class.Lee {cacIRT}

Computes classification accuracy and consistency with Lee's approach.

Description

Computes classification accuracy and consistency with Lee's approach. The probability of each possible total score conditional on ability is found with recursive.raw. Those probabilities are grouped according to the cut scores and used to estimate the indices. See references or code for details.

Usage

class.Lee(cutscore, ip, ability = NULL, rdm = NULL, quadrature = NULL, D = 1.7)
Lee.D(cutscore,  ip, quadrature, D = 1.7)
Lee.P(cutscore,  ip, theta, D = 1.7)

Arguments

cutscore

A scalar or vector of cut scores on the True Score scale. If you have cut scores on the theta scale, you can transform them with irf (See example for irf). Should not include 0 or the max total score, as the end points are added internally.

ip

Matrix of item parameters, columns are discrimination, difficultly, guessing, respectively. For 1PL and 2PL, still give a Jx3 matrix, with ip[,1] = 1 and ip[,3] = 0 for the 1PL for example.

ability, theta

Ability estimates for each subject.

rdm

The response data matrix with rows as subjects and columns as items

quadrature

A list containing 1) The quadrature points and 2) Their corresponding weights

D

Scaling constant for IRT parameters, defaults to 1.7, alternatively often set to 1.

Details

Must give only one ability, rdm, or quadrature. If ability is given, those scores are used for the P method. If rdm is given, ability is estimated with MLE (perfect response patterns given a -4 or 4) and used for the P method. If quadrature, the D method is used. class.Lee calls Lee.D or Lee.P.

Value

Marginal

A matrix with two columns of marginal accuracy and consistency per cut score (and simultaneous if multiple cutscores are given)

Conditional

A list of two matrixes, one for conditional accuracy and one for conditional consistency. Each matrix has one row per subject (or quadrature point).

Note

In order to score above a cut, an examinee must score at or above the cut score. Since we are working on the total score scale, be aware that if a cut score is given with a decimal (like 2.4), the examinee must have a total score at the next integer or more (so 3 or more) to score above the cut.

Author(s)

Quinn N. Lathrop

References

Lee, W. (2010) Classification consistency and accuracy for complex assessments using item response theory. Journal of Educational Measurement, 47, 1–17.

Examples

##from rdm, item parameters denote 4 item 1PL test, cut score at x=2
##only print marginal indices

params<-matrix(c(1,1,1,1,-2,1,0,1,0,0,0,0),4,3)
rdm<-sim(params, rnorm(100))

class.Lee(2, params, rdm = rdm)$Marginal

##or from 40 quadrature points and weights, 2 cut scores

quad <- normal.qu(40)

class.Lee(c(2,3), params, quadrature = quad, D = 1)$Marginal