IprNcdif {DFIT}

NCDIF for Item parameter replication

Description

Calculates the NCDIF index on a list of item parameters such as those produced by the Ipr function

Usage

IprNcdif(
  itemParameterList,
  irtModel = "2pl",
  focalAbilities = NULL,
  focalDistribution = "norm",
  subdivisions = 5000,
  logistic = TRUE,
  focalDistrExtra = list(mean = 0, sd = 1)
)

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".

focalAbilities

If NULL, NCDIF is calculated by numerical integration of focal distribution. If not NULL, must be a numerical vector containing the abilities for the individuals in the focal group.

focalDistribution

A string stating the distribution name to be used for integrating. Only used if focalAbilities is NULL.

subdivisions

A numeric value indicating the number of subdivisions for numerical integration. Only used if focalAbilities is NULL.

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.

focalDistrExtra

A list stating the extra parameters needed by the focal distribution function.

Value

ncdif A numeric matrix with the NCDIF values for all the item parameter in each set of itemParameterList

Author(s)

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

References

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
# #
# # 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)
# #
# # threePlNcdifIpr <- IprNcdif(itemParameterList = threePlIpr, irtModel = '3pl', logistic = TRUE)