Performs a Likelihood Ratio Test between two nested IRT models.
Usage
## S3 method for class 'gpcm'
anova(object, object2, simulate.p.value = FALSE,
B = 200, verbose = getOption("verbose"), seed = NULL, ...)
## S3 method for class 'grm'
anova(object, object2, ...)
## S3 method for class 'ltm'
anova(object, object2, ...)
## S3 method for class 'rasch'
anova(object, object2, ...)
## S3 method for class 'tpm'
anova(object, object2, ...)
Arguments
object
an object inheriting from either class gpcm, class grm, class ltm, class rasch
or class tpm, representing the model under the null hypothesis.
object2
an object inheriting from either class gpcm, class grm, class ltm, class rasch,
or class tpm, representing the model under the alternative hypothesis.
simulate.p.value
logical; if TRUE, the reported p-value is based on a parametric Bootstrap approach.
B
the number of Bootstrap samples.
verbose
logical; if TRUE, information is printed in the console during the parametric Bootstrap.
seed
the seed to be used during the parametric Bootstrap; if NULL, a random seed is used.
...
additional arguments; currently none is used.
Details
anova.gpcm() also includes the option to estimate the p-value of the LRT using a parametric Bootstrap approach.
In particular, B data sets are simulated under the null hypothesis (i.e., under the generalized partial credit model
object), and both the null and alternative models are fitted and the value of LRT is computed. Then the p-value is
approximate using [1 + {# T_i > T_{obs}}]/(B + 1), where T_{obs}
is the value of the likelihood ratio statistic in the original data set, and T_i the value of the statistic in the ith
Bootstrap sample.
In addition, when simulate.p.value = TRUE objects of class aov.gpcm have a method for the plot() generic function
that produces a QQ plot comparing the Bootstrap sample of likelihood ration statistic with the asymptotic chi-squared distribution. For instance,
you can use something like the following: lrt <- anova(obj1, obj2, simulate.p.value = TRUE); plot(lrt).
Value
An object of either class aov.gpcm, aov.grm, class aov.ltm or class aov.rasch with components,
nam0
the name of object.
L0
the log-likelihood under the null hypothesis (object).
nb0
the number of parameter in object; returned only in aov.gpcm.
aic0
the AIC value for the model given by object.
bic0
the BIC value for the model given by object.
nam1
the name of object2.
L1
the log-likelihood under the alternative hypothesis (object2).
nb1
the number of parameter in object; returned only in aov.gpcm.
aic1
the AIC value for the model given by object2.
bic1
the BIC value for the model given by object2.
LRT
the value of the Likelihood Ratio Test statistic.
df
the degrees of freedom for the test (i.e., the difference in the number of parameters).
p.value
the p-value of the test.
Warning
The code does not check if the models are nested! The user is responsible to supply nested models in
order the LRT to be valid.
When object2 represents a three parameter model, note that the
null hypothesis in on the boundary of the parameter space for the guessing parameters. Thus, the Chi-squared reference
distribution used by these function might not be totally appropriate.
## LRT between the constrained and unconstrained GRMs
## for the Science data:
fit0 <- grm(Science[c(1,3,4,7)], constrained = TRUE)
fit1 <- grm(Science[c(1,3,4,7)])
anova(fit0, fit1)
## LRT between the one- and two-factor models
## for the WIRS data:
anova(ltm(WIRS ~ z1), ltm(WIRS ~ z1 + z2))
## An LRT between the Rasch and a constrained
## two-parameter logistic model for the WIRS data:
fit0 <- rasch(WIRS)
fit1 <- ltm(WIRS ~ z1, constraint = cbind(c(1, 3, 5), 2, 1))
anova(fit0, fit1)
## An LRT between the constrained (discrimination
## parameter equals 1) and the unconstrained Rasch
## model for the LSAT data:
fit0 <- rasch(LSAT, constraint = rbind(c(6, 1)))
fit1 <- rasch(LSAT)
anova(fit0, fit1)
## An LRT between the Rasch and the two-parameter
## logistic model for the LSAT data:
anova(rasch(LSAT), ltm(LSAT ~ z1))