calcEscore-methods function

Calculate expected scores

calcEscore is a function for calculating expected scores. methods

calcEscore(object, theta)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Arguments

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

Returns

• item object:: calcEscore a vector containing expected score of the item at the theta values.
• item_pool object:: calcEscore returns a vector containing the pool-level expected score at the theta values.

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)

ICC_item_1 <- calcEscore(item_1, seq(-3, 3, 1))
ICC_item_2 <- calcEscore(item_2, seq(-3, 3, 1))
ICC_item_3 <- calcEscore(item_3, seq(-3, 3, 1))
ICC_item_4 <- calcEscore(item_4, seq(-3, 3, 1))
ICC_item_5 <- calcEscore(item_5, seq(-3, 3, 1))
ICC_item_6 <- calcEscore(item_6, seq(-3, 3, 1))
TCC_pool   <- calcEscore(itempool_science, seq(-3, 3, 1))

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.