pwrRasch (version 0.1-4)

simul.rasch: Simulate data according to the Rasch model

Description

This function simulates data according to the Rasch model based on user-specified item and person parameters and an optionally specified test booklet design.

Usage

simul.rasch(persons, items, design = NULL, sum0 = TRUE)

Value

Returns a 0-1 matrix according to the Rasch model.

Arguments

persons

Either a vector of specified person parameters, an integer indicating the number of persons, or a list with vectors of specified person parameters or integers corresponding to the number of bookelts specified in design. The number of persons for a test booklet design with unequal number of persons per booklet is specified in a list.

items

Either a vector of specified item parameters or an integer indicating the number of items.

design

Test booklet design matrix with 0 (item not administered) and 1 (item administered) entries.

sum0

If TRUE, specified item parameters need to be normalized to sum-0.

Author

Takuya Yanagida , Jan Steinfeld

Details

If persons is an integer value, the corresponding parameter vector is drawn from N(0, 1.5). If items is an integer value, the corresponding parameter vector is equally spaced between [-3, 3]. Note that item parameters need to be normalized to sum-0. This precondition can be overruled using argument sum0 = FALSE. If !is.null(design), the integer value represents the number of persons in each booklet. Note that unequal number of persons per booklet is specified in a list corresponding to the number of booklets.

References

Kubinger, K. D., Rasch, D., & Yanagida, T. (2009). On designing data-sampling for Rasch model calibrating an achievement test. Psychology Science Quarterly, 51, 370-384.

Kubinger, K. D., Rasch, D., & Yanagida, T. (2011). A new approach for testing the Rasch model. Educational Research and Evaluation, 17, 321-333.

See Also

aov.rasch, pwr.rasch

Examples

if (FALSE) {

# simulate Rasch model based data
# 100 persons, 20 items,
# person parameter drawn from a normal distribution: N(0, 1.5)
# item parameters equally spaced between [-3, 3]
simul.rasch(100, items = 20)

# simulate Rasch model based data
# 100 persons, 17 items
# person parameter drawn from a uniform distribution: U[-4, 4]
# item parameters: [-4.0, -3.5, -3.0, ... , 3.0, 3.5, 4.0]
simul.rasch(runif(100, -4, 4), items = seq(-4, 4, by = 0.5))

# specify test booklet design with three items
design <- matrix(c(1, 1, 0, 1, 0, 1, 0, 1, 1), ncol = 3)
# 100 persons in each booklet
# person parameter drawn from a normal distribution: N(0, 1.5)
# item parameters equally spaced between [-3, 3]
simul.rasch(100, items = 3, design = design)

# 100 persons in each booklet
# person parameter drawn from a uniform distribution: U[-4, 4]
# item parameters equally spaced between [-3, 3]
simul.rasch(runif(100, -4, 4), items = 3, design = design)

# 10 persons in booklet 1 / 20 persons in booklet 2 / 30 persons in booklet 3
# person parameter drawn from a normal distribution: N(0, 1.5)
# item parameters equally spaced between [-3, 3]
simul.rasch(list(10, 20, 30), items = 3, design = design)

# 10 persons in booklet 1 / 20 persons in booklet 2 / 30 persons in booklet 3
# person parameter drawn from a uniform distribution: U[-4, 4]
# item parameters equally spaced between [-4, 4]
simul.rasch(list(runif(10, -4, 4), runif(20, -4, 4), runif(30, -4, 4)), 
            items = seq(-4, 4, length.out = 3), design = design)
}