# predict.pcmodel

##### Predict Methods for Item Response Models

Prediction of (cumulated) response probabilities and responses based on fitted item response models.

- Keywords
- regression

##### Usage

```
# S3 method for pcmodel
predict(object, newdata = NULL, type = c("probability",
"cumprobability", "mode", "median", "mean", "category-information",
"item-information", "test-information"), ref = NULL, …)
```

##### Arguments

- object
a fitted model object whose item parameters should be used for prediction.

- newdata
an optional (possibly named) vector of person parameters used for prediction. If

`NULL`

(the default), the person parameters of the subjects used to fit the model in`object`

are used.- type
character of length one which determines the type of prediction (see details below).

- ref
arguments passed over to internal calls of

`itempar`

or`threshpar`

. Not used for models estimated via MML.- …
further arguments which are currently not used.

##### Details

Depending on the value of `type`

either probabilities, responses or
some form of information under the model specified in `object`

are
returned:

If `type`

is `"probability"`

, the category response probabilities
are returned.

If `type`

is `"cumprobability"`

, the cumulated category response
probabilities are returned, i.e., \(P(X_{ij} \geq k)\) with \(k\)
corresponding to the categories of item \(j\).

If `type`

is `"mode"`

, the most probable category response for a
given subject and item is returned.

If `type`

is `"median"`

, the first category \(k\) where
\(P(X_{ij} = k) \geq 0.5\) is returned.

If `type`

is `"mean"`

, the rounded expected category response,
i.e., \(E(X_{ij}|\theta_{i})\), is returned.

If `type`

is `"category-information"`

, the item-category
information as suggested by Bock (1972) is returned.

If `type`

is `"item-information"`

, the item information as
suggested by Samejima (1974) is returned.

If `type`

is `"test-information"`

, the sum over the individual
item information values is returned.

##### Value

A (possibly named) numeric matrix with rows corresponding to subjects and
columns corresponding to the whole test, the single items or categories. The
exact content depends on the value of `type`

(see details above).

##### References

Bock RD (1972).
Estimating Item Parameters and Latent Ability When Responses Are Scored in
Two or More Nominal Categories.
*Psychometrika*, **37**(1), 29--51.

Samejima F (1974).
Normal Ogive Model on the Continuous Response Level in the Multidimensional
Latent Space.
*Psychometrika*, **39**(1), 111--121.

##### See Also

The help page of the generic function `predict`

and other
predict methods (e.g., `predict.lm`

, `predict.glm`

,
…)

##### Examples

```
# NOT RUN {
o <- options(digits = 4)
## load verbal aggression data
data("VerbalAggression", package = "psychotools")
## fit a partial credit model to first ten items
pcmod <- pcmodel(VerbalAggression$resp[, 1:10])
## predicted response probabilities for each subject and category (the default)
head(predict(pcmod), 3)
## predicted mode (most probable category) for certain subjects whose person
## parameters are given via argument "newdata"
predict(pcmod, type = "mode",
newdata = c("Sarah" = 1.2, "Michael" = 0.1, "Arnd" = -0.8))
## rounded expected category value for the same subjects
predict(pcmod, type = "mean",
newdata = c("Sarah" = 1.2, "Michael" = 0.1, "Arnd" = -0.8))
## in the Rasch model mode, mean and median are the same
raschmod <- raschmodel(VerbalAggression$resp2[, 1:10])
med <- predict(raschmod, type = "median")
mn <- predict(raschmod, type = "mean")
mod <- predict(raschmod, type = "mode")
head(med, 3)
all.equal(med, mn)
all.equal(mod, mn)
options(digits = o$digits)
# }
```

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