R: Predict Methods for Item Response Models

predict.pcmodel {psychotools} | R Documentation

## Predict Methods for Item Response Models

### Description

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

### Usage

    ## S3 method for class '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`.
`...` | 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} ≥q 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) ≥q 0.5 is returned.

If `type` is `"mean"`, the rounded expected category response, i.e., E(X_{ij}|θ_{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 informations 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, 29–51.

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

### See Also

The help page of the generic function `predict` and other predict methods (e.g., `predict.lm`, `predict.glm`, ...)

### Examples

    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))

    ## 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)
    head(mn)
    head(mod)

    all.equal(med, mn)
    all.equal(mod, mn)

    options(digits = o$digits)

[Package psychotools version 0.4-2 Index]