Least Squares Estimation of Item Response Theory Linking Coefficients

Three types of least squares estimation (generalized, unweighted, and weighted) for item response theory linking coefficients are discussed. Unweighted least squares estimation gives somewhat large asymptotic standard errors. Although generalized least squares has the smallest asymptotic standard errors, it frequently gives biased estimates. Thus, weighted least squares estimation is the preferred method. In weighted least squares estimation, the ordinary weights are replaced with their powers. Results from a monte carlo simulation study showed that the weighted least squares method generally reduced bias without increasing the asymptotic standard errors, in comparison to other least squares methods.