Calculates the Mantel-Haenszel theoretical parameter when a dichotomous IRT model holds

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Description

Calculates the Mantel-Haenszel theoretical parameter when a dichotomous IRT model holds

Usage

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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.

focalDistrExtra

A list of extra parameters for the focal distribution function.

referenceDistribution

A string stating the distribution assumed for the reference group.

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.

Value

mh A list containing the asymptotic matrices for each item

Author(s)

Victor H. Cervantes <vcervantes at icfes.gov.co> <vhcervantesb at unal.edu.co>

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.

Examples

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data(dichotomousItemParameters)
threePlMh <- IrtMh(itemParameters = dichotomousItemParameters,  irtModel = "3pl",
                   focalDistribution = "norm", referenceDistribution = "norm",
                   focalDistrExtra = list(mean = 0, sd = 1),
                   referenceDistrExtra = list(mean = 0, sd = 1), groupRatio = 1,
                   logistic = FALSE)

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