# Calculates NCDIF index for an item with given item parameters of focal and reference groups. ```r 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. ## Returns ncdif Numeric vector with the NCDIF index value for each item. ## Examples ```r 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) ``` ## 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 ## Author(s) Victor H. Cervantes

Ncdif function