Derivations of Observed Score Linear Equating Methods Based on Test Score Models for the Common Item Nonequivalent Populations Design

Linear equating methods for the common item nonequivalent populations design are derived from explicitly stated test score models. The models are congeneric type models for tests administered in two distinct populations. Though the data collected in the design are incomplete, procedures for estimating all parameters necessary for equating are derived. The equating methods developed are compared with previously developed methods to which they are similar. By developing explicit models for the problem, insight is gained into the assumptions required for its solution.