# Calculates Raju's Signed Area Measure index for an item with given item parameters of focal and reference groups. ```r SignedArea( itemParameters, irtModel = "2pl", subdivisions = 5000, logistic = TRUE ) ``` ## 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". - `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. ## Returns sam A numeric matrix with the Signed Area Measure values for all the item parameter in each set of itemParameterList ## 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), ] sam3pl <- SignedArea(itemParameters = threePlParameters, irtModel = "3pl", subdivisions = 5000, logistic = TRUE) ``` ## References Cohen, A., Kim, S-H and Baker , F. (1993). Detection of differential item functioning in the Graded Response Moodel. Applied psychological measurement, 17(4), 335-350. doi:10.1177/014662169301700402 Raju, N. (1988). The area between two item characteristic cureves. Psychometricka, 53(4), 495--502. doi:10.1007/bf02294403 ## Author(s) Victor H. Cervantes

SignedArea function