itempar {psychotools} | R Documentation |
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 '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, 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, 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).
personpar
, threshpar
, discrpar
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)