estimateThetas function

Estimates of Ability Parameters for a Dataset of Response Profiles

Estimates the expected value of the ability parameter $\theta$, conditioned on the observed answers, prior, and the item parameters for complete response profiles for a dataset of respondents.

## S4 method for signature 'Cat'
estimateThetas(catObj, responses)

Arguments

• catObj: An object of class Cat
• responses: A dataframe of complete response profiles

Returns

The function estimateThetas returns a vector containing respondents' estimated ability parameters.

Details

Estimation approach is specified in estimation slot of Cat object.

The expected a posteriori approach is used when estimation slot is "EAP". This method involves integration. See Note for more information.

The modal a posteriori approach is used when estimation slot is "MAP". This method is only available using the normal prior distribution.

The maximum likelihood approach is used when estimation slot is "MLE". When the likelihood is undefined, the MAP or EAP method will be used, determined by what is specified in the estimationDefault slot in Cat object.

The weighted maximum likelihood approach is used when estimation slot is "WLE". Estimating $\theta$ requires root finding with the ``Brent'' method in the GNU Scientific Library (GSL) with initial search interval of [-5,5].

Note

This function is to allow users to access the internal functions of the package. During item selection, all calculations are done in compiled C++ code.

This function uses adaptive quadrature methods from the GNU Scientific Library (GSL) to approximate single-dimensional integrals with high accuracy. The bounds of integration are determined by the lowerBound and upperBound slots of the Cat object.

Examples

## Loading ltm Cat object
data(ltm_cat)

## Set different estimation procedures and estimate ability parameter
data(npi)
setEstimation(ltm_cat) <- "EAP"
estimateThetas(ltm_cat, responses = npi[1:25, ])

See Also

Cat-class, estimateTheta

Author(s)

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