Standard errors of a chain of linear equatings

Abstract

A general delta method is described for computing the standard error (SE) of a chain of linear equatings. The general delta method derives the SEs directly from the moments of the score distributions obtained in the equating chain. The partial derivatives of the chain equating function needed for computing the SEs are derived numerically. The method can be applied to equatings using the common-items nonequivalent populations design. Computer simulations were conducted to evaluate the SEs of a chain of two equatings using the Levine and Tucker methods. The general delta method was more accurate than a method that assumes the equating processes in the chain are statistically independent. Index terms: chain equating, delta method, equating, linear equating, standard error of equating.