calcProb-methods: Calculate item response probabilities

In TestDesign: Optimal Test Design Approach to Fixed and Adaptive Test Construction

Calculate item response probabilities

Description

calcProb is a function to calculate item response probabilities.

Usage

calcProb(object, theta)

## S4 method for signature 'item_1PL,numeric'
calcProb(object, theta)

## S4 method for signature 'item_2PL,numeric'
calcProb(object, theta)

## S4 method for signature 'item_3PL,numeric'
calcProb(object, theta)

## S4 method for signature 'item_PC,numeric'
calcProb(object, theta)

## S4 method for signature 'item_GPC,numeric'
calcProb(object, theta)

## S4 method for signature 'item_GR,numeric'
calcProb(object, theta)

## S4 method for signature 'item_pool,numeric'
calcProb(object, theta)

## S4 method for signature 'item_1PL,matrix'
calcProb(object, theta)

## S4 method for signature 'item_2PL,matrix'
calcProb(object, theta)

## S4 method for signature 'item_3PL,matrix'
calcProb(object, theta)

## S4 method for signature 'item_PC,matrix'
calcProb(object, theta)

## S4 method for signature 'item_GPC,matrix'
calcProb(object, theta)

## S4 method for signature 'item_GR,matrix'
calcProb(object, theta)

## S4 method for signature 'item_pool,matrix'
calcProb(object, theta)

## S4 method for signature 'item_pool_cluster,numeric'
calcProb(object, theta)

Arguments

object	an item or an item_pool object.
theta	theta values to use.

Value

item object:

calcProb returns a (nq, ncat) matrix of probability values.

item_pool object:

calcProb returns a length ni list, each containing a matrix of probability values.

notations

• nq denotes the number of theta values.

• ncat denotes the number of response categories.

• ni denotes the number of items in the item_pool object.

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

item_1      <- new("item_1PL", difficulty = 0.5)
item_2      <- new("item_2PL", slope = 1.0, difficulty = 0.5)
item_3      <- new("item_3PL", slope = 1.0, difficulty = 0.5, guessing = 0.2)
item_4      <- new("item_PC", threshold = c(-1, 0, 1), ncat = 4)
item_5      <- new("item_GPC", slope = 1.2, threshold = c(-0.8, -1.0, 0.5), ncat = 4)
item_6      <- new("item_GR", slope = 0.9, category = c(-1, 0, 1), ncat = 4)

prob_item_1 <- calcProb(item_1, seq(-3, 3, 1))
prob_item_2 <- calcProb(item_2, seq(-3, 3, 1))
prob_item_3 <- calcProb(item_3, seq(-3, 3, 1))
prob_item_4 <- calcProb(item_4, seq(-3, 3, 1))
prob_item_5 <- calcProb(item_5, seq(-3, 3, 1))
prob_item_6 <- calcProb(item_6, seq(-3, 3, 1))
prob_pool   <- calcProb(itempool_science, seq(-3, 3, 1))

TestDesign documentation built on Feb. 16, 2023, 7:19 p.m.