# Mantel Haenszel for Item parameter replication Calculates the Mantel-Haenszel theoretical parameter under IRT assumptions on a list of item parameters such as those produced by the Ipr function ```r IprMh( itemParameterList, irtModel = "2pl", focalDistribution = "norm", focalDistrExtra = list(mean = 0, sd = 1), referenceDistribution = "norm", referenceDistrExtra = list(mean = 0, sd = 1), groupRatio = 1, subdivisions = 5000, logistic = TRUE ) ``` ## 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". - `focalDistribution`: A string stating the distribution assumed for the focal group. - `focalDistrExtra`: A list stating the extra parameters needed by the focal distribution function. - `referenceDistribution`: A string stating the distribution assumed for the reference group. - `referenceDistrExtra`: A list stating the extra parameters needed by the reference distribution function. - `groupRatio`: A positive value indicating how many members of the reference group are expected for each member of the focal group. - `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 mh A numeric matrix with the Mantel Haenszel values for all the item parameter in each set of itemParameterList ## Examples ```r # # 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) # # # # threePlMhIpr <- IprMh(itemParameterList = threePlIpr, irtModel = '3pl', logistic = TRUE) ``` ## 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 Roussos, L., Schnipke, D. & Pashley, P. (1999). A generalized formula for the Mantel-Haenszel Differential Item Functioning parameter. Journal of educational and behavioral statistics, 24(3), 293--322. doi:10.3102/10769986024003293 ## Author(s) Victor H. Cervantes

IprMh function