simResp {TestDesign}

Simulate item response data

Description

simResp is a function for simulating item response data.

Usage

simResp(object, theta)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

## S4 method for signature 'item_pool_cluster,list'
simResp(object, theta)

Arguments

object

an item or an item_pool object.

theta

theta values to use.

Details

notations

• nq denotes the number of theta values.

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

Value

item object:

simResp returns a length nq vector containing simulated item response data.

item_pool object:

simResp returns a (nq, ni) matrix containing simulated item response data.

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)

sim_item_1 <- simResp(item_1, seq(-3, 3, 1))
sim_item_2 <- simResp(item_2, seq(-3, 3, 1))
sim_item_3 <- simResp(item_3, seq(-3, 3, 1))
sim_item_4 <- simResp(item_4, seq(-3, 3, 1))
sim_item_5 <- simResp(item_5, seq(-3, 3, 1))
sim_item_6 <- simResp(item_6, seq(-3, 3, 1))
sim_pool   <- simResp(itempool_science, seq(-3, 3, 1))