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Standard Errors of Item Response Theory Equating/Linking by Response Function Methods

Asymptotic standard errors (SEs) of item response theory equating coefficient estimates are derived using response functions or their transformations. SEs are obtained by the method for the two- and three-parameter logistic models when the asymptotic variance-covariance matrix of the item parameter estimates is given. Two variations of the item and test response function methods and SEs of their parameter estimates are presented that use logit transformations of the item response functions. Numerical examples are given that show that the SEs of the item and test response function methods are smaller than those of other methods, particularly for the three-parameter model.