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

Performs a parametric Bootstrap test for Rasch and Generalized Partial Credit models.

1 2 3 |

`object` |
an object inheriting from either class |

`simulate.p.value` |
logical; if |

`B` |
the number of Bootstrap samples. See |

`seed` |
the seed to be used during the parametric Bootstrap; if |

`...` |
additional arguments; currently none is used. |

`GoF.gpcm`

and `GoF.rasch`

perform a parametric Bootstrap test based on Pearson's chi-squared statistic defined as

*∑_{r=1}^{2^p} (O_r - E_r)^2 / E_r,*

where *r*
represents a response pattern, *O_r* and *E_r* represent the observed and expected frequencies,
respectively and *p* denotes the number of items. The Bootstrap approximation to the reference distribution is preferable compared with
the ordinary Chi-squared approximation since the latter is not valid especially for large number of items
(=> many response patterns with expected frequencies smaller than 1).

In particular, the Bootstrap test is implemented as follows:

- Step 0:
Based on

`object`

compute the observed value of the statistic*T_{obs}*.- Step 1:
Simulate new parameter values, say

*θ^**, from*N(\hat{θ}, C(\hat{θ}))*, where*\hat{θ}*are the MLEs and*C(\hat{θ})*their large sample covariance matrix.- Step 2:
Using

*θ^**simulate new data (with the same dimensions as the observed ones), fit the generalized partial credit or the Rasch model and based on this fit calculate the value of the statistic*T_i*.- Step 3:
Repeat steps 1-2

`B`

times and estimate the*p*-value using*[1 + {\# T_i > T_{obs}}]/(B + 1).*

Furthermore, in `GoF.gpcm`

when `simulate.p.value = FALSE`

, then the *p*-value is based on the asymptotic
chi-squared distribution.

An object of class `GoF.gpcm`

or `GoF.rasch`

with components,

`Tobs` |
the value of the Pearson's chi-squared statistic for the observed data. |

`B` |
the |

`call` |
the matched call of |

`p.value` |
the |

`simulate.p.value` |
the value of |

`df` |
the degrees of freedom for the asymptotic chi-squared distribution (returned on for class |

Dimitris Rizopoulos [email protected]

`person.fit`

,
`item.fit`

,
`margins`

,
`gpcm`

,
`rasch`

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drizopoulos/ltm documentation built on April 19, 2018, 2:37 a.m.

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