cacIRT (version 1.4)

Lee.poly: Computes classification accuracy and consistency with Lee's approach for polytomous IRT models.

Description

Computes classification accuracy and consistency with Lee's approach for polytomous tests. The probability of each possible total score conditional on ability is found with gen.rec.raw(). Those probabilities are grouped according to the cut scores and used to estimate the indices.

Usage

Lee.poly.D(cutscore, Pij, quadrature)
Lee.poly.P(cutscore, Pij, theta)

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

Pij

An NxMxJ array of probabilities. Each slice of the array represents an item. Within a slice, each row corresponds to the respective element in theta and each column represents a response category from 0, 1, ..., M. At a minimum, M=1, in which

theta

Ability estimates for each subject. Must correspond to the first dimension of Pij.

quadrature

A list containing 1) The quadrature points and 2) Their corresponding weights. Must correspond to the first dimension of Pij.

Value

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

Details

The polytomous generalization to class.Lee. Requires the user build the Pij array.

References

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

Examples

#Same example as \code{class.Lee()}, 
  #build \code{Pij} the same as in the example for \code{gen.rec.raw()}.

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

Pij.flat <- irf(params, theta)$f
Pij.array <- array(NA, dim = c(length(theta), 2, nrow(params)))
Pij.array[,1,] <- 1 - Pij.flat #P(X_j = 0 | theta_i)
Pij.array[,2,] <- Pij.flat     #P(X_j = 1 | theta_i)

Lee.poly.P(2, Pij.array, theta)$Marginal

#in the dichotomous case, identical to \code{Lee.P()}
Lee.P(2, params, theta)$Marginal

#For Rudner and polytomous tests, compute the theta estimate and se and use those as input
theta.est <- theta 
#just for example

theta.se <- SEM(params, theta.est) 
#also for example, SEM() assumes 3PL model, 
#but if you use mirt or similar package, 
#the theta estimates and their se will be available

Rud.P(.5, theta.est, theta.se)$Marginal