GoF | R Documentation |
Performs a parametric Bootstrap test for Rasch and Generalized Partial Credit models.
GoF.gpcm(object, simulate.p.value = TRUE, B = 99, seed = NULL, ...) GoF.rasch(object, B = 49, ...)
object |
an object inheriting from either class |
simulate.p.value |
logical; if |
B |
the number of Bootstrap samples. See Details section for more info. |
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:
Based on object
compute the observed value of the statistic T_{obs}.
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.
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.
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 p-value of the test. |
simulate.p.value |
the value of |
df |
the degrees of freedom for the asymptotic chi-squared distribution (returned on for class |
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
person.fit
,
item.fit
,
margins
,
gpcm
,
rasch
## GoF for the Rasch model for the LSAT data: fit <- rasch(LSAT) GoF.rasch(fit)
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