pwr.rasch {pwrRasch}

Simulation to Estimate Statistical Power of a Rasch Model Test

Description

This function conducts a simulation to estimate statistical power of a Rasch model test for user-specified item and person parameters.

Usage

pwr.rasch(b, ipar = list(), ppar = list("rnorm(b, mean = 0, sd = 1.5)",
  "rnorm(b, mean = 0, sd = 1.5)"), runs = 1000, H0 = TRUE,
  sig.level = 0.05, method = c("loop", "vectorized"), output = TRUE)

Arguments

b

Either a vector or an integer indicating the number of observations in each group.

ipar

Item parameters in both groups specified in a list.

ppar

Person parameters specified by a distribution for each group.

runs

Number of simulation runs.

H0

If TRUE, null hypothesis condition is simulated.

sig.level

Nominal significance level.

method

Simulation method: for-loop or vectorized.

output

If TRUE, output is shown.

Details

The F-test in a three-way analysis of variance design (A \succ \mathbf{B}) x C(A > B) x C with mixed classification (fixed factor A = subgroup, random factor B = testee, and fixed factor C = items) is used to simulate statistical power of a Rasch model test. This approach using a F-distributed statistic, where the sample size directly affects the degree of freedom enables determination of the sample size according to a given type I and type II risk, and according to a certain effect of model misfit which is of practical relevance. Note, that this approach works as long as there exists no main effect of A (subgroup). Otherwise an artificially high type I risk of the A x C interaction F-test results - that is, the approach works as long as no statistically significant main effect of A occurs.

Value

Returns a list with following entries:

b	number of observations in each group
ipar	item parameters in both subgroups
c	number of items
ppar	distribution of person parameters
runs	number of simulation runs
sig.level	nominal significance level
H0.AC.p	p-values of the interaction A x C in the null hypothesis condition (if H0 = TRUE)
H1.AC.p	p-values of the interaction A x C in the alternative hypothesis condition
power	estimated statistical power
type1	estimated significance level

Author(s)

Takuya Yanagida [e-mail], Jan Steinfeld [e-mail]

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

Examples

## Not run: 

# item parameters
ipar2 <- ipar1 <- seq(-3, 3, length.out = 20)
# model differential item function (DIF)
ipar2[10] <- ipar1[11]
ipar2[11] <- ipar1[10]
# simulation for b = 200
pwr.rasch(200, ipar = list(ipar1, ipar2))

# simulation for b = 100, 200, 300, 400, 500
pwr.rasch(seq(100, 500, by = 100), ipar = list(ipar1, ipar2))

# simulation for b = 100, 200, 300, 400, 500
# uniform distribution [-3, 3] of person parameters
pwr.rasch(200, ipar = list(ipar1, ipar2), ppar = list("runif(b, -3, 3)", "runif(b, -3, 3)"))

## End(Not run)