DFIT (version 1.1)

IprUam: Unsigned Area Measure for Item parameter replication

Description

Calculates Raju's Unsigned Area Measure index on a list of item parameters such as those produced by the Ipr function

Usage

IprUam(
  itemParameterList,
  irtModel = "2pl",
  subdivisions = 5000,
  logistic = TRUE
)

Arguments

itemParameterList

A list where each element is a list containing "focal" and "reference" item Parameters. Item parameters are assumed to be on the same scale. Item parameters for each group should be 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

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

References

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

Oshima, T., Raju, N. & Nanda, A. (2006). A new method for assessing the statistical significance in the Differential Functioning of Items and Tests (DFIT) framework. Journal of educational measurement, 43(1), 1--17. doi:10.1111/j.1745-3984.2006.00001.x

Examples

# NOT RUN {
# # Not run
# #
# # 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), ]
# #
# # threePlAse <- list()
# # threePlAse[["focal"]]     <- AseIrt(itemParameters = threePlParameters[["focal"]],
# #                                     logistic = TRUE,
# #                                     sampleSize = 10000,
# #                                     irtModel = "3pl")
# # threePlAse[["reference"]] <- AseIrt(itemParameters = threePlParameters[["reference"]],
# #                                     logistic = TRUE,
# #                                     sampleSize = 10000,
# #                                     irtModel = "3pl")
# #
# # set.seed(41568)
# # threePlIpr <- Ipr(itemParameters = threePlParameters, itemCovariances = threePlAse,
# #                   nReplicates = 100)
# #
# # threePlUamIpr <- IprUam(itemParameterList = threePlIpr, irtModel = '3pl', logistic = TRUE)

# }