Ncdif {DFIT}

Calculates NCDIF index for an item with given item parameters of focal and reference groups.

Description

Calculates NCDIF index for an item with given item parameters of focal and reference groups.

Usage

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

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".

focalAbilities

If NULL, NCDIF is calculated by numerical integration of focal distribution. If not NULL, it 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

Extra parameters for the focal group distribution function if needed.

Value

ncdif Numeric vector with the NCDIF index value for each item.

Author(s)

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

References

Raju, N. S., van der Linden, W. J., & Fleer, P. F. (1995). IRT-based internal measures of differential functioning of items and tests. Applied Psychological Measurement, 19, 353–368. doi:10.1177/014662169501900405

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), ]

threePlNcdif <- Ncdif(itemParameters = threePlParameters, irtModel = '3pl',
                      focalAbilities = NULL, focalDistribution = "norm",
                      subdivisions = 5000, logistic = TRUE)