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ltm (version 0.9-8)

GoF: Goodness of Fit for Rasch Models

Description

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

Usage

GoF.gpcm(object, simulate.p.value = TRUE, B = 99, seed = NULL, ...)

GoF.rasch(object, B = 49, ...)

Arguments

object
an object inheriting from either class gpcm or class rasch.
simulate.p.value
logical; if TRUE, the reported $p$-value is based on a parametric Bootstrap approach. Otherwise the $p$-value is based on the asymptotic chi-squared distribution.
B
the number of Bootstrap samples. See Details section for more info.
seed
the seed to be used during the parametric Bootstrap; if NULL, a random seed is used.
...
additional arguments; currently none is used.

Value

  • An object of class GoF.gpcm or GoF.rasch with components,
  • Tobsthe value of the Pearson's chi-squared statistic for the observed data.
  • Bthe B argument specifying the number of Bootstrap samples used.
  • callthe matched call of object.
  • p.valuethe $p$-value of the test.
  • simulate.p.valuethe value of simulate.p.value argument (returned on for class GoF.gpcm).
  • dfthe degrees of freedom for the asymptotic chi-squared distribution (returned on for class GoF.gpcm).

Details

GoF.gpcm and GoF.rasch perform a parametric Bootstrap test based on Pearson's chi-squared statistic defined as $$\sum\limits_{r = 1}^{2^p} \frac{{O(r) - E(r)}^2}{E(r)},$$ 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: [object Object],[object Object],[object Object],[object Object] Furthermore, in GoF.gpcm when simulate.p.value = FALSE, then the $p$-value is based on the asymptotic chi-squared distribution.

See Also

person.fit, item.fit, margins, gpcm, rasch

Examples

Run this code
## GoF for the Rasch model for the LSAT data:
fit <- rasch(LSAT)
GoF.rasch(fit)

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