anova.rasch {ltm} | R Documentation |
Performs either a parametric Bootsrap goodness-of-fit test based on the
Pearson chi-squared or a Likelihood Ratio Test between a rasch
model and
an ltm
model.
anova.rasch(object, ltm.obj = NULL, B = 49, ...)
object |
an object inheriting from class rasch . |
ltm.obj |
an object inheriting from class ltm . |
B |
the number of Bootstrap samples. See Details section for more info. |
... |
additional arguments; currently none is used. |
If only object
is supplied anova.rasch
performs a parametric
Bootstrap test based on Pearson's chi-squared statistic. 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
{# T_i > T_{obs}}.
If both object
and ltm.obj
are supplied, then a likelihood ratio test between the two fitted
models is performed.
An object of class aov.rasch
with components,
Tobs |
the value of the Pearson's chi-squared statistic for the observed data. Returned if only object is supplied. |
p.value |
the estimated p-value for the test. Returned if only object is supplied. |
B |
the B argument specifying the number of Bootstrap samples used. Returned if only object is supplied. |
call |
the matched call of object . Returned if only object is supplied. |
nam0 |
the name of object . Returned if ltm.obj is also supplied. |
L0 |
the log-likelihood under the null hypothesis (object ). Returned if ltm.obj is also supplied. |
aic0 |
the AIC value for the model given by object . Returned if ltm.obj is also supplied. |
bic0 |
the BIC value for the model given by object . Returned if ltm.obj is also supplied. |
nam1 |
the name of ltm.obj . Returned if ltm.obj is also supplied. |
L1 |
the log-likelihood under the null hypothesis (ltm.obj ). Returned if ltm.obj is also supplied. |
aic1 |
the AIC value for the model given by ltm.obj . Returned if ltm.obj is also supplied. |
bic1 |
the BIC value for the model given by ltm.obj . Returned if ltm.obj is also supplied. |
LRT |
the value of the Likelihood Ratio Test statistic. Returned if ltm.obj is also supplied. |
df |
the degrees of freedom for the test (i.e., the difference in the number of parameters). Returned if ltm.obj is also supplied. |
p.value |
the p-value of the test. |
When the manifest (response) variables matrix contains missing values the Pearson chi-squared is not computed.
## GoF for the Rasch model for the Wirs data: ## using 99+1 bootstrap samples m <- rasch(Wirs) anova(m, B=99) ## GoF for the Rasch model for the Lsat data: m <- rasch(Lsat) anova(m) ## An LRT between the Rasch and the one-factor model ## for the Wirs data: m0 <- rasch(Wirs) m1 <- ltm(Wirs~z1) anova(m0, m1) ## An LRT between the Rasch and the one-factor model ## for the Lsat data: m0 <- rasch(Lsat) m1 <- ltm(Lsat~z1) anova(m0, m1)