr(x, a, b)
Arguments
x |
the theta value. The number of columns should correspond to the number of dimensions.
For |
b , d |
the difficulty parameter. |
a |
the a-parameter. |
c |
the c-parameter. |
Details
e_*()
functions accept a single theta value, and array_p_*()
functions accept multiple theta values.
Supports unidimensional and multidimensional models.
e_1pl()
,array_e_1pl()
: 1PL modelse_2pl()
,array_e_2pl()
: 2PL modelse_3pl()
,array_e_3pl()
: 3PL modelse_pc()
,array_e_pc()
: PC (partial credit) modelse_gpc()
,array_e_gpc()
: GPC (generalized partial credit) modelse_gr()
,array_e_gr()
: GR (graded response) modelse_m_2pl()
,array_e_m_2pl()
: multidimensional 2PL modelse_m_3pl()
,array_e_m_3pl()
: multidimensional 3PL modelse_m_gpc()
,array_e_m_gpc()
: multidimensional GPC modelse_m_gr()
,array_e_m_gr()
: multidimensional GR 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, 397-479. Reading, MA: Addison-Wesley.
Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47(2), 149-174.
Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43(4), 561-573.
Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16(2), 159-176.
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph, 17.
Examples
x <- 0.5
e_1pl(x, 1)
e_2pl(x, 1, 2)
e_3pl(x, 1, 2, 0.25)
e_pc(x, c(0, 1))
e_gpc(x, 2, c(0, 1))
e_gr(x, 2, c(0, 2))
x <- matrix(seq(-3, 3, 1)) # three theta values, unidimensional
array_e_1pl(x, 1)
array_e_2pl(x, 1, 2)
array_e_3pl(x, 1, 2, 0.25)
array_e_pc(x, c(0, 1))
array_e_gpc(x, 2, c(0, 1))
array_e_gr(x, 2, c(0, 2))