Linear Equating for the NEAT Design: Parameter Substitution Models and Chained Linear Relationship Models

Abstract

This paper analyzes five linear equating models for the nonequivalent groups with anchor test (NEAT) design with internal anchors (i.e., the anchor test is part of the full test). The analysis employs a two-dimensional framework. The first dimension contrasts two general approaches to developing the equating relationship. Under a parameter substitution (PS) approach, estimates of the means and variances for the two tests for some target population are substituted into a generic equating formula; under a chained linear relationship (CLR) approach, expressions for the anchor test scores as functions of total test scores for each of the test forms are simply “equated” to each other. In order to implement either of these approaches, some relationships must be assumed invariant across the groups. The second dimension involves three different choices for the invariant relationships, the regressions of test scores (X or Y) on anchor scores (V), the regression of anchor scores on test scores, or a basic scaling/equating relationship between anchor scores and test scores. If we adopt a scaling/equating relationship of Y with V and X with V as the invariant relationship, the resulting equating relationship is the same for the PS and CLR approaches. So, five distinct regression models yielding five different equating relationships are developed within the two-dimensional framework. The equating relationships for the Tucker, Chained Linear, and Levine Observed-score methods are derived under the PS approach. The equating relationships for the Levine True-score, Chained Linear, and a Tucker-like method (Angoff Design V) are derived under the CLR approach.