Extract Item Parameters of Item Response Models
A class and generic function for representing and extracting the item parameters of a given item response model.
itempar(object, ...) ## S3 method for class 'raschmodel' itempar(object, ref = NULL, alias = TRUE, vcov = TRUE, ...) ## S3 method for class 'rsmodel' itempar(object, ref = NULL, alias = TRUE, vcov = TRUE, ...) ## S3 method for class 'pcmodel' itempar(object, ref = NULL, alias = TRUE, vcov = TRUE, ...) ## S3 method for class 'plmodel' itempar(object, ref = NULL, alias = TRUE, vcov = TRUE, ...) ## S3 method for class 'gpcmodel' itempar(object, ref = NULL, alias = TRUE, vcov = TRUE, ...) ## S3 method for class 'btmodel' itempar(object, ref = NULL, alias = TRUE, vcov = TRUE, log = FALSE, ...)
object |
a fitted model or tree object whose item parameters should be extracted. |
ref |
a vector of labels or position indices of item parameters or a
contrast matrix which should be used as restriction/for normalization. If
|
alias |
logical. If |
vcov |
logical. If |
log |
logical. Whether to return the estimated model parameters
on the logit ( |
... |
further arguments which are currently not used. |
itempar is both, a class to represent item parameters of item
response models as well as a generic function. The generic function can be
used to extract the item parameters of a given item response model.
For Rasch models and n-parameter logistic models, itempar returns the
estimated item difficulty parameters \hat{β}_{j} under the
restriction specified in argument ref. For rating scale models,
itempar returns computed item location parameters \hat{β}_{j}
under the restriction specified in argument ref. These are computed
from the estimated item-specific parameters \hat{ξ}_{j} (who mark the
location of the first category of an item on the latent theta axis). For
partial credit models and generalized partial credit models, itempar
returns ‘mean’ absolute item threshold parameters, \hat{β}_{j}
= \frac{1}{p_{j}} ∑_{k = 1}^{p_{j}}\hat{δ}_{jk}, i.e., a single
parameter per item is returned which results as the mean of the absolute item
threshold parameters \hat{δ}_{jk} of this item. Based upon these
‘mean’ absolute item threshold parameters \hat{β}_{j}, the
restriction specified in argument ref is applied. For all models, the
variance-covariance matrix of the returned item parameters is adjusted
according to the multivariate delta rule.
For objects of class itempar, several methods to standard generic
functions exist: print, coef, vcov. coef and
vcov can be used to extract the estimated calculated item parameters
and their variance-covariance matrix without additional attributes. Based on
this Wald tests or confidence intervals can be easily computed, e.g., via
confint.
Two-sample item-wise Wald tests for DIF in the item parameters can be
carried out using the function anchortest.
A named vector with item parameters of class itempar and additional
attributes model (the model name), ref (the items or parameters
used as restriction/for normalization), alias (either FALSE or a
named character vector with the removed aliased parameter, and vcov
(the adjusted covariance matrix of the estimates if vcov = TRUE or an
NA-matrix otherwise).
o <- options(digits = 4)
## load verbal aggression data
data("VerbalAggression", package = "psychotools")
## fit a Rasch model to dichotomized verbal aggression data
raschmod <- raschmodel(VerbalAggression$resp2)
## extract item parameters with sum zero or use last two items as anchor
ip1 <- itempar(raschmod)
ip2a <- itempar(raschmod, ref = 23:24) # with position indices
ip2b <- itempar(raschmod, ref = c("S4WantShout", "S4DoShout")) # with item label
ip1
ip2a
all.equal(ip2a, ip2b)
## extract vcov
vc1 <- vcov(ip1)
vc2 <- vcov(ip2a)
## adjusted standard errors,
## smaller with more items used as anchors
sqrt(diag(vc1))
sqrt(diag(vc2))
## Wald confidence intervals
confint(ip1)
confint(ip2a)
options(digits = o$digits)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.