An Empirical Example of Change Analysis by Linking Longitudinal Item Response Data From Multiple Tests

Abstract

Linking, equating, and calibrating refer to a series of statistical methods for comparing scores from tests (scales, measures, etc.) that do not contain the same exact set of measurements but presume to measure the same underlying construct. Lord (1955a,1955b) provided one of the first examples of this kind where one test (x) was administered to 1,200 people, while two other tests (y ₁ & y ₂ ) were each only administered to a different half of the group. The resulting data and analysis were reprinted in Cudeck (2000), who showed that the assumption of a single factor model for all three tests (x, y ₁ , y ₂ ) made it possible to identify a maximum likelihood estimator of the correlation among the two variables that were never measured on the same persons (y ₁ & y ₂ ). In contemporary terms the common score (x) served as an anchor for the correlation of the other two scores, and this simple design is one version of what is termed a nonequivalent anchor test (von Davier, Holland, & Thayer,2004b).