Asymptotic Standard Errors of IRT Equating Coefficients Using Moments

The asymptotic standard errors of the IRT equating coefficients given by the mean/sigma, mean/mean and mean/geometric mean methods are derived when the two-parameter logistic model holds and item parameters are obtained by the marginal maximum likelihood estimation. The case of two nonequivalent examinee-groups and the case of single group are considered. The numerical examples show that the mean/mean and mean/geometric mean methods are superior to the mean/sigma method. The results also show that the number of quadrature points in the numerical approximation to the integration of ability parameters is crucial to the estimation of the asymptotic standard errors.