catSurv (version 1.5.0)

tpmCat: Computerized Adaptive Testing Birnbaum's Three Parameter Model

Description

This function fits Birnbaum's three parameter model for binary data and populates the fitted values for discrimination, difficulty, and guessing parameters to an object of class Cat.

Usage

# S4 method for data.frame
tpmCat(data, quadraturePoints = 21, ...)
# S4 method for tpm
tpmCat(data, quadraturePoints = NULL, ...)

Value

The function tpmCat returns an object of class Cat with changes to the following slots:

• difficulty A vector consisting of difficulty parameters for each item.

• discrimination A vector consisting of discrimination parameters for each item.

• model The string "tpm", indicating this Cat object corresponds to Birnbaum's three parameter model.

See Cat-class for default values of Cat object slots. See Examples and setters for example code to change slot values.

Arguments

data

A data frame of manifest variables or an object of class tpm.

quadraturePoints

A numeric to be passed into the tpm function indicating the number of Gauss-Hermite quadrature points. Only applicable when data is a data frame. Default value is 21.

...

arguments to be passed to methods. For more details about the arguments, see tpm in the ltm package.

Author

Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil

Details

The data argument of the function tpmCat is either a data frame or an object of class tpm from the ltm package. If it is a data frame each row represents a respondent and each column represents a question item. If it is an object of the class tpm, it is output from the tpm function in the ltm package.

The quadraturePoints argument of the function tpmCat is used only when the data argument is a data frame. quadraturePoints is then passed to the tpm function from the ltm package when fitting Birnbaum's three parameter model to the data and is used when approximating the value of integrals.

References

Baker, Frank B. and Seock-Ho Kim. 2004. Item Response Theory: Parameter Estimation Techniques. New York: Marcel Dekker.

Birnbaum, Allan. 1968. Some Latent Trait Models and their Use in Inferring an Examinee's Ability. In F. M. Lord and M. R. Novick (Eds.), Statistical Theories of Mental Test Scores, 397-479. Reading, MA: Addison-Wesley.

Rizopoulos, Dimitris. 2006. ``ltm: An R Package for Latent Variable Modeling and Item Response Theory Analyses." Journal of Statistical Software 17(5):1-25.

See Also

Cat-class, ltmCat, polknowMT, probability

Examples

## Creating Cat objects from large datasets is computationally expensive
## Load the Cat object created from the above code
data(tpm_cat)

## Slots that have changed from default values
getModel(tpm_cat)
getDifficulty(tpm_cat)
getDiscrimination(tpm_cat)

## Changing slots from default values
setEstimation(tpm_cat) <- "MLE"
setSelection(tpm_cat) <- "MFI"