ltm (version 0.8-9)

GoF.rasch: Goodness of Fit for Rasch Models

Description

Performs a parametric Bootstrap test for Rasch models.

Usage

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

Arguments

object

an object inheriting from class rasch.

B

the number of Bootstrap samples. See Details section for more info.

...

additional arguments; currently none is used.

Value

• An object of class GoF.rasch with components,
• Tobs
  the value of the Pearson's chi-squared statistic for the observed data.
• B
  the B argument specifying the number of Bootstrap samples used.
• call
  the matched call of object.
• p.value
  the $p$-value of the test.

Details

GoF.rasch performs 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]

See Also

person.fit, item.fit, margins, rasch

Examples

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