# threshpar

##### Extract Threshold Parameters of Item Response Models

A class and generic function for representing and extracting the item threshold parameters of a given item response model.

- Keywords
- classes

##### Usage

```
threshpar(object, …)
# S3 method for raschmodel
threshpar(object, type = c("mode", "median", "mean"),
ref = NULL, alias = TRUE, relative = FALSE, cumulative = FALSE, vcov = TRUE,
…)
# S3 method for rsmodel
threshpar(object, type = c("mode", "median", "mean"),
ref = NULL, alias = TRUE, relative = FALSE, cumulative = FALSE, vcov = TRUE,
…)
# S3 method for pcmodel
threshpar(object, type = c("mode", "median", "mean"),
ref = NULL, alias = TRUE, relative = FALSE, cumulative = FALSE, vcov = TRUE,
…)
# S3 method for plmodel
threshpar(object, type = c("mode", "median", "mean"),
ref = NULL, alias = TRUE, relative = FALSE, cumulative = FALSE, vcov = TRUE,
…)
# S3 method for gpcmodel
threshpar(object, type = c("mode", "median", "mean"),
ref = NULL, alias = TRUE, relative = FALSE, cumulative = FALSE, vcov = TRUE,
…)
```

##### Arguments

- object
a fitted model object whose threshold parameters should be extracted.

- type
character of length one which determines the type of threshold parameters to return (see details below).

- ref
a vector of labels or position indices of (relative) threshold parameters or a contrast matrix which should be used as restriction/for normalization. For partial credit models, argument

`ref`

can also be a list of contrasts. If`NULL`

(the default), for all models except models etimated via MML, the relative threshold parameters are centered around their item-specific means and the absolute threshold parameters are centered around their global mean. For models estimated via MML (`plmodel`

s and`gpcmodel`

s), the parameters are by default identified via the distributional parameters of the person parameters (mean and variance of a normal distribution). Nevertheless, a restriction on the interval scale can be applied.- alias
logical. If

`TRUE`

(the default), the aliased parameter is included in the return vector (and in the variance-covariance matrix if`vcov`

= TRUE). If`FALSE`

, it is removed. If the restriction given in`ref`

depends on several parameters, the first parameter of the restriction specified is (arbitrarily) chosen to be removed if`alias`

is`FALSE`

.- relative
logical. If set to

`FALSE`

(default), absolute item threshold parameters are returned. If set to`TRUE`

, relative item threshold parameters with the contrast specified in argument`ref`

are returned.- cumulative
logical. If set to

`TRUE`

, cumulative threshold parameters are returned. These correspond to the cumulative sum over the absolute or relative item threshold parameters (after the restriction given in argument`ref`

has been applied).- vcov
logical. If

`TRUE`

(the default), the (transformed) variance-covariance matrix of the (relative) threshold parameters is attached as attribute`vcov`

. If`FALSE`

, a`NA`

-matrix is attached.- …
further arguments which are currently not used.

##### Details

`threshpar`

is both, a class to represent threshold parameters of item
response models as well as a generic function. The generic function can be
used to extract the threshold parameters of a given item response model.

For objects of class `threshpar`

, methods to standard generic functions
`print`

and `coef`

can be used to print and extract the threshold
parameters.

Depending on argument `type`

, different item threshold parameters are
returned. For `type = "mode"`

, the returned item threshold parameters
correspond to the location on the theta axis where the probability of category
\(k\) equals the probability of category \(k-1\). For Rasch and partial
credit models, item threshold parameters of this type correspond directly to
the estimated absolute item threshold parameters of these models. For
`type = "median"`

, the returned item threshold parameters correspond to
the location on the theta axis where the probability of choosing category
\(k\) or higher, i.e., \(P(X_{ij} >= k)\), equals 0.5. For ```
type =
"mean"
```

, the returned absolute item threshold parameters correspond to the
location on the theta axis where the expected category response is in the
middle between two categories, i.e. 0.5, 1.5, …. An illustration of
these threshold parameters can be found on page 104 in Masters & Wright
(1995).

##### Value

A named list with item threshold parameters of class `threshpar`

and
additional attributes `model`

(the model name), `type`

(the type of
item threshold parameters returned, see details above), `ref`

(the items
or parameters used as restriction/for normalization), `relative`

(whether
relative or absolute item threshold parameters are returned),
`cumulative`

(whether the cumulative item threshold parameters are
returned), `alias`

(either `FALSE`

or a named character vector or
list with the removed aliased parameters), and `vcov`

(the estimated and
adjusted variance-covariance matrix).

##### References

Masters GN, Wright BD (1997).
The Partial Credit Model.
In Van der Linden WJ, Hambleton RK (eds.).
*Handbook of Modern Item Response Theory*.
Springer, New York.

##### See Also

##### Examples

```
# NOT RUN {
o <- options(digits = 4)
## load verbal aggression data
data("VerbalAggression", package = "psychotools")
## fit a rasch model to dichotomized verbal aggression data
raschmod <- raschmodel(VerbalAggression$resp2)
## extract threshold parameters with sum zero restriction
tr <- threshpar(raschmod)
tr
## compare to item parameters (again with sum zero restriction)
ip <- itempar(raschmod)
ip
all.equal(coef(tr), coef(ip))
## rating scale model example
rsmod <- rsmodel(VerbalAggression$resp)
trmod <- threshpar(rsmod, type = "mode")
trmed <- threshpar(rsmod, type = "median")
trmn <- threshpar(rsmod, type = "mean")
## compare different types of threshold parameters
cbind("Mode" = coef(trmod, type = "vector"),
"Median" = coef(trmod, type = "vector"),
"Mean" = coef(trmn, type = "vector"))
if(requireNamespace("mirt")) {
## fit a partial credit model and a generalized partial credit model
pcmod <- pcmodel(VerbalAggression$resp)
gpcmod <- gpcmodel(VerbalAggression$resp)
## extract the threshold parameters with different default restrictions and
## therefore incompareable scales
tp <- threshpar(pcmod)
tg <- threshpar(gpcmod)
plot(unlist(tp), unlist(tg), xlab = "PCM", ylab = "GPCM")
abline(a = 0, b = 1)
## extract the threshold parameters with the first as the reference leading
## to a compareable scale visualizing the differences due to different
## discrimination parameters
tp <- threshpar(pcmod, ref = 1)
tg <- threshpar(gpcmod, ref = 1)
plot(unlist(tp), unlist(tg), xlab = "PCM", ylab = "GPCM")
abline(a = 0, b = 1)
options(digits = o$digits)
}
# }
```

*Documentation reproduced from package psychotools, version 0.5-1, License: GPL-2 | GPL-3*