grmCat {catSurv}

Computerized Adaptive Testing Graded Response Model

Description

This function fits the graded response model for ordinal polytomous data and populates the fitted values for discrimination and difficulty parameters to an object of class Cat.

Usage

## S4 method for signature 'data.frame'
grmCat(data, quadraturePoints = 21, ...)

## S4 method for signature 'grm'
grmCat(data, quadraturePoints = NULL, ...)

Arguments

data

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

quadraturePoints

A numeric to be passed into the grm 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 grm in the ltm package.

Details

The data argument of the function grmCat is either a data frame or an object of class grm 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 grm, it is output from the grm function in the ltm package.

The quadraturePoints argument of the function grmCat is used only when the data argument is a data frame. quadraturePoints is then passed to the grm function from the ltm package when fitting the graded response model to the data and is used when approximating the value of integrals.

Value

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

• difficulty A list of difficulty parameters, where each element in the list corresponds to the difficulty parameters for an item.

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

• model The string "grm", indicating this Cat object corresponds to a graded response model.

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

Note

In case the Hessian matrix at convergence is not positive definite try to use start.val = "random".

Author(s)

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

References

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

Samejima, Fumiko. 1969. “Estimation of Latent Ability Using a Response Pattern of Graded Scores." Psychometrika monograph supplement 34(4):100-114.

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, gpcmCat, nfc, probability

Examples

## Not run: 
## Creating Cat object with raw data
data(nfc)
grm_cat1 <- grmCat(nfc, quadraturePoints = 100)

## Creating Cat object with fitted object of class grm
grm_fit <- grm(nfc, control = list(GHk = 100)) ## from ltm package
class(grm_fit)
grm_cat2 <- grmCat(grm_fit)

## Note the two Cat objects are identical
identical(grm_cat1, grm_cat2)

## End(Not run)

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

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

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