Description Usage Arguments Details Value Author(s) References See Also Examples

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

1 2 3 |

`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 |

`sig.level` |
Nominal significance level. |

`method` |
Simulation method: for-loop or vectorized. |

`output` |
If |

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.

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 |

Takuya Yanagida [email protected], Jan Steinfeld [email protected]

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.

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)
``` |

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