Dtf {DFIT}

Calculates DTF index for a set of items with given item parameters of focal and reference groups.

Description

Calculates DTF index for a set of items with given item parameters of focal and reference groups.

Usage

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

Arguments

cdif

A numeric vector of CDIF values for the test items. If NULL it is calculated using itemParameters and the other arguments.

itemParameters

A list containing "focal" and "reference" item parameters. Item parameters are assumed to be on the same scale. Only used if cdif is NULL. 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". Only used if cdif is NULL.

focalAbilities

If NULL, CDIF 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. Only used if cdif is NULL.

focalDistribution

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

subdivisions

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

focalDistrExtra

Extra parameters for the focal group distribution function if needed.

Value

dtf Numeric vector with the CDIF 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

# # 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), ]
# #
# # threePlCdif <- Cdif(itemParameters = threePlParameters, irtModel = '3pl',
# #                     focalAbilities = NULL, focalDistribution = "norm",
# #                     subdivisions = 5000, logistic = TRUE)
# # threePlDtf  <- Dtf(cdif = threePlCdif)