Computes classification accuracy and consistency with Rudner's approach.

Description

Computes classification accuracy and consistency with Rudner's approach. For each examinee, a normal distribution is created with mean at the ability estimate and standard deviation equal to the standard error of the ability estimate. Rudner's method assumes the standard error is conditionally normally distributed. The area under this normal curve between cut scores is used to estimate the indices. See references.

Usage

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

Arguments

cutscore

A scalar or vector of cut scores on the theta scale. Should not include +- inf, the function will include them.

ip

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

ability, theta

Ability estimates for each subject.

se, sem

Standard errors of ability estimates

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

The scaling constant for the IRT parameters, defaults to 1.7, alternatively often set to 1.

Details

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

Value

Marginal

A matrix with two columns of marginal accuracy and consistency per cut score and/or simultaneous

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

class.Rud is a wrapper for Rud.P and Rud.D.

Author(s)

Quinn Lathrop

References

Rudner, L. M. (2001) Computing the expected proportions of misclassified examinees. Practical Assessment, Research & Evaluation, 7(14), 1–5.

Rudner, L. M. (2005) Expected classification accuracy. Practical Assessment Research & Evaluation, 10(13), 1–4.

Examples

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##from rdm, item parameters denote 4 item 1PL test, cut score at theta=.5
##only return 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.Rud(.5, params, rdm = rdm)$Marginal

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

quad <- normal.qu(40)

class.Rud(c(-.5,1.5), params, quadrature = quad, D = 1)$Marginal