# Calculates the Mantel-Haenszel theoretical parameter when a dichotomous IRT model holds ```r IrtMh( itemParameters, irtModel = "2pl", focalDistribution = "norm", referenceDistribution = "norm", focalDistrExtra = list(mean = 0, sd = 1), referenceDistrExtra = list(mean = 0, sd = 1), groupRatio = 1, logistic = TRUE, subdivisions = 5000 ) ``` ## Arguments - `itemParameters`: A list containing the "focal" and "reference" item parameters. Item parameters are assumed to be on the same scale. - `irtModel`: A string stating the irtModel used. May be one of "1pl", "2pl", or "3pl". - `focalDistribution`: A string stating the distribution assumed for the focal group. - `referenceDistribution`: A string stating the distribution assumed for the reference group. - `focalDistrExtra`: A list of extra parameters for the focal distribution function. - `referenceDistrExtra`: A list of extra parameters for 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. - `logistic`: A logical indicating whether the logistic or the normal metric should be used. - `subdivisions`: A numeric value stating the maximum number of subdivisions for adaptive quadrature. ## Returns mh A list containing the asymptotic matrices 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), ] threePlMh <- IrtMh(itemParameters = threePlParameters, irtModel = "3pl", focalDistribution = "norm", referenceDistribution = "norm", focalDistrExtra = list(mean = 0, sd = 1), referenceDistrExtra = list(mean = 0, sd = 1), groupRatio = 1, logistic = FALSE) ``` ## References 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

IrtMh function