GoF {ltm} | 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 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. |
GoF.gpcm
and GoF.rasch
perform 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:
object
compute the observed value of the statistic T_{obs}.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 B argument specifying the number of Bootstrap samples used. |
call |
the matched call of object . |
p.value |
the p-value of the test. |
simulate.p.value |
the value of simulate.p.value argument (returned on for class GoF.gpcm ). |
df |
the degrees of freedom for the asymptotic chi-squared distribution (returned on for class GoF.gpcm ). |
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)