SignedArea {DFIT}

Calculates Raju's Signed Area Measure index for an item with given item parameters of focal and reference groups.

Description

Calculates Raju's Signed Area Measure index for an item with given item parameters of focal and reference groups.

Usage

SignedArea(
  itemParameters,
  irtModel = "2pl",
  subdivisions = 5000,
  logistic = TRUE
)

Arguments

itemParameters

A list containing "focal" and "reference" item parameters. Item parameters are assumed to be on the same scale. Item parameters for each group should me a matrix with nrow equal to the number of items.

irtModel

A string stating the irtModel to be used. Should be one of "1pl", "2pl", "3pl", "grm" or "pcm".

subdivisions

A numeric value indicating the number of subdivisions for numerical integration.

logistic

A logical value stating if the IRT model will use the logistic or the normal metric. Defaults to using the logistic metric by fixing the D constant to 1. If FALSE the constant is set to 1.702 so that the normal metric is used.

Value

sam A numeric matrix with the Signed Area Measure values for all the item parameter in each set of itemParameterList

Author(s)

Victor H. Cervantes <vhcervantesb at unal.edu.co>

References

Cohen, A., Kim, S-H and Baker , F. (1993). Detection of differential item functioning in the Graded Response Moodel. Applied psychological measurement, 17(4), 335-350. doi:10.1177/014662169301700402

Raju, N. (1988). The area between two item characteristic cureves. Psychometricka, 53(4), 495–502. doi:10.1007/bf02294403

Examples

data(dichotomousItemParameters)

threePlParameters <- dichotomousItemParameters
isNot3Pl          <- ((dichotomousItemParameters[['focal']][, 3] == 0) |
                      (dichotomousItemParameters[['reference']][, 3] == 0))

threePlParameters[['focal']]          <- threePlParameters[['focal']][!isNot3Pl, ]
threePlParameters[['reference']]      <- threePlParameters[['reference']][!isNot3Pl, ]
threePlParameters[['focal']][, 3]     <- threePlParameters[['focal']][, 3] + 0.1
threePlParameters[['reference']][, 3] <- threePlParameters[['reference']][, 3] + 0.1
threePlParameters[['focal']][, 2]     <- threePlParameters[['focal']][, 2] + 1.5
threePlParameters[['reference']][, 2] <- threePlParameters[['reference']][, 2] + 1.5
threePlParameters[['focal']]          <- threePlParameters[['focal']][-c(12, 16, 28), ]
threePlParameters[['reference']]      <- threePlParameters[['reference']][-c(12, 16, 28), ]

sam3pl <- SignedArea(itemParameters = threePlParameters, irtModel = "3pl",
                     subdivisions = 5000, logistic = TRUE)