# pwr.rasch: Simulation to Estimate Statistical Power of a Rasch Model... In pwrRasch: Statistical Power Simulation for Testing the Rasch Model

## Description

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

## Usage

 ```1 2 3``` ```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 > 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 takuya.yanagida@univie.ac.at, Jan Steinfeld jan.steinfeld@univie.ac.at

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18``` ```## 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) ```

pwrRasch documentation built on May 1, 2019, 10:37 p.m.