GoF.rasch {ltm}R Documentation

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.

Details

GoF.rasch performs a parametric Bootstrap test based on Pearson's chi-squared statistic defined as

sum_{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 theta^*, from N(hat{theta}, C(hat{theta})), where hat{theta} are the MLEs and C(hat{theta}) their large sample covariance matrix.
Step 2:
Using theta^* simulate new data (with the same dimensions as the observed ones), fit 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).

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.

Author(s)

Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl

See Also

person.fit, item.fit, margins, rasch

Examples


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


[Package ltm version 0.8-7 Index]