estimateTheta | R Documentation |
Estimates the expected value of the ability parameter θ, conditioned on the observed answers, prior, and the item parameters.
estimateTheta(catObj)
catObj |
An object of class |
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 θ requires root finding with the “Brent” method in the GNU Scientific
Library (GSL) with initial search interval of [-5,5]
.
The function estimateTheta
returns a numeric consisting of the expected value of the respondent's ability parameter.
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.
Haley Acevedo, Ryden Butler, Josh W. Cutler, Matt Malis, Jacob M. Montgomery, Tom Wilkinson, Erin Rossiter, Min Hee Seo, Alex Weil
van der Linden, Wim J. 1998. "Bayesian Item Selection Criteria for Adaptive Testing." Psychometrika 63(2):201-216.
Van der Linden, Wim J., and Peter J. Pashley. 2009. "Item Selection and Ability Estimation in Adaptive Testing." Elements of Adaptive Testing. Springer New York, 3-30.
Cat-class
, estimateSE
## Loading ltm Cat object data(ltm_cat) ## Store example answers setAnswers(ltm_cat) <- c(1,0,1,0,1, rep(NA, 35)) ## Set different estimation procedures and estimate ability parameter setEstimation(ltm_cat) <- "EAP" estimateTheta(ltm_cat) setEstimation(ltm_cat) <- "MAP" estimateTheta(ltm_cat) setEstimation(ltm_cat) <- "MLE" estimateTheta(ltm_cat) setEstimation(ltm_cat) <- "WLE" estimateTheta(ltm_cat)
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